For each all-in, I collected the player's equity in the pot at the time of
the all-in and the proportion of the pot the player won (1.0 for a win, 0.0
for a loss, 0.5 for a two-way split, etc.) The pot equity of a hand is the
average proportion of the pot that a player would win over the long run.
For example, in the following sample Hold 'Em Showdown output,
990 pots with board cards: Tc 9d 7s
% chance of outright win 74.040404 24.343434
% chance of win or split 75.656566 25.959596
expected return, % of pot 74.848485 25.151515
fair pot odds:1 0.336032 2.975904
pots won: 741.00 249.00
--the "expected return, % of pot" result shows the pot equity of each hand.
The chi square statistic does not indicate significant variance of actual
from expected (3392.7 on 3421 hands). A plot of rolling 30-"bin" averages
of sorted equity vs. pots won looks linear; the linear regression is
y = 0.9908x + 0.0045
which is not significantly different from the theoretical y = 1.0x + 0 that
describes the "no dealing bias" case.
Looking at the "big" favorites/underdogs, and expressing the favorite's
chances as odds against the underdog:
Odds at least # of hands Avg equity Avg pot won
2:1 1121 0.8123 0.8134
3:1 753 0.8617 0.8597
4:1 623 0.8806 0.8777
9:1 260 0.9383 0.9321
In sum, I see no evidence that "bad beats" are more frequent than expected.
(I am grateful to Paul Pudaite for analytical guidance, but any errors are
For mail, please use my surname where indicated:
st...@surname.reno.nv.us (Steve Brecher)
<snip some details of a much needed study>
> In sum, I see no evidence that "bad beats" are more frequent than expected.
> (I am grateful to Paul Pudaite for analytical guidance, but any errors are
> my own.)
A couple of questions:
What do you mean by: "Using emailed hand histories"?
Did the hand histories come from multiple sources and if so how were
they chosen and controlled?
Do you, Paul Pudaite, or anyone involved in this study work in the
poker industry or financially related fields.
Did PokerStars provide any assistance with your study.
You are a well known and I believe respected RGP poster. I am sure
you are also well known personally by many on RGP. I am not trying to
undermine your work but I think it is important to know where it is
coming from. This is not just your theory or strictly an opinion. It
is a presentation of data and conclusions and as such could assume the
status of fact.
This is great stuff if not tainted either by sample size, statistical
problems, or other bias. The crux of the question surrounding online
poker site dealing/randomness integrity revolves around lack of
accountability. When any audit is done factors in addition to the
results assume equal importance. Integrity is important when
I would simplly like to see the bar set higher for acceptance of
results in terms of non-statistical bias. Lord knows if you posted
something that appeared statistically biased you would hear about it
here on RGP. Let's make the accountability requirements equally high.
That is, at least as much as can be done in the anonymous world of
newsgroup personalities and unregulated offshore online poker sites.
>I am also curious about the buy in amounts of these tournament hand
histories. >Do higher buy in's make a difference in any way? Do $100
tourney's have less>"suck out" potential than freerolls? And what
portions did your hand histories>represent?
Don't forget sunspots and tides.
A good conspiracy theory cannot be killed.
I am not doubting Steve's work, and I think it is good that he did it.. I am
not a math whiz nor am I a conpiracy subscriber... but common sense tells me
that less skilled players may be in the freerolls more than in the higher buy
in tourney's and therefore, more likely to move in chips with KQ get called by
JT and 77 and have AA also call and go down in flames. Doesn't skill play some
part in the outcome - i.e. less likely for the opportunity of certain suck
>garyc...@alumni.northwestern.edu (Gary Carson)
Is this a 'planet X' reference, Gary?
Posted using RecPoker.com - http://www.recpoker.com
>I am not doubting Steve's work, and I think it is good that he did
it.. I am
>not a math whiz nor am I a conpiracy subscriber... but common sense
>that less skilled players may be in the freerolls more than in the
>in tourney's and therefore, more likely to move in chips with KQ get
>JT and 77 and have AA also call and go down in flames. Doesn't skill
>part in the outcome - i.e. less likely for the opportunity of certain
I see, my sarcasm was misplaced, sorry about that.
You don't fully understand what he did.
You're probably right that games with more people willing to go allin
when far behind will have more longshot draws hit. That's just
because they'll have more longshot draws.
There's no real way to test whether more draws are attempted than
expected because the number of draws expected depends on playing
What he looked at was the number of draws made given a certain number
of attempts. We can compute that expected number. We can't predict
how many times people draw to gutshots, but we can predict how often
those attempts will get there. That's what he looked at -- the
frequency of hits relative to the frequency of attempts.
Yoiu might expect the frequency of gutshots made to be higher in
smaller events, but not the relative frequency.
No, they came from a signle source -- myself. The hand histories are
those of all the PokerStars tournaments in which I have played.
> Do you, Paul Pudaite, or anyone involved in this study work in the
> poker industry or financially related fields.
> Did PokerStars provide any assistance with your study.
They were all hold 'em tournaments (I forgot to mention that in my original
post). Almost all were no-limit or pot-limit; a couple were limit. The
majority were $50+5; some were $200+15 and a few were other buy-in amounts.
None were freerolls.
I don't have any breakdowns of the results by type of tournament.
> And what portions did your hand histories represent?
(If this means what portion of each tournament--) The portion from the
start of the tournament until I busted out or won, for all-in hands at
tables at which I was playing.
Perhaps -- I don't know -- there may be more all-ins and hence a higher
absolute number of suck outs in some kinds of events as opposed to other
kinds. What I was studying, however, was, given that two or more players
were all in, how well hands held up vis-a-vis how well they should hold up
if the cards dealt to the board were randomly selected from the set of
> ... The hand histories are
> those of all the PokerStars tournaments in which I have played.
Correction: I started collecting hand histories after I played some
tournaments. So the hand histories used in the study were those of all the
PokerStars tournaments in which I have played since I started collecting
>I see, my sarcasm was misplaced, sorry about that.
sarcasm only works on me when the subject matter isn't already over my head..
though, I figured it for (most likely) that - I took the opportunity to clarify
the reason for my question.
As for the rest of your post, it will take me awhile to digest, expect an
answer in 2004 :-)
Side question : in NL holdem preflop all-ins, for the different hands,
how much ev is won/lost in comparison with folding before the all-in
bet ? Raising hands can afford to have negative ev when called since
they win when not called. Calling hands should have positive ev, but
is this true for the KQ and JT that many people take all in ?
Additional classication possibilities : (players left to act * all-in
move / pot size) , Steve Brecher / random pokerstar players