Help with variance - how bad can it get?
Dave Scharf
This year at the poker table (excluding tournaments) has been... well...
wild.
Back on March 30th I was up $4984 in 127 hours (mostly 5-10 some 10-20).
As of tonight's session I am up $327 for the year in 250 hours. Ouch.
Talk about running bad for the last 123 hours! Course, talk about
running good for the first 127.
I have, of course, searched my soul and analysed my game as best I can.
I have, I think, plugged a couple of leaks and am playing better for the
last 50 hours or so than I ever have.
So, I know that we have gone over variance many times in this group, but
maybe somebody could explain life to me one more time. It seems to me
that I *must* be doing something wrong.
Background info on the game... Mostly 5-10. Very passive. Typically, 7
callers in an unraised pot and 5 in a raised pot (pre-flop).
I need encouragement... I need help... I think I need to take a break. I
think I need to cream you guys this weekend at BARGE just so I can get
my confidence back.
Regards,
Dave
HitTheFlop
I can not count on a winning month, the time cycles
of poker fortune are long. I'm not certain that a 2000
hour sample will smooth out the effects of running
good or bad.
Best,
Ed
Best Luck,
Ed (no, not that Ed!)
I used to be a heavy gambler. But now I just make
mental bets. That's how I lost my mind. Steve Allen
tha...@nmia.com
LouKrieger
From: Dave Scharf
This year at the poker table (excluding tournaments) has been... well...wild.
Back on March 30th I was up $4984 in 127 hours (mostly 5-10 some 10-20). As of
tonight's session I am up $327 for the year in 250 hours. I know that we have
gone over variance many times in this group, but maybe somebody could explain
life to me one more time.<<
Dave,Using Wilson's Turbo Texas Hold'em I ran some simulations once where I had
the same player profile at a table and simulated 30 years of poker (8 hours a
day, 50 weeks a year for 30 years).
After all was said and done, there was still a variance of more than one
percent -- an incredible amount considering the profil;es were identical, do
not go on tilt, etc. So even after a simulated lifetime of poker, my
conclusion is that one to one-and-one half percent of your results can be
attributed to luck.
My point is that the ephemeral "long run" takes much longerto reach than we
would like to think. That does not in anyway mitigate the fact that poor
results generally beget poor play too, even if only for a little while. It's
true for me, you, and probably most poker players out there -- and is something
we always have to guard against. Good play also tends to beget good play, so
streaks tend to become self-enhancing...and it's worth keeping tht firmly in
mind.
The other thing you can do is take your winnings in Yankee dollars; pay your
debts in Loonies!
Keep flopping aces,
Lou Krieger
Earl
>
> Looking for insight or general help...
>
> wild.
> Background info on the game... Mostly 5-10. Very passive. Typically, 7
> callers in an unraised pot and 5 in a raised pot (pre-flop).
>
Sounds like maybe a high variance game you are playing in -- I'd also
wonder about the effects of the rake at 5-10. Play in a different
(bigger?) game where no one knows you.
poker4fun
Dave Scharf wrote in message <35BD5BB8...@canadianpoker.com>...
>Looking for insight or general help...
>
>This year at the poker table (excluding tournaments) has been... well...
>wild.
>
>
>Talk about running bad for the last 123 hours! Course, talk about
>running good for the first 127.
>
>I have, of course, searched my soul and analysed my game as best I can.
>I have, I think, plugged a couple of leaks and am playing better for the
>last 50 hours or so than I ever have.
>
>So, I know that we have gone over variance many times in this group, but
>maybe somebody could explain life to me one more time. It seems to me
>that I *must* be doing something wrong.
>>
excuse in poker even though a real concept when flipping a coin or playing
blackjack. Good players win from bad players and yes, sometimes bad things
happen to good players. If you're running bad consistently over a period of
time...a slump like hitting in baseball, (I might add that I did and this is
how I recovered) Look at what you are doing differently. Has your game
changed? Mine did! I wasn't playing my game. Are you more timid/aggressive
at the table? Are you playing the right hands in the right position? Do some
games play more to your style (i.e., tight aggressive vs. maniacal vs. loose
aggressive vs. loose passive)? Do some players beat you consistently vs.
players who you beat consistently?
Look closely at the leaks in your game and see if you notice any differences
between previous play and your current play. If you play in the same games,
with the same players, you may not be adding enough deception to your play
meaning some players have a good read on you.
Every player has their tendencies and a strategy that works for them. Make
sure that your winning strategy hasn't changed.
Good luck,
poker4fun
Earl
>
> >>Subject: Help with variance - how bad can it get?
> So even after a simulated lifetime of poker, my
> conclusion is that one to one-and-one half percent of your results can be
> attributed to luck.
>
> would like to think.
>
Within the realm of the "long run" this simply means that we should not
pound at small edges (in limit poker, no matter how good the hand, it
has only a certain betting value). While the average joe may disdain the
concept of variance from a mathematical perspective, understanding the
effects of table composition on bankroll fluctations can never be
underestimated, particularly for those on a short bankroll.
William Chen
Dave Scharf <da...@canadianpoker.com> wrote:
>Looking for insight or general help...
>
>This year at the poker table (excluding tournaments) has been... well...
>wild.
>
>Back on March 30th I was up $4984 in 127 hours (mostly 5-10 some 10-20).
>
>As of tonight's session I am up $327 for the year in 250 hours. Ouch.
>Talk about running bad for the last 123 hours! Course, talk about
>running good for the first 127.
>
>I have, of course, searched my soul and analysed my game as best I can.
>I have, I think, plugged a couple of leaks and am playing better for the
>last 50 hours or so than I ever have.
I think what you are feeling is partly psychological. Suppose you had lost 5K for
the first three months and then got back to even. You might be really happy now and
even a little proud of the fact that you were able to come back.
You asked for some encouragement:
A $327 net isn't so bad unless you are a pro or are otherwise under pressure to win--90% of
the players probably would trade places with you. How have your previous years' records
been like? If this is your first year of keeping records/playing seriously then look at it
this way--you are playing well enough to beat the rake.
If you've consistantly booked significant wins in previous years (at a decent hourly rate)
but aren't doing so hot this year, welcome to the club. I've also made virtually no profit
the first half of this year and have previously made around $20/hr in 6-12 for a few
thousand hours. Maybe it's a statistical anomaly. maybe it's my play. Many factors have
changed--now I have a full-time job and only get to play poker occasionally. I've also
noticed some possible "out of practice" missed tells and reads.
Examining your game is always good. But it could just be variance. I lost 5K in a couple
of months a couple of years ago (during the summer coincidently) playing mostly 6-12 and
some 15-30. In retrospect I don't think my game changed very much--the loss was surrounded
by two 10K winning periods. I can also trace the losses to the three or so sessions where
I lost over 1K. Can you imagine getting stuck 800 in a 6-12 hold'em game and being forced
to buy that 5th rack? Been there, done that. Or playing a 10-20 Omaha game and being in
for 2K??
Bill
Barbara Yoon
> ...wild. I was up $4984 in 127 hours (mostly 5-10 some 10-20).
> ...[now] I am up $327 for the year in 250 hours. Ouch. Talk about
> running bad for the last 123 hours! Course, talk about running good
> times in this group, but maybe somebody could explain life to me
> one more time.
If your "standard deviation" (square root of variance) is, say for example
here, in the neighborhood of $100/hour, then it's not out of the question
for you to do $200 or $300 better or worse than your long-run hourly
average in any one especially "hot" or "cold" single hour -- and over a
span of 123 or 127 hours, you could multiply those swings by 11 or so
(the square root of 123 or 127 being a little more than 11)... And so yes,
your big swings here can be characterized as "extreme," and likely are
a result of something more than just normal good and bad luck...
Nathaniel Silver
>Can you imagine getting stuck 800 in a 6-12 hold'em game
>and being forced to buy that 5th rack?
Was it at gunpoint?
Been there, done that. Or playing a 10-20 Omaha game and being in
>for 2K??
Bill, surely you exaggerate. You always can cut it down to a max of one K
by drawing only to the nuts.
NS
William Chen
"Nathaniel Silver" <mat...@worldnet.att.net> wrote:
>William Chen wrote:
>
>>Can you imagine getting stuck 800 in a 6-12 hold'em game
>>and being forced to buy that 5th rack?
>
>Was it at gunpoint?
Well forced to buy in or quit.
>
>Been there, done that. Or playing a 10-20 Omaha game and being in
>>for 2K??
>
>
>Bill, surely you exaggerate. You always can cut it down to a max of one K
>by drawing only to the nuts.
Yeah but thee's lots of jamming on the turn in the game I play and _I_
do some jamming myself. I mean you can have nut low with the nut flush draw and lose
everything on the river right? You are still going to go 4 bets on the turn in a multiway
pot if there isn't a pair on the board. Omaha hi-lo can be quite a high variance game.
Oh it was a half-kill to 15-30 but I don't think that matters much since the higher limit
some of the time is offset by tighter play by me.
Bill
William Chen
"Barbara Yoon" <by...@erols.com> wrote:
Yes, Barbara, but you are assuming his std deviation is 100/hr, which seems a bit
low. In truth we should have him post his std deviation results (we should also separate
the 5/10 and 10/20 games since they are two different games) to determine whether this case
is "extreme" or not
Bill
Nathaniel Silver
>>>Or playing a 10-20 Omaha game and being in for 2K??
>>Bill, surely you exaggerate. You always can cut it down to
>a max of one K by drawing only to the nuts.
>Yeah but there's lots of jamming on the turn in the game I play and _I_
>do some jamming myself. I mean you can have nut low with the nut flush
>draw and lose everything on the river right? You are still going to go 4
bets
>on the turn in a multiway pot if there isn't a pair on the board.
Try to avoid going to war unless you have both the nuts
(or a draw to the nuts) and other outs. I mean unless
you hold better cards.
>Omaha hi-lo can be quite a high variance game.
>Oh it was a half-kill to 15-30 but I don't think that
>matters much since the higher limit some of the
>time is offset by tighter play by me.
There you have it. You mean "better" play.
And you do understand it.
Can you imagine playing 10-20 like it were
15-30? You might even win.
NS
William Chen
"Nathaniel Silver" <mat...@worldnet.att.net> wrote:
>William Chen wrote
>>>>Or playing a 10-20 Omaha game and being in for 2K??
>>>Bill, surely you exaggerate. You always can cut it down to
>>a max of one K by drawing only to the nuts.
>
>>Yeah but there's lots of jamming on the turn in the game I play and _I_
>>do some jamming myself. I mean you can have nut low with the nut flush
>>draw and lose everything on the river right? You are still going to go 4
>bets
>>on the turn in a multiway pot if there isn't a pair on the board.
>
>Try to avoid going to war unless you have both the nuts
>(or a draw to the nuts) and other outs. I mean unless
>you hold better cards.
WHAT? If you don't think the nut low with the nut flush draw is worth jamming with in
a 5 way pot, please explain why. Unless you get counterfieted (6 outs) you have some share
of the pot (most likely quarter but not always). If your flush gets there without pairing
the odd card then you are potentially scooping. I think I make my share in Omaha (I
actaully have more of an edge in Omaha than holdem probably) it's just that I play a
higher variance game. I mean I try to avoid plays which increase my variance greatly while
being marginal in EV but I don't think the above is one of them.
>
>>Omaha hi-lo can be quite a high variance game.
>>Oh it was a half-kill to 15-30 but I don't think that
>>matters much since the higher limit some of the
>>time is offset by tighter play by me.
>
>
>There you have it. You mean "better" play.
>And you do understand it.
>Can you imagine playing 10-20 like it were
>15-30? You might even win.
>
Wow. You mean think about playing tighter because of the limit and not the fact that you
have to put in a kill if you win the pot? Hmm... BTW I do win, I mean on average. I'm
just saying a 1 session loss of 2K isn't that unrealistic in 10/20 w/ half kill, no matter
what the stats say.
Bill
Abdul Jalib
A tight professional will have a standard deviation of about 15 small
bets per hour, possibly as high as 20 in a loose game. The player in
question probably has a standard deviation around 25 small bets per hour.
But the $10-$20 sessions will be weighted heavily. So, maybe his
overall standard deviation was $200/hour.
Anyway, there is an illusion that I'd like to quantify mathematically,
but I don't know how. When you start your record today, and end after
a predetermined number of hours, then your chance of being ahead can
be computed if you know your expected value and variance. You can
compute how many standard deviations you are from expected. But when
you look backwards, suddenly things seem much more chaotic. You may
have had a -4 standard deviation session last night, wiping out the
results of a +3 standard deviation run you had for the previous week,
which helped offset the -2 standard deviation run you have had for the
last 6 months. It's misleading to even refer to those runs in terms
of standard deviations from the norm. That may be what happened with
the original poster.
Maybe Barbara or someone else could supply some math to help quantify
this "effect". For example, someone has been playing hold'em for 10 years,
20 hours per week, with a constant frictionless expected value of 2 small
bets per hour and a standard deviation of 15 small bets per hour; what is
the probability that at least one 6 month period in this time would have
been a -4 standard deviation result, had we started and ended the
statistics on that period? A -4 SD result for 6 months would be a loss of
328 units. I am assuming an infinite number of 6 month periods within
10 years, not just twenty 6 month periods, but you can divide the periods
at the scale of an hour if you like.
Maybe there's a better way to quantify the effect, but that gives you an
idea of what I want.
--
Abdul Jalib wearing the hat of | Currently running at +3 SD's.
Professional Degenerate Gambler|
AbdulJ_...@PosEV.com | (Delete _DELETE_ to reply via email.)
Barbara Yoon
>>>> ...wild. I was up $4984 in 127 hours (mostly 5-10 some 10-20).
>>>> ...[now] I am up $327 for the year in 250 hours. Ouch. Talk about
>>>> running bad for the last 123 hours! Course, talk about running good
>>>> group, but maybe somebody could explain life to me one more time.
B.Y.:
>>> If your "standard deviation" (square root of variance) is, say for example
>>> ...$100/hour, then it's not out of the question for you to do $200 or $300
>>> better or worse than...average in any one especially "hot" or "cold" single
>>> hour -- ...span of 123 or 127 hours, you could multiply those swings by 11...
>>> ...your big swings here can be characterized as "extreme," and likely are
>>> a result of something more than just normal good and bad luck...
William Chen:
>> ...but you are assuming his std deviation is 100/hr, which seems a bit low.
>> ...we should have him post his std deviation results (...also separate the
>> 5/10 and 10/20 games since they are two different games) to determine
>> whether this case is "extreme" or not...
Abdul Jalib:
> ...tight professional will have a standard deviation of about 15 small bets
> per hour, possibly as high as 20 in a loose game. ...there is an illusion
> that I'd like to quantify mathematically, but I don't know how. ...start your
> record today...end after a predetermined number of hours...your chance
> of being ahead can be computed if you know your expected value and
> variance. But when you look backwards, suddenly things seem much
> more chaotic. ...misleading to even refer to those runs in terms of
> standard deviations from the norm. Maybe Barbara or someone else
> could supply some math to help quantify this "effect". For example,
> someone has been playing hold'em for 10 years, 20 hours per week,
> with a constant frictionless expected value of 2 small bets per hour and
> a standard deviation of 15 small bets per hour; what is the probability
> that at least one 6 month period in this time would have been a -4
> standard deviation result...? ...-4 SD result for 6 months would be a loss
> of 328 units. ...assuming an infinite number of 6 month periods within
> 10 years, not just twenty 6 month periods... Maybe there's a better way
> to quantify the effect, but that gives you an idea of what I want.
Excellent question, clearly stated, and very difficult too (me too..."always
wanted to know, but afraid to ask")... Give me some time (if William Chen
doesn't come up with something first) to noodle out at least some clue...
Barbara Yoon
>> ...an illusion that I'd like to quantify mathematically, but I don't know how.
>> ...start your record today...end after a predetermined number of hours...
>> variance. But when you look backwards, suddenly things seem much
>> more chaotic. ...misleading to even refer to those runs in terms of
>> playing hold'em for 10 years, 20 hours per week...expected value of 2
>> small bets per hour...standard deviation of 15 small bets per hour; what
>> is the probability that at least one 6 month period in this time would have
>> of 6 month periods within 10 years, not just twenty 6 month periods...
OK, Abdul, here are some results from an UN-checked computer model
simulating 100 separate players with expected values of +$26.25/hr.,
standard deviation +/-$179.59, playing 500 hours each every 6 months for
10 years (not exactly what you specified, but close)... Example of reading
output: Player #1's WORST 6 months (ANY 6 months, starting/ending
any times, not just 20 discrete 6-month intervals) was a gain of $2,040,
and his BEST 6 months was a gain of $23,575. Do you see any hints of
program bugs? Any other comments?
1 min= 2040 max=23575
2 min= 3895 max=26230
3 min= 1960 max=25295
4 min= 3650 max=26200
5 min= 905 max=23265
6 min= 3240 max=24320
7 min= 4960 max=25185
8 min= 150 max=22425
9 min= 1050 max=24050
10 min= 1315 max=22405
11 min= 2875 max=25010
12 min= 3515 max=23840
13 min= 3660 max=24740
14 min= 5525 max=23235
15 min= 2495 max=22940
16 min= 5670 max=25045
17 min= 4015 max=24210
18 min= 4915 max=25030
19 min= 1510 max=18350 never better than lousy +$18,350?!
20 min= 765 max=24555
21 min= 2175 max=23120
22 min= 860 max=23195
23 min= -115 max=25970 actually with a LOSING 6 months...
24 min= 3410 max=26955
25 min= 325 max=20545
26 min= 1615 max=24435
27 min= 5260 max=22700
28 min= 1080 max=27320
29 min= 1760 max=21150
30 min= 2295 max=22120
31 min= 2090 max=26170
32 min=-3820 max=21680 big-time -$3,820 losing streak...
33 min= 6280 max=24300
34 min= 320 max=23885
35 min= 1135 max=24935
36 min= 3730 max=22905
37 min= -40 max=29210 small $40 "crater"...but also +$29,210!!
38 min= 3870 max=23390
39 min= 3565 max=20065
40 min= 390 max=21720
41 min= -695 max=21680 another loser...
42 min= 3410 max=22320
43 min= 1105 max=24830
44 min= 4825 max=25530
45 min= 3235 max=26835
46 min= 1920 max=26805
47 min=-2030 max=21635 another loser...
48 min= 1625 max=22120
49 min= 3460 max=22915
50 min= 1515 max=21265
51 min= 700 max=24305
52 min= 4480 max=23925
53 min=-1825 max=24430 another loser...
54 min= 3570 max=20865
55 min= 5855 max=25915
56 min= 3995 max=24400
57 min= 5820 max=25010
58 min= 4440 max=23700
59 min= 5275 max=21210
60 min= 3545 max=22185
61 min= 3195 max=23440
62 min= 4900 max=22510
63 min= 2610 max=25965
64 min= 6045 max=25105
65 min= 1190 max=24950
66 min= 5565 max=20575
67 min= 3125 max=23650
68 min= 2275 max=23870
69 min= 2340 max=23145
70 min= 795 max=24465
71 min= -445 max=26535 another loser...
72 min= 4120 max=20000
73 min= 475 max=21195
74 min= 2140 max=21750
75 min= 1695 max=24045
76 min= -785 max=25300 another loser...
77 min= 2000 max=19910
78 min= 2740 max=25570
79 min=-1420 max=23700 another loser.....
80 min= 4750 max=23790
81 min= 1020 max=23645
82 min= 3170 max=21910
83 min= 3790 max=24105
84 min= 4405 max=25075
85 min= 2720 max=25155
86 min= 5730 max=24740
87 min= 2545 max=24070
88 min= 4430 max=24705
89 min= 6900 max=24635 never worse than +$6,900!
90 min= 6850 max=23620
91 min= 4235 max=21120
92 min= 5595 max=26415
93 min= 5400 max=22240
94 min=-1530 max=21165 another loser...
95 min= 6615 max=26560
96 min= 4675 max=23510
97 min= 5140 max=22620
98 min= 2970 max=24645
99 min= -125 max=25200 another loser...
100 min= 3980 max=24995
Joseph Carta
with many of the same opponents over a period of time. They may have a
read on your play. I enjoy going to a different casino from time to
time. It's fun when no one has a clue to your style;also, you'll find it
stimulating to try to get a read on new opponents. Just an idea.
Dave Scharf
Joseph Carta wrote:
Out here in the backwoods of Canada... that's not an option. But, I too
find that a new field will often have positive results.
Regards,
Dave
Barbara Yoon
> ...example, someone has been playing hold'em for 10 years, 20 hours
> per week...expected value of 2 small bets per hour...standard deviation
> of 15 small bets per hour; what is the probability that at least one 6 month
> period in this time would have been a -4 standard deviation result...?
> ...assuming an infinite number of 6 month periods within 10 years, not
> just twenty 6 month periods...
Ran another 1,000 "players" through UN-checked ("quick and dirty") computer
model, and 135 of them experienced at least one negative 6-month span in
10-year careers -- 6 months as bad as -$4,850 (versus as good as +$31,160)
-- all players expected values +$26.25/hr., standard deviation +/-$179.59,
playing 500 hours each every 6 months for 10 years... The main reason the
computer model doesn't exactly match your (Abdul's) player specifications is
just plain old "clunkiness" -- the Basic program has "hard-wired" in that the
results of any single hour come from the following table of 100 equally likely
possibilities (thus difficult to fine-tune e.v., s.d.):
100 DATA -500,-400,-350,-300,-250,-200,-195,-190,-185,-180
101 DATA -175,-170,-165,-160,-155,-150,-145,-140,-135,-130
102 DATA -125,-120,-115,-110,-105,-100, -95, -90, -85, -80
103 DATA -75, -70, -65, -60, -55, -50, -45, -40, -35, -30
104 DATA -25, -20, -15, -10, -5, 5, 10, 15, 20, 25
105 DATA 30, 35, 40, 45, 50, 55, 60, 65, 70, 75
106 DATA 80, 85, 90, 95, 100, 105, 110, 115, 120, 125
107 DATA 130, 135, 140, 145, 150, 155, 160, 165, 170, 175
108 DATA 180, 185, 190, 195, 200, 205, 210, 215, 220, 225
109 DATA 230, 235, 240, 245, 250, 300, 350, 400, 500, 600
Let me know if you would like to adjust some of these numbers...
Tad Perry
Hey! I think I can contribute to a math thread! I think you got it
exactly right where the problem in the model is. The weighting you use
is incorrect (the equally likely thing).
The reason is that the competent player is playing against
not-so-competent players. (The games Abdul plays, I play, all of us
play (hopefully).) We can be very skillful at getting a lot of money
into a pot when we know we're the best going into the river, and then
have the river card destroy us. As this occurs when a weak player,
having hit a negative expectation hand, is *finally* willing to stick
it to you, you've in essence stuck it to yourself. It's the very
reason the river card is so frustrating and people are even proposing
getting rid of it.
So: The biggest confrontations: you LOSE. The medium to pretty large ones:
You win. The little ones: the opponent wins. I'm going on heads up
experience to state this, but it applies always I think. Okay?
Tad Perry
Barbara Yoon
>>> ...example, someone has been playing hold'em for 10 years, 20 hours
>>> per week...expected value of 2 small bets per hour...standard deviation
>>> of 15 small bets per hour; what is the probability that at least one 6 month
>>> period in this time would have been a -4 standard deviation result...?
B.Y.:
>> Ran another 1,000 "players" through UN-checked ("quick and dirty") computer
>> model, and 135 of them experienced at least one negative 6-month span in
>> 10-year careers -- 6 months as bad as -$4,850 (versus as good as +$31,160)
>> -- all players expected values +$26.25/hr., standard deviation +/-$179.59,
>> playing 500 hours each every 6 months for 10 years... The main reason the
>> computer model doesn't exactly match your (Abdul's) player specifications is
>> just plain old "clunkiness" -- the Basic program has "hard-wired" in that the
>> results of any single hour come from the following table of 100 equally likely
>> possibilities (thus difficult to fine-tune e.v., s.d.):
>>
>> 100 DATA -500,-400,-350,-300,-250,-200,-195,-190,-185,-180
>> 101 DATA -175,-170,-165,-160,-155,-150,-145,-140,-135,-130
>> 102 DATA -125,-120,-115,-110,-105,-100, -95, -90, -85, -80
>> 103 DATA -75, -70, -65, -60, -55, -50, -45, -40, -35, -30
>> 104 DATA -25, -20, -15, -10, -5, 5, 10, 15, 20, 25
>> 105 DATA 30, 35, 40, 45, 50, 55, 60, 65, 70, 75
>> 106 DATA 80, 85, 90, 95, 100, 105, 110, 115, 120, 125
>> 107 DATA 130, 135, 140, 145, 150, 155, 160, 165, 170, 175
>> 108 DATA 180, 185, 190, 195, 200, 205, 210, 215, 220, 225
>> 109 DATA 230, 235, 240, 245, 250, 300, 350, 400, 500, 600
Tad Perry:
> Hey! I think I can contribute to a math thread! I think you got it exactly right
> where the problem in the model is. The weighting you use is incorrect (the
> equally likely thing). ... The biggest confrontations: you LOSE. The medium
> to pretty large ones: You win. The little ones: the opponent wins. I'm going
> on heads up experience to state this, but it applies always I think. Okay?
While the model is "clunky," it does readily allow for adjustment -- so if you
think a "+20" is five times as likely as a "-75" (and remember these results
in the table are HOURLY), then we can change the table to have one "-75"
and five "+20" entries...OK?
Tad Perry
OK :-)
Tad Perry
jw...@lehigh.edu
writes:
>Dave Scharf:
>>>>> ...wild. I was up $4984 in 127 hours (mostly 5-10 some 10-20).
>>>>> ...[now] I am up $327 for the year in 250 hours. Ouch. Talk about
>>>>> running bad for the last 123 hours! Course, talk about running good
>>>>> for the first 127. ...we have gone over variance many times in this
>>>>> group, but maybe somebody could explain life to me one more time.
>
>B.Y.:
>>>> If your "standard deviation" (square root of variance) is, say for example
>>>> ...$100/hour, then it's not out of the question for you to do $200 or $300
>>>> better or worse than...average in any one especially "hot" or "cold" single
>>>> hour -- ...span of 123 or 127 hours, you could multiply those swings by 11.
..
>>>> ...your big swings here can be characterized as "extreme," and likely are
>>>> a result of something more than just normal good and bad luck...
>
>William Chen:
>>> ...but you are assuming his std deviation is 100/hr, which seems a bit low.
>>> ...we should have him post his std deviation results (...also separate the
>>> 5/10 and 10/20 games since they are two different games) to determine
>>> whether this case is "extreme" or not...
>
>Abdul Jalib:
>> ...tight professional will have a standard deviation of about 15 small bets
>> that I'd like to quantify mathematically, but I don't know how. ...start you
r
>> of being ahead can be computed if you know your expected value and
>> variance. But when you look backwards, suddenly things seem much
>> more chaotic. ...misleading to even refer to those runs in terms of
>> could supply some math to help quantify this "effect". For example,
>> someone has been playing hold'em for 10 years, 20 hours per week,
>> a standard deviation of 15 small bets per hour; what is the probability
>> that at least one 6 month period in this time would have been a -4
>> of 328 units. ...assuming an infinite number of 6 month periods within
>> 10 years, not just twenty 6 month periods... Maybe there's a better way
>> to quantify the effect, but that gives you an idea of what I want.
>
>
>Excellent question, clearly stated, and very difficult too (me too..."always
>wanted to know, but afraid to ask")... Give me some time (if William Chen
>doesn't come up with something first) to noodle out at least some clue...
>
Xi is the amount(measured in big bets)won or lost during i-th hour
X1, X2, X3,....,Xn are independent random variables, each having the
normal distribution, with paramaeters, mux=2 and sigmax=15
X1+x2+x3+...,+Xn is total amount won or lost in n hours of play
X1+X2+X3+...,+Xn is a random variable, having the normal distribution,
with paramaters n*mux and 15*sqrt(n)
Zn is the standardized form of X1+X2+X3+,...,Xn
The probabilility that X1+X2+X3+,...,Xn does not exceed a specified
number, say C, is the same as the probability that Zn does not exceed the
number (C-2*n)/(15*sqrt(n)). Sqrt(n) means the square root of n, and *
means multiply.
The probability that the standardized form of a random variable, having
the normal distribution, does not exceed any specified number(positive or
negative)can be determined by looking in the tables of the normal
distribution. The spreadsheet EXCEL has routines for computing normal
probabilities.
EXAMPLE: n=100 hours, C=300 big bets
(C-2*n)/(15*sqrt(n))=(300-200)/(15*10)=.6667
The probability that the player's total winnings, after 100 hours of
play, do not exceed 300 big bets is the same as the probability that a
standardized, normal random variable does not exceed .6667. This
probability, computed by a routine in the IMSL library, is approximately
.748.
Conversely, the probability that the player's total winnings, after
100 hours of play, do exceed 300 big bets is approximately .252.
The probability can be computed for any specified values of n, C, mux and
sigmax.
John W. Adams
Bethlehem, PA
>
>
Joseph Carta
Do they play Omaha h/l at your local casino?
Dave Scharf
Joseph Carta wrote:
> Where are the backwoods of Canada? Sorry, you don't have some options.
> Do they play Omaha h/l at your local casino?
Saskatoon, SK... nope. Hold'em, 7-stud only. They are looking at omaha
split and/or 7 card/8 or better.
Regards,
Dave
William Chen
"Barbara Yoon" <by...@erols.com> wrote:
>>
>Abdul Jalib:
>> ...tight professional will have a standard deviation of about 15 small bets
>> per hour, possibly as high as 20 in a loose game. ...there is an illusion
>> that I'd like to quantify mathematically, but I don't know how. ...start
your
>> record today...end after a predetermined number of hours...your chance
>> of being ahead can be computed if you know your expected value and
>> variance. But when you look backwards, suddenly things seem much
>> more chaotic. ...misleading to even refer to those runs in terms of
>> standard deviations from the norm. Maybe Barbara or someone else
>> could supply some math to help quantify this "effect". For example,
>> someone has been playing hold'em for 10 years, 20 hours per week,
>> with a constant frictionless expected value of 2 small bets per hour and
>> a standard deviation of 15 small bets per hour; what is the probability
>> that at least one 6 month period in this time would have been a -4
>> standard deviation result...? ...-4 SD result for 6 months would be a loss
>> of 328 units. ...assuming an infinite number of 6 month periods within
>> 10 years, not just twenty 6 month periods... Maybe there's a better way
>> to quantify the effect, but that gives you an idea of what I want.
>
>
>Excellent question, clearly stated, and very difficult too (me too..."always
>wanted to know, but afraid to ask")... Give me some time (if William Chen
>doesn't come up with something first) to noodle out at least some clue...
>
>
>
I haven't been ignoring the question, I just can't answer it (at least not in
closed form). I do have some observations. It doesn't matter if the player in
question is a winning or losing player, since we're talking about his worst 6
month period of deviation from the norm since we are assuming his win rate is
static. Actually we can restate the problem as a player plays 20 time periods
with zero mean and std deviation 1 for each time period. What is the
probability that this player experiences a period of length 1 where he loses 4
or more units? (Say we can assume gaussian if we need.) As Abdul hinted a
lower bound would be the probability that this -4 loss happens in a length one
time segment with integer endpoints. This is 1 - (1-Normal(-4))^20.
How good a lower bound is this? (Where Normal (-4) is the integral of the
normal from infinity to -4.)
Maybe if we now divide into 40 periods of length 1/2... Feel free to jump in any
time Barbara. BTW, how well deos the lower bound compare with your simulations?
Bill
Abdul Jalib
The problem I have with this and the similar other posted answer is that
you are assuming that every window of N hours is independent from every
other. This is clearly not the case. If we did badly on the first window
of N hours, chances are very good that we also did badly on the second window
of N hours. Conversely, if we did well initially, we probably did well
slightly later. This implies that your approach would yield an *upper*
bound on the answer for dividing time windows at the level of hours, and
no bound at all for the infinitesimal time division case.
> Maybe if we now divide into 40 periods of length 1/2... Feel free to
> jump in any time Barbara. BTW, how well deos the lower bound compare
> with your simulations?
Here's another, perhaps more interesting, way to phrase the problem.
You've just played N hours with known expected value and variance.
What is the average worst deviation from norm you can find if you
start at the end and work backwards, comparing the deviation of the
result of hour N to deviation of the result of hour N-1 plus
hour N, and so on? If you can compute that, then what about
with an infinitesimal scale?
--
Abdul
post...@nospam.com
that you can know a player's expectation, and that it's
some kind of constant or predictible value. But in fact
a player's expectation varies drastically from game to
game and from hour to hour. And you can't even use
results to determine it, because the results vary from
the variance, which should not be used in a calculation
of expectation.
If you use something like Turbo Texas Holdem to
simulate a lot of hours, you're eliminating too many
variables which affect a real game but not TTH. Such
as the fact that a particular player who seems easy
to beat one month may seem hard to beat the next
month and easy the next, or maybe the next three
months. And when you move to a different city it
takes a while for the average player to be able to
predict your play. TTH can't take such factors into
account. The real variance a player should expect
is a lot higher than what all the calculations and
simulations seemingly predict. And when things
seem to be going smoothly, and your calculated
variance fits reality to a T, that's because the real
variance happened to drift into that range for a
while.
In reality, to be a successful professional poker
player, your expected value should be so high
that you come out ahead even in your worst
period of a few months. And in that case there
is no real need to actually calculate your expected
value nor variance, which can't be calculated
anyway. But it does make it easy to determine
whether you really have what it takes to be a
successful pro.
For those whose expectation is borderline, such
that they can't quite justify being a pro, they might
do much better as an amateur. Amateurs have
a big advantage in that they don't have to worry
about the money as much.
And even those who can justify being a pro, it still
makes sense to be an amateur. The test of a
really successful person is that he can show his
grandchildren what he accomplished in life and
hope they follow in his footsteps. To be that kind
of person, you need a profession you can really
be proud of. How many professional poker players
hope their grandchildren will be professional
poker players? By being an amateur poker player,
you have enough spare time away from poker to
develop a true profession that can give you the
kind of pride a really successful person has.
Besides that, the talents that can make you a
successful poker player can also make you a top
executive in business. Why spend your life aiming
for that elusive million dollars, when you could have
many millions of dollars in salary and stock options?
Abdul Jalib
> The big flaw in all these calculations is the whole idea
> that you can know a player's expectation, and that it's
> some kind of constant or predictible value. But in fact
> a player's expectation varies drastically from game to
> game and from hour to hour. And you can't even use
> results to determine it, because the results vary from
> the variance, which should not be used in a calculation
> of expectation.
The idea is to see what kinds of swings are typical in theory,
and to try to mathematically quantify the psychological effect of
feeling like you're experiencing a bad run, because you're biasing
the data by looking back at your last peak before your current valley.
If your actual results are within the mathematically reasonable bounds,
then you should not be complaining. Of course, in the real world your
swings should be larger than in theory, because of playing games that
vary in quality over time as well as your skill changing (hopefully
improving) over time.
> In reality, to be a successful professional poker
> player, your expected value should be so high
> that you come out ahead even in your worst
> period of a few months. And in that case there
> is no real need to actually calculate your expected
> value nor variance, which can't be calculated
> anyway. But it does make it easy to determine
> whether you really have what it takes to be a
> successful pro.
I don't know whether I agree with that or not. If you're
a professional 300-600 player making 1 small bet per hour,
you're making good money, but the swings will be brutal,
and you certainly could be behind after a few months of play.
And of course what is really happening is that sometimes you're
the fish, and sometimes you're a winning player, and it's
averaging out to 1 small bet per hour, for your recent history.
On the other hand, I read Roy Cooke's article where he whined
about losing every day one week until the last day, when he won
only enough to make a small profit for the week. Poor, poor Roy.
Only a small profit for the week. Is this the worst he does?
A higher stakes professional poker player I know claimed to have never
experienced a losing month. I cannot make such claims, nor would I
have considered a losing week something to be alarmed about before
hearing Roy whine about a small win for one week.
I was skeptical about their claims, but I resolved to change my game
so that I too could whine about only a small win for the week. Reducing
your standard deviation below 14 small bets per hour is *really* hard,
and probably hazardous to your EV, so let's assume a standard deviation
of 14 small bets per hour. Roy plays only about 4 hours per day,
tops, and I'm just as lazy (worse, actually, not even considering
Roy's real estate business.) So a -2 SD run for 7 days,
4 hours per day, 14 small bets per hour standard deviation,
would be 148 small bets. Therefore, you need to win about 148 small bets
divided by 28 hours or 5.3 small bets per hour with a standard deviation
of 14 small bets per hour in order to have only a very small chance of a
losing week. I've been running at about 6.6 small bets per hour for the
several months since I made my "win like Roy" resolution. Shrug.
It seems hard to believe that my average will continue like this, but
only time will tell.
> And even those who can justify being a pro, it still
> makes sense to be an amateur. The test of a
> really successful person is that he can show his
> grandchildren what he accomplished in life and
> hope they follow in his footsteps. To be that kind
> of person, you need a profession you can really
> be proud of. How many professional poker players
> hope their grandchildren will be professional
> poker players? By being an amateur poker player,
> you have enough spare time away from poker to
> develop a true profession that can give you the
> kind of pride a really successful person has.
>
> Besides that, the talents that can make you a
> successful poker player can also make you a top
> executive in business. Why spend your life aiming
> for that elusive million dollars, when you could have
> many millions of dollars in salary and stock options?
The talents are not exactly the same. In poker, your people skills
can be extremely poor, so long as you can read people.
I was a software engineer, before becoming a professional degenerate gambler.
Being a slave in a corporation offers poor compensation, high stress,
and limited free time. True, if you can rise to the top of the corporate
ladder, you may have good compensation, but you'll have even more stress
and less free time. If you're not on the corporate executive track,
and you work very hard and get the highest ratings, you get a 5% pay raise.
If you work a minimal amount and get medicore ratings, you get a 4.5% pay
raise. I like the fact that in gambling my expected reward equals what
I "deserve", even if the actual reward is rather random.
It's not that hard to make $25/hour gambling, but that's considered
a nontrivial salary in the corporate world. Making $100/hour gambling
is quite reasonable if you have a sizable bankroll in addition to the
necessary knowledge/skill (say, 2.5 small bets per hour in $40-$80
hold'em, or 2 small bets per hour betting $50-$300 on double deck blackjack,
or knowledgable sports betting, or some video poker opportunities),
but such a salary is fairly outrageous in the corporate world. To become
truly rich, I think you should look to gambling opportunities other than
poker, but poker is a good fall-back when you don't have any higher EV
gambling opportunities to do at the moment, or when you want a fairly
high EV relative to standard deviation. Poker is almost like having a
salary, if, like Roy Cooke, you almost never have a losing week.
--
Abdul Jalib wearing the hat of | I'm my own boss.
Barbara Yoon
> Xi is the amount won or lost during i-th hour...X1, X2, X3,....,Xn are
> independent random variables, each having the normal distribution,
> amount won or lost in n hours of play X1+X2+X3+...,+Xn is a random
> variable, having the normal distribution, with paramaters n*mux and
> (C-2*n)/(15*sqrt(n))=(300-200)/(15*10)=.6667
> The probability that the player's total winnings, after 100 hours of play,
> do not exceed 300 big bets is the same as the probability that a
> standardized, normal random variable does not exceed .6667.
OK...but your calculation method is for discrete specified periods, whereas
Abdul Jalib inquired about "an infinite number of 6 month periods within
10 years, not just twenty 6 month periods..." -- in other words, if the 10 years
spanned from 1987 through 1996, then one such six-month period would be
from January '94 through June '94, and another would be from February '94
through July '94, even though overlapping for five of the months...see?!
Barbara Yoon
> The problem I have with this and the similar other posted answer is
> that you are assuming that every window of N hours is independent
> from every other. This is clearly not the case. If we did badly on the
> first window of N hours, chances are very good that we also did badly
> on the second window of N hours.
True...if January '94 through June '94 was a "bad" six months for you,
then it's quite likely that February '94 through July '94 also was a "bad"
six months... The "quick and dirty" computer model handles this
"non-independence" properly -- have you mulled its output?
tha...@nmia.com
>
>The big flaw in all these calculations is the whole idea
>that you can know a player's expectation, and that it's
>some kind of constant or predictible value. But in fact
>a player's expectation varies drastically from game to
>game and from hour to hour. And you can't even use
>results to determine it, because the results vary from
>the variance, which should not be used in a calculation
>of expectation.
>
I agree with this. I don't think it is worth the time spent on it except if you
enjoy doing it. I think a lot of players simply enjoy calculating their
expectation and their variance which is great. I'm an amatuer and I keep
records because I just want to know where I stand but I don't bother with
variance and I don't worry about my expectation. I know what kinds of games
have a high variance and I know what types of games are profitable for me.
The only thing that I see that is detrimental is that players seem to want to
use these statistics to justify playing in a game that could put them in some
jeopardy. I think if you have any doubts play cheaper and if it isn't enough to
pay the rent get a bigger bankroll or get a job.
>If you use something like Turbo Texas Holdem to
>simulate a lot of hours, you're eliminating too many
>variables which affect a real game but not TTH. Such
>as the fact that a particular player who seems easy
>to beat one month may seem hard to beat the next
>month and easy the next, or maybe the next three
>months. And when you move to a different city it
>takes a while for the average player to be able to
>predict your play. TTH can't take such factors into
>account. The real variance a player should expect
>is a lot higher than what all the calculations and
>simulations seemingly predict. And when things
>seem to be going smoothly, and your calculated
>variance fits reality to a T, that's because the real
>variance happened to drift into that range for a
>while.
>
I think a lot of players use TTH2 as a research tool but I agree with what you
are saying.
>In reality, to be a successful professional poker
>player, your expected value should be so high
>that you come out ahead even in your worst
>period of a few months. And in that case there
>is no real need to actually calculate your expected
>value nor variance, which can't be calculated
>anyway. But it does make it easy to determine
>whether you really have what it takes to be a
>successful pro.
>
I agree with this statement in principle but I'm not sure it's possible for most
players if they want to make an upper middle class level income and above by
strictly playing poker. It might be but I'm not sure.
>For those whose expectation is borderline, such
>that they can't quite justify being a pro, they might
>do much better as an amateur. Amateurs have
>a big advantage in that they don't have to worry
>about the money as much.
>
I definitely agree with this statement.
>And even those who can justify being a pro, it still
>makes sense to be an amateur. The test of a
>really successful person is that he can show his
>grandchildren what he accomplished in life and
>hope they follow in his footsteps. To be that kind
>of person, you need a profession you can really
>be proud of. How many professional poker players
>hope their grandchildren will be professional
>poker players? By being an amateur poker player,
>you have enough spare time away from poker to
>develop a true profession that can give you the
>kind of pride a really successful person has.
>
We'll part company some on this one. I think if you enjoy playing poker full
time and are having a lot of fun doing it, then you can explain that to your
grandchildren. As Abdul implies, the coporate world is not for everyone. Of
course I realize that you didn't say that an individual has to work for an
employer in the corporate world to have a profession. And I think that is
something that a lot of people are conditioned to do feel that they can only
have a profession if they have an employer. A lot of people have their own
businesses and/or do free lance work.
>Besides that, the talents that can make you a
>successful poker player can also make you a top
>executive in business. Why spend your life aiming
>for that elusive million dollars, when you could have
>many millions of dollars in salary and stock options?
>
Again I will disagree and try to be as diplomatic as possible by saying that the
corporate world has it's share of dishonorable and unethical executives running
the show.
Barbara Yoon
>> ...playing hold'em for 10 years, 20 hours per week...expected value of
>> 2 small bets per hour...standard deviation of 15 small bets per hour; what
>> is the probability that at least one 6 month period in this time would have
>> 6 month periods within 10 years, not just twenty 6 month periods...
> ...1,000 "players"...computer model...135 of them experienced at least one
> negative 6-month span in 10-year[s] -- 6 months as bad as -$4,850 (versus
> as good as +$31,160) -- all players expected values +$26.25/hr., standard
> deviation $179.59, playing 500 hours each every 6 months for 10 years...
Another 1,000 players, this time with averages of +$22.75, standard deviations
$191.76. Perhaps William Chen can attest that all that really matters here is the
s.d./ave. ratio -- and these two runs "bracket" Abdul's original 15/2 = 7.5 ratio.
438 of the players experienced at least one negative 6-month span (and 1 other
a break-even) -- 6 months as bad as -$7,805 (versus as good as +$32,075).
Players' best/worst 6 month periods seem NOT normally distributed -- average
"worst" was +$160, with extremes of -$7,805 and +$6,075, and average "best"
was +$22,588, with extremes of +$32,075 and +$16,580...
Barbara Yoon
hourly results, averaging +$22.75, standard deviation +/-$179.71...
100 DATA -450,-400,-350,-325,-300,-275,-260,-245,-230,-215
101 DATA -200,-190,-180,-170,-160,-150,-140,-130,-120,-110
102 DATA -100, -95, -90, -85, -80, -75, -70, -65, -60, -55
103 DATA -50, -45, -40, -35, -30, -25, -20, -15, -10, -5
104 DATA -5, -5, -5, -5, -5, 5, 5, 5, 5, 5
105 DATA 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
106 DATA 55, 60, 65, 70, 75, 80, 85, 90, 95, 100
107 DATA 105, 110, 115, 120, 125, 130, 135, 140, 145, 150
108 DATA 160, 170, 180, 190, 200, 210, 220, 230, 240, 250
109 DATA 265, 280, 295, 310, 325, 350, 375, 400, 450, 500
Monte Carlo simulating 1,000 such players for 10 years, 309 of them
experienced 6-month spans for net losses (and 2 others break-even)
-- extremes listed below:
6 months results
-------------------------------
worst worst -$7,290
best worst +$6,305
worst best +$15,995
best best +$30,780
Barbara Yoon
> I read Roy Cooke's article where he whined about losing every day
> one week until the last day, when he won only enough to make a
> small profit for the week. Poor, poor Roy. Only a small profit for
> the week. Is this the worst he does? A higher stakes professional
> poker player I know claimed to have never experienced a losing month.
> I cannot make such claims, nor would I have considered a losing week
> something to be alarmed about before hearing Roy whine about a
These claims are possibly true -- IF they restricted their play to the local
Charity Home for Retarded Polish (or even quite probable with Irish)...
sh...@asu.uswest.net
>In article <35cdfc28...@nntp.ix.netcom.com>, post...@nospam.com says...
>>game and from hour to hour. And you can't even use
>>results to determine it, because the results vary from
>>the variance, which should not be used in a calculation
>>of expectation.
>
>I agree with this. I don't think it is worth the time spent on it except if you
>enjoy doing it. I think a lot of players simply enjoy calculating their
>expectation and their variance which is great.
> I'm an amatuer and I keep
>records because I just want to know where I stand but I don't bother with
>variance and I don't worry about my expectation.
I was surprised to read this. I *just* got home from playing poker,
and updated my spreadsheet, which uses Malmuth's variance
approximation. In fact, Excel is still on my windows bar thingy. The
whole updating process took 90 seconds, maybe.
>>And even those who can justify being a pro, it still
>>makes sense to be an amateur. The test of a
>>really successful person is that he can show his
>>grandchildren what he accomplished in life and
>>hope they follow in his footsteps.
>We'll part company some on this one. I think if you enjoy playing poker full
>time and are having a lot of fun doing it, then you can explain that to your
>grandchildren. As Abdul implies, the coporate world is not for everyone.
I agree with you, but I hate these 'ethics/work product' threads.
Join Big Brothers. Volunteer at your religious center. Say what you
do, and do what you say. Then go play pocker. There are a lot of
useless and/or detrimental ways to earn a buck that are completely
acceptable to mainstream society.
-Rob Vega
Now, back to variance. . .
Tad Perry
True or false:
Theoretically the difference here:
> worst worst -$7,290
> best worst +$6,305
Should be the same as the difference here:
> worst best +$15,995
> best best +$30,780
?? (which I noticed it was very close to being.)
Tad Perry
William Chen
Abdul Jalib <AbdulJ_...@PosEV.com> wrote:
>William Chen <w_c...@ix.netcom.com> writes:
>>>
>> I haven't been ignoring the question, I just can't answer it (at least not in
>> closed form). I do have some observations. It doesn't matter if the player in
>> question is a winning or losing player, since we're talking about his worst 6
>> month period of deviation from the norm since we are assuming his win rate is
>> static. Actually we can restate the problem as a player plays 20 time periods
>> with zero mean and std deviation 1 for each time period. What is the
>> probability that this player experiences a period of length 1 where he loses 4
>> or more units? (Say we can assume gaussian if we need.) As Abdul hinted a
>> lower bound would be the probability that this -4 loss happens in a length one
>> time segment with integer endpoints. This is 1 - (1-Normal(-4))^20.
>> How good a lower bound is this? (Where Normal (-4) is the integral of the
>> normal from infinity to -4.)
>
>The problem I have with this and the similar other posted answer is that
>you are assuming that every window of N hours is independent from every
>other. This is clearly not the case. If we did badly on the first window
>of N hours, chances are very good that we also did badly on the second window
>of N hours. Conversely, if we did well initially, we probably did well
>slightly later. This implies that your approach would yield an *upper*
>bound on the answer for dividing time windows at the level of hours, and
>no bound at all for the infinitesimal time division case.
Wait a minute. Windows are independent if they are non-overlapping. For my lower
bound approximation, I divided the 10 years into 20 non-overlapping windows of 6
months. Now how well or badly you do in one window in independent of the next 6
month window. Losing 4 sigmas in one of these 20 discrete 6-month windows is a
stronger statement than losing 4 sigmas in a 6-month window. Hence my lower bound
of 1 - (1-Normal(-4))^20 is really a lower bound since it estimates the probability
of going -4 sigma in one of these 20 windows. OK?
Let's see what we get. Normal (-4) (using MATLAB) is 3.167e-5.
So the lower bound comes out to be 6.e33e-4 or less than one in a thousand.
Well I never said it was a good lower bound.
Bill
Robert Copps
>
>
> Besides that, the talents that can make you a
> successful poker player can also make you a top
> executive in business.
>
I think it was Jack Welch, fabled president of GE, who said that the main
job of a CEO is spotting the articulate non-performer. Does sound like
poker, doesn't it?
--Bob
Dan Hanson
variable, related to your past results. I believe that hot and cold runs at
poker are longer than the pure math would suggest, because your past results
change your future results. They aren't independant variables.
For example, when you're running bad, it inspires opponents to take runs at
you, increasing your variance. It may also inspire your opponents to play
better against you, decreasing your expectation. Depending on the player,
you may play better or worse after a bad run of cards, but rarely will a
player play exactly the same.
The extreme example would be players who go on 'tilt'. They may play solid
cards, and have a long stretch of wins. Then they put a couple of losses
together, and the next thing you know they are -EV players, losing every
session, and wondering what in the hell happened.
On the other hand, when you're hitting like crazy, it may inspire your
opponents to play poorly against you, increasing you expectation. You may
also play better, increasing expectation even more.
The big question is, "How much of an effect is this?"
Dan