tournament 'deals' ...
Barbara Yoon
> Some [*methods for calculating tournament prize money settlement 'deal'
> amounts*] are biased to the big stack (McEvoy's for example), some
> are favor the small stack (Landrum-Burns maybe?) So far as I can tell
> there are five labelled ways to do this, Malmuth, McEvoy, Landrum-Burns,
> Weitzman, Weideman, and Card Player Mag via '96 or '97. Wouldn't it
> be in the interests of all here to compare these by discussing the strengths
> and weaknesses of all? ... Anything past five fingers is a tough one for me.
Gary.....I am familiar with the "Malmuth," "McEvoy," "Weitzman,"
and the "Card Player Mag via '96 or '97" material. The different flaws
in "Malmuth," and "McEvoy" are by now almost in the category of
'common knowledge,' and "Weitzman" is much more difficult to use,
and it also gives WORSE answers than "Malmuth" (even though
Malmuth's book mistakenly declares his own method as being,
"a little less accurate...but...considerably faster and easier"***),
and "Card Player Mag via '96 or '97" was, as I recall it, is quite sound
and accurate. Can anybody else fill us in here on the "Landrum-Burns,"
and "Weideman" methods?!
***..."considerably faster and easier" is true, but "Malmuth"
is also actually MORE accurate than Weitzman" too...
lvdlrs
> Gary (...) Philips:
>
>>Some [*methods for calculating tournament prize money settlement 'deal'
>>amounts*] are biased to the big stack (McEvoy's for example), some
>>are favor the small stack (Landrum-Burns maybe?) So far as I can tell
>>Weitzman, Weideman, and Card Player Mag via '96 or '97. Wouldn't it
>>be in the interests of all here to compare these by discussing the strengths
>>and weaknesses of all?
>
> and the "Card Player Mag via '96 or '97" material. The different flaws
> in "Malmuth," and "McEvoy" are by now almost in the category of
> 'common knowledge,' and "Weitzman" is much more difficult to use,
> and it also gives WORSE answers than "Malmuth" (even though
> Malmuth's book mistakenly declares his own method as being,
> "a little less accurate...but...considerably faster and easier"***),
> and "Card Player Mag via '96 or '97" was, as I recall it, is quite sound
> and accurate. Can anybody else fill us in here on the "Landrum-Burns,"
> and "Weideman" methods?!
>
>
> ***..."considerably faster and easier" is true, but "Malmuth"
> is also actually MORE accurate than Weitzman" too...
Steve Landrum and Jazbo Burns are I believe the originators of the
Landrum-Burns method. Patti Beadles knows it well. Patti?
Tom Weideman is the author of the aptly named Weideman method.
Tom?
Gary (...) Philips
wamplerr
With N players left and T chips in play, first place pays F, and the
total prizes for the players left total to P.
Then a player with C chips has an equity of:
((T-C)/T * (P-F)/(N-1)) + C*F/T
So with three players left, chip counts of
A=500
B=300
C=200
And a payout of $1000, $600 and $300
You would get a deal giving:
A $725
B $623
C $560
* Posted via RGP ACCESS at http://www.liveactionpoker.com
* New Poker Magazine:
http://www.liveactionpoker.com/magazine/magazine.html
lvdlrs
> The Landrum-Burns formula:
>
> With N players left and T chips in play, first place pays F, and the
> total prizes for the players left total to P.
>
> Then a player with C chips has an equity of:
>
> ((T-C)/T * (P-F)/(N-1)) + C*F/T
>
> So with three players left, chip counts of
> A=500
> B=300
> C=200
> And a payout of $1000, $600 and $300
>
> You would get a deal giving:
> A $725
> B $623
> C $560
First off, thank you for posting this.
B's payout would be $615 as the $623 would payout a total
of $1908 instead of $1900.
How does this formula rate in accuracy for the 3 players.
What about 4,5, or 6 players?
Gary (...) Philips
Iceman
>The Landrum-Burns formula:
>
>With N players left and T chips in play, first place pays F, and the
>total prizes for the players left total to P.
>
>Then a player with C chips has an equity of:
>
>((T-C)/T * (P-F)/(N-1)) + C*F/T
>
>So with three players left, chip counts of
>A=500
>B=300
>C=200
>And a payout of $1000, $600 and $300
>
>You would get a deal giving:
>A $725
>B $623
>C $560
Let's say the chip counts are 90-9-1, and the payouts are 50-30-20.
A 47.5
B 27.25
C 25.25
That's too much for Player C and not enough for Player B.
Barbara Yoon
> The Landrum-Burns formula: With N players left and T chips in play,
> first place pays F, and the total prizes for the players left total to P.
> Then a player with C chips has an equity of:
>
> ((T-C)/T * (P-F)/(N-1)) + C*F/T
>
> So with three players left, chip counts of
> A=500 B=300 C=200
> And a payout of $1000, $600 and $300
> You would get a deal giving: A $725 B $623 C $560
"wamplerr".....first of all, your "B $623" here doesn't jibe with that formula...
And then in words, the "C*F/T" gives each player his chips-proportional
(C/T) share of the 1st-place prize (F) -- and then doesn't the rest of the
formula in effect re-set 2nd and 3rd prizes to be equal to each other
(by the "(P-F)/(N-1)" -- can anyone else support this interpretation?)
-- which is obviously unfairly biased in favor of the small stacks?!
The "Malmuth" formula, which is known to be flawed in favor of the
small stacks, would give the small stack here $526 -- and so with the $560
here for the small stack, this "Landrum - Burns" formula is even WORSE...!!
wamplerr
$623 would payout a total of $1908 instead of $1900."
Oops, you're right. I mixed and matched when I was comparing them to
the use of conditional probabilities. So to answer your second question
(I think), the conditional prob payout would be
A $752
B $623
C $525
How does this formula rate in accuracy for the 3 players. What about
4,5, or 6 players?
Let's see what happens and throw in a 5 player chop.
Chip count is
A 500
B 400
C 300
D 200
E 100
Payout is $1000, $600, $400, $250, $150
The chop by Landrum-Burns (Conditional Prob):
A 567 (625)
B 523 (569)
C 480 (500)
D 437 (413)
E 393 (293)
Looks like Landrum-Burns tends to value a short stack significantly
more. Look at the short stack (100 chips out of 2400) essentially
locking up third place money ($393) in this chop. My instinct says this
is way too much for someone who has half the chips of the next highest
player.
Barbara Yoon
>>> The Landrum-Burns formula: With N players left and T chips in play,
>>> first place pays F, and the total prizes for the players left total to P.
>>> Then a player with C chips has an equity of:
>>>
>>> ((T-C)/T * (P-F)/(N-1)) + C*F/T
>>>
>>> So with three players left, chip counts of
>>> A=500 B=300 C=200
>>> And a payout of $1000, $600 and $300
>>> You would get a deal giving: A $725 B $623 C $560
>> "wamplerr".....first of all, your "B $623" here doesn't jibe with that
>> formula...
>>
>> And then in words, the "C*F/T" gives each player his chips-proportional
>> (C/T) share of the 1st-place prize (F) -- and then doesn't the rest of the
>> formula in effect re-set 2nd and 3rd prizes to be equal to each other[***]
>> (by the "(P-F)/(N-1)" -- can anyone else support this interpretation?)
>> -- which is obviously unfairly biased in favor of the small stacks?!
>> The "Malmuth" formula, which is known to be flawed in favor of the
>> small stacks, would give the small stack here $526 -- and so with the $560
>> here for the small stack, this "Landrum - Burns" formula is even WORSE...!!
***...that is, while "wamplerr" specifies 2nd and 3rd prizes here as
$600 and $300, the "Landrum - Burns" formula treats those prizes
as $450 each (clearly to advantage of smaller stacks)...
Barbara Yoon
>> The Landrum-Burns formula: With N players left and T chips in play,
>> first place pays F, and the total prizes for the players left total to P.
>> Then a player with C chips has an equity of:
>> ((T-C)/T * (P-F)/(N-1)) + C*F/T
"Iceman":
> Let's say the chip counts are 90-9-1, and the payouts are 50-30-20.
> A 47.5 B 27.25 C 25.25
> That's too much for Player C and not enough for Player B.
"Iceman".....right...as is pointed out elsewhere in this thread, this
"Landrum - Burns" formula works by the simplifying approximation
of in effect 'flattening' the lower prizes -- in your example here, by
'flattening' the 2nd and 3rd prizes of "30-20" to 25-25...see?!
lvdlrs
(Math)" posted 6/26/97:
With three players left A's share would be,
[A*P1 + B*(A*P2+C*P3)/(A+C) + C*(A*P2+B*P3)/(A+B)]/T
To solve for B and C just rename the players using the formula above.
Where:
A is player A's chip holdings;
B is player B's chip holdings, etc.
T is the total number of chips in play;
P1 is first-place prize (or percentage);
P2 is second-place prize, etc.
In the case where A=2, B=1, C=1, and prize % were 50, 30, 20, Harry
gets A=38.33%, B=30.33%, and C=30.33%
He says it's a compromise between Weideman's first place of 38.57%
and Malmuth's 38%.
BTW what is a Markov-chain program?
Gary (...) Philips
Gary Carson
>BTW what is a Markov-chain program?
>
It's a mathematical model of a process that moves from one "state" to another
"state" that assumes such movement is independent on the past, dependent only
on what state you are in, not on how you got to that state.
That state in this problem would probably be number of chips.for each player.
--
Gary Carson
http://garycarson.com