I apologize if this is a duplicate for anyone. I posted it three days ago
and it hasn't shown up on Google, recpoker, or my newsreader, so I assume
it did not go out the first time.
(Best viewed in a fixed font such as Courier 10)
A number of people have reported the same bad experience with online
poker: They win for a while, but once they cash out some winnings
they seem to run bad and bust. To some people, this is solid evidence
that online poker must be rigged; that by cashing out some winnings,
players incur the wrath of the online operators, who will set a switch
on the player's account, dooming them to lose thereafter.
Is the "rigged theory" the best explanation for the trends that people
are observing?
To explore the possibilities, I wrote a simple program to do a Monte
Carlo simulation to examine the luck factor in small bankroll play
where players take money off the table in the form of cashouts. I
don't claim it perfectly models the real world. I do suspect the
trends that the sim demonstrates are probably correct.
Program Inputs:
(SB stands for Small Bets)
Player's standard deviation in SB/hr
Player's true EV in SB/hr
Starting bankroll in SB
Cashout Point in SB
Cashout Amount in SB
It works like this: The player's Standard Deviation in SB/hr is a
measure of how much their bankroll fluctuates due to chance. For
example, a setting of 10 would mean that about 68% of the time they
would experience a fluctuation of 10 SB or less over the course of an
hour, and about 95% of the time they would see fluctuations of 20 SB
or less. These fluctuations would be positive sometimes, and negative
other times, and would tend to balance out in the long run.
In the Sim, with each passing hour I apply the players true EV, and
randomly generate fluctuation for that hour. I do this by generating
a random number from .001 to .999, seeing where it falls on the normal
curve, and applying that many times their SD setting.
On the normal curve, .001 is about -3.09 SDs; .250 is -0.67449
SDs; 0.500 is 0, and so on up to 0.999 which is +3.09, etc.
So, for a player with SD set to 10 and True EV set to +2 SB/hr, if the
random number for a given hour was .250, I would take the player's
bankroll and add:
[(-0.67449) * (10)] + 2
The Starting Bankroll is the number of SB they begin with. The
Cashout Point is a goal, in SB, at which they will take the Cashout
Amount off the table, never to return.
The only other tweaking I did was to make some adjustments when a
player ended an hour with a bankroll smaller than his SD. Without
this tweak high variance players were managing to outperform their
expected EV by considerable margins (e.g., small -EV / high SD losers
were winning). Effectively, you cannot allow someone who starts a
period with, let's say, one-half of a SB remaining post a positive
triple SD (where SD=30) the next period.
Now I just need some Sim players.
I searched RGP's old posts looking for some real life SD stats from
reputable sources. I chose an SD of 16 SB / hour based on one of
Abdul's posts suggesting 7.5 to 8 BB /hr was the SD for a "tight pro"
(his words). I chose an EV of +2 SB / hr. So I had my EV and SD for
a tight winning pro.
I wanted to compare this with a more aggressive pro, who plays more
hands, perhaps because he's a super reader or can outplay people on
later streets. The more aggressive pro will have the same EV, but an
SD of 30, which may be a little high, but I'm not shooting for exact
figures - only trends.
For bankroll requirements, all sim players will start with a 100 SB
bankroll (e.g. $300 for 3/6) and every time they run it up to 200 SB
or more, they'll take 100 SB out of play. I picked these numbers on
feel. I doubt many online players buy in for the oft-quoted 300 BB
bankroll recommended to outlive most fluctuations. That would be
$1800 at $3/$6.
Let's call our two players TightProbot (SD=16) and AggressiveProbot
(SD=30), respectively. Now let's clone them 100,000 times and send
each one out on its mission: Take 100 SB and double it up as many
times as you can. Take 100 SB off the table every time you reach or
exceed 200 SB. Keep playing until you bust out. Money taken off the
table never comes back into play.
Here's what happened:
Player: TightProbot AggressiveProbot
Set EV: +2 +2
SD: 16 30
=============================================
Hours Played 24.6M 3.8M
Tot Cashouts 591,265 174,114
Cash Before Bust 83,248 58,700
Cash Before Bust % 83.2% 58.7% [1]
Avg Hrs to Bust 246.4 38.2
Max Cashouts 72 33
Sim EV +1.99 +1.94
Hours Played: The sum of hours played by all 100,000 "bots" before
busting. M denotes "million."
Tot Cashouts: Total number of 100 unit cashouts achieved by all
100,000 bots.
Cash Before Bust: Total number of bots that achieved at least 1
cashout before busting.
Cash Before Bust %: Percentage of bots who achieved at least 1
cashout before busting.
Avg Hrs To Bust: Average run, in hours, before busting. I'd like to
capture the median too, but I didn't get to that yet.
Hours per Cashout: Number of hours played for each cashout generated.
Max Cashouts: The most cashouts by any one "bot" before busting.
Sim EV: The calculated EV, in SB/hr, at the end of the sim (net units
/ total hours played).
The exact numbers, being SIMed, may be of limited value, but I think
the trends are probably useful. And what do the trends tell us?
Notice that the TightProbots cashed out 591,000 times compared to
AggressiveProbot's 174,000 times. Yet their EV was almost identical.
How can this be? The answer lies in play time. AggressiveProbot
lives life in the fast lane. Although his EV is the same as
TightProbot's, his variance (i.e. "luck") comes in stronger doses. He
can double up a lot faster, and he can burn off a buy-in far faster as
well. Notice he busts once every 38 hours, compared to once every 246
hours for TightProbot. AggressiveProbot "eats variance for lunch," as
someone once wrote.
Another observation is that even tight, winning players who start with
100 SB will bust before doubling up more than 1 time in 6. And loose,
winning players can burn off better than two out of every five 100 SB
buyins without doubling.
So, for winning players, it is probably more apparent that the tight
ones are winners. The looser players experience more extreme bankroll
swings, and bust out far more often. Even though loose players may
ultimately have the same EV as tight players, it may be far harder to
observe through all the fluctuation.
Finally, for winning players, the chances of making a long run of
cashouts increase as you go from loose to tight, because you're less
exposed to luck and more likely to show your true, winning nature.
Let's see how the losing players did now.
Note: I suspect many online players have an SD higher than Loosebot.
I might have to do another pass with a Maniacbot.
Results - Losers Summary Chart, 100,000 Trials each, initial bankroll
= 100 SB, cashout point = 200 SB, cashout amount = 100 SB:
Player: Broomcorn WeakTight Earnest Loose
Set EV: -1 -1 -1 -1
SD: 5 16 23 30
===========================================================
Hours Played 10.1M 5.9M 3.7M 2.5M
Tot Cashouts 32 41,956 64,093 76,043
Cash Before Bust 32 28,458 36,534 39,546
Cash Before Bust % 0.032% 28.5% 36.5% 39.6%
Avg Hrs To Bust 100.8 59.2 36.6 24.8
Max Cashouts 1 9 13 17
Sim EV -0.99 -0.98 -0.98 -0.97
First of all, the tighter you are the more obvious it will be that you
are a loser -- just as tight winners are more obvious.
BroomcornsUnclebot, for example, will cashout less than 1 time in
every 3000 buyins. But as you get looser the fluctuations become more
and more wild, and in the short run it become harder and harder to
tell if you're a winner or loser. Loosebot, for example, will manage
to double up a buy in just about 40% percent of the time.
Notice that all the losing bots have the same EV. But Loosebot, for
example, enjoys many more total cashouts and "higher" multiple cashout
runs than WeakTightbot, and tremendously more than BroomcornsUnclebot.
How can this be if they have the same EV? Where is the downside? The
answer is that Loosebot will experience more extreme swings in
fluctuation (i.e., "luck.") But all those positive "peaks" in luck
that result in cashouts will be balanced by "valleys" which represent
awful runs where the loose player busts out rapidly.
As losers move from tighter to looser, all else being equal, their
"cash before bust" rate rises (this is the opposite of winning
players), and they enjoy higher multiple-cashout runs, but their
average bankroll life expectancy plummets to balance it out.
The trends suggest that for real players who play on relatively low
bankrolls, and who take cash off the table as it grows, busting will
be an absolutely common event -- for long term winners and losers
alike. And OF COURSE busting will occur more often after a cashout,
for winners and losers alike, because by taking money off the table
you have increased your exposure to ruin by fluctuation. That bears
repeating:
You OBVIOUSLY increase your probability of busting out after you've
taken a cashout, because you have increased your exposure to ruin by
short term fluctuation. It's expected to work that way.
Because high variation is so effective at camouflaging a small loss
rate, many players mistakenly (or wishfully) think they are playing a
winning game when they are not. When forced into the undeniable
accounting that playing online imposes, some players grasp for
possible causes other than poor play. They remember reading posts
claiming online poker is rigged because of the "cashout then bustout"
effect. They are quite likely to have had a similar experience. Now
a superstition is born.
Conclusion:
===========
If you think that you win pretty often, you're probably right. If
you think you experience brutally bad runs pretty often, you're
probably right. If you think you bust out rapidly more often after a
cashout, you're almost certainly right. Does this mean online poker
is rigged? It could be, but there is a far more simple way to explain
these patterns: You are experiencing *exactly what is predicted* for
players who maintain a limited bankroll and take winnings off the
table -- even if they are winning players. It's normal fluctuation.
Loose players in particular will frequently run extremely well for a
period of time, then suddenly run extremely poorly for a period of
time -- even if they are playing winning poker. If they don't
understand fluctuation, it probably will feel exactly as though "a
switch has been flipped."
Addendum:
=========
Even if you don't buy in short, fluctuation can still cloud the water.
Check out the results for Loosebot with a buy-in of the often
recommended "outlive variance" size: 600 SB. I set the cashout point
at double the starting point, 1200 SB. By our 3/6 standards, this
means buying in at $1,800 and not cashing out any money until you run
it up to $3,600. I suspected very few Loosebots would achieve a
cashout. I was wrong:
Player: Loosebot
Set EV: -1
SD: 30
===========================
Hours Played 44.9M
Tot Cashouts 24,966
Cash Before Bust 19,601
Cash Before Bust % 19.6%
Avg Hrs To Bust 449.1
Hours per Cashout 1,800
Max Cashouts 6
Sim EV -1.00
Under Loosebot conditions, 1 in every 5 starting bankrolls would get
doubled up! That is a run of +$1,800 at 3/6. A player experiencing
these results would be very likely to believe he was playing a winning
game, even though he's not. And after he cashes out, he faces an 80%
probability of going bust before doubling up again. Easy prey for
superstition.
Last observation: Always book your "last longer" bets against players
who are looser than you.
Take care,
Bob D.
[1] For comparison:
SD/EV 16/+2 30/+2
Cash Before Bust % 83.2% 58.7%
Bust before cash 16.8% 41.3%
The ChenWeideman formula predicts bustout rates of 21% and 64%
respectively. It is hard to make a direct comparison, because in my
sim money comes off the table. 100% eventually bust. Also, my
bustout numbers represent bustouts before doubling - surely some of my
bots would bust after doubling. But overall I get the gut feeling
that ChenWeideman is compatible with my results.
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