Results of flop analysis over Paradise Poker hands
Tony H
I've just completed a starting cards, flop, and board analysis over 37,867
hands I've played at low limits on Paradise Poker. There may be errors in
the calculations here, but I've tried to make it as accurate as possible. If
someone could check the "expected" numbers I've posted, that would be great.
This took a lot of work to finish, and it's been something I've been working
on over the past 1-2 weeks! Hope this is helpful. Here are the results
(warning, lengthy post):
STARTING CARD ANALYSIS:
Total hands you were dealt cards: 37867
All suited starters dealt: 8982 (23.72%)
All suited starters expected: 8910 (23.5%)
All connected starters dealt: 5980 (15.79%)
All connected starters expected: 5940 (15.7%)
Suited connector starters dealt: 1486 (3.92%)
Suited connector starters expected: 1485 (3.92%)
Paired starters dealt: 2264 (5.979%)
Paired starters expected: 2227 (5.88%)
AKo dealt: 363 (0.959%)
AKo expected: 343 (0.905%)
AKs dealt: 98 (0.259%)
AKo expected: 114 (0.302%)
Any AK dealt: 461 (1.217%)
Any AK expected:457 (1.21%)
A's dealt: 157 (0.415%)
K's dealt: 140 (0.370%)
Q's dealt: 184 (0.486%)
J's dealt: 168 (0.444%)
T's dealt: 183 (0.483%)
9's dealt: 167 (0.441%)
8's dealt: 185 (0.489%)
7's dealt: 182 (0.481%)
6's dealt: 192 (0.507%)
5's dealt: 178 (0.470%)
4's dealt: 186 (0.491%)
3's dealt: 162 (0.428%)
2's dealt: 180 (0.475%)
Each pair expected: 171 (0.452%)
FLOP ANALYSIS:
(Note that only data for hands where a flop was dealt are used.
Hands where no flop was dealt are skipped.)
Total hands you were dealt cards: 37867
Times a flop dealt when you were dealt cards: 35691 (94.25%)
When user dealt AK, flops at least one A or K: 154 (34.45%)
expected: 145 (32.4%)
USER HAS ANY TWO SUITED CARDS (dealt 8546 times):
Using both user's hole cards, flopped a:
3 flush:3593 (42.04%) expected: 3554 (41.6%)
4 flush:922 (10.79%) expected: 935 (10.9%)
5 flush:70 (0.82%) expected: 72 (0.842%)
Three cards on the flop make up a:
3 straight:293 (3.43%) expected: 272 (3.18%)
2 flush:4698 (54.97%) expected: 4710 (55.1%)
3 flush:463 (5.42%) expected: 446 (05.22%)
any pair:1470 (17.20%) expected: 1447 (16.9%)
Hand user flops:
High card:4453 (52.1%) expected: 4497 (52.6%)
Pair: 3503 (41.0%) expected: 3453 (40.4%)
Two pair:373 (4.36%) expected: 345 (4.04%)
3 of a kind:107 (1.25%) expected: 134 (1.57%)
Straight:32 (0.37%) expected: 35 (0.412%)
Flush: 70 (0.82%) expected: 71 (0.835%)
Full house:7 (0.082%) expected: 8 (0.0918%)
Four of a kind: 1 (0.012%)expected: 1 (0.0102%)
Straight flush: 0 (0.000%)expected: 1 (0.00589%)
Royal flush:0 (0.000%) expected: 0 (0.000654%)
USER HAS ANY PAIR (dealt 2196 times):
Using both user's hole cards, flopped a:
Underpair (to flop): 523 (23.82%) expected: 515 (23.5%)
Overpair (to flop): 496 (22.59%) expected: 515 (23.5%)
Set:238 (10.84%)
expected: 253 (11.51%)
Quads: 5 (0.228%)expected: 5 (0.245%)
Three cards on the flop make up a:
3 straight:81 (3.69%) expected: 70 (3.18%)
2 flush:1198 (54.55%) expected: 1209 (55.0%)
3 flush:120 (5.46%) expected: 113 (5.16%)
any pair:376 (17.12%) expected: 376 (17.1%)
Hand user flops:
High card:0 (0.0%) expected: 0 (0.00%)
Pair: 1584 (72.1%) expected: 1578 (71.8%)
Two pair:363 (16.53%) expected: 355 (16.2%)
3 of a kind:230 (10.47%)expected: 237 (10.8%)
Straight:0 (0.00%) expected: 0 (0.00%)
Flush: 0 (0.00%) expected: 0 (0.00%)
Full house:14 (0.638%) expected: 22 (0.980%)
Four of a kind: 5 (0.228%)expected: 5 (0.245%)
Straight flush: 0 (0.000%)expected: 0 (0.00%)
Royal flush:0 (0.000%) expected: 0 (0.00%)
USER HAS OFFSUIT CONNECTORS FROM 54o to JTo (dealt 2264 times):
Using both user's hole cards, flopped a:
Open ended:219 (9.67%) expected: 194 (8.55%)
Double belly:16 (0.71%) expected: 12 (0.531%)
Straight:38 (1.68%) expected: 29 (1.26%)
Three cards on the flop make up a:
3 straight:77 (3.40%) expected: 71 (3.15%)
2 flush:1224 (54.06%) expected: 1246 (55.0%)
3 flush:132 (5.83%) expected: 117 (5.16%)
any pair:423 (18.68%) expected: 383 (16.9%)
Hand user flops:
High card:1143 (50.5%) expected: 1192 (52.6%)
Pair: 933 (41.2%) expected: 915 (40.4%)
Two pair:106 (4.68%) expected: 91 (4.04%)
3 of a kind:38 (1.68%) expected: 36 (1.57%)
Straight:39 (1.72%) expected: 28 (1.23%)
Flush: 0 (0.00%) expected: 0 (0.00%)
Full house:5 (0.221%) expected: 2 (0.0918%)
Four of a kind: 0 (0.000%)expected: 0 (0.0102%)
Straight flush: 0 (0.000%)expected: 0 (0.00%)
Royal flush:0 (0.000%) expected: 0 (0.00%)
ALL FLOPS SEEN BY THE USER:
Three cards on the flop make up a:
3 straight:1145 (3.21%) expected: 1137 (3.19%)
2 flush:19715 (55.24%) expected: 19651 (55.1%)
3 flush:1881 (5.27%) expected: 1848 (5.18%)
any pair:6182 (17.32%) expected: 6046 (16.9%)
Hand user flops:
High card:17810 (49.9%) expected: 17888 (50.1%)
Pair: 15068 (42.2%) expected: 15082 (42.3%)
Two pair:1786 (5.00%) expected: 1697 (4.75%)
3 of a kind:750 (2.10%) expected: 754 (2.11%)
Straight:146 (0.41%) expected: 140 (0.392%)
Flush: 70 (0.20%) expected: 70 (0.197%)
Full house:54 (0.151%) expected: 51 (0.144%)
Four of a kind: 7 (0.020%)expected: 9 (0.0240%)
Straight flush: 0 (0.000%)expected: 0 (0.00139%)
Royal flush:0 (0.000%) expected: 0 (0.000154%)
FIVE CARD BOARD ANALYSIS:
(Note that only data for hands where a river was dealt are used.
Hands where no river was dealt are skipped. This will bias the
data to include only times where a showdown was seen.)
Total hands you were dealt cards: 37867
Total final boards seen when you were dealt cards: 26216
USER HAS ANY TWO SUITED CARDS (dealt 6293 times):
Four flushes flopped: 729 (11.58%)
expected: 689 (10.9%)
When flop four flush, got flush:251 (34.43%)
expected: 255 (35.0%)
Hand user has at river:
High card:1145 (18.2%) expected: 1097 (17.4%)
Pair: 2673 (42.5%) expected: 2683 (42.6%)
Two pair:1350 (21.45%) expected: 1391 (22.1%)
3 of a kind:251 (3.99%) expected: 273 (4.33%)
Straight:318 (5.05%) expected: 287 (4.56%)
Flush: 411 (6.53%) expected: 410 (6.51%)
Full house:131 (2.082%) expected: 140 (2.22%)
Four of a kind: 10 (0.159%)expected: 8 (0.126%)
Straight flush: 4 (0.064%)expected: 4 (0.0663%)
Royal flush:0 (0.000%) expected: 0 (0.00781%)
USER HAS ANY PAIR (dealt 1685 times):
A set flopped: 197 (11.69%)
expected: 190 (11.3%)
When flop set, got boat or quads:75 (38.07%)
expected: 66 (33.4%)
Hand user rivers:
High card: 0 (0.0%) expected: 0 (0.00%)
Pair: 609 (36.1%) expected: 598 (35.5%)
Two pair:654 (38.81%) expected: 666 (39.5%)
3 of a kind:201 (11.93%)expected: 198 (11.7%)
Straight:33 (1.96%) expected: 32 (1.90%)
Flush: 44 (2.61%) expected: 33 (1.95%)
Full house:130 (7.715%) expected: 144 (8.54%)
Four of a kind: 14 (0.831%)expected: 14 (0.842%)
Straight flush: 0 (0.000%)expected: 0 (0.0160%)
Royal flush:0 (0.000%) expected: 0 (0.00182%)
USER HAS OFFSUIT CONNECTORS FROM 54o to JTo (dealt 1678 times):
Flopped open ended: 167 (9.95%)
expected: 144 (8.55%)
When open ended, got straight: 47 (28.14%)
expected: 51 (30.7%)
Hand user rivers:
High card:281 (16.7%) expected: 289 (17.2%)
Pair: 749 (44.6%) expected: 717 (42.7%)
Two pair:361 (21.51%) expected: 374 (22.3%)
3 of a kind:65 (3.87%) expected: 73 (4.35%)
Straight:153 (9.12%) expected: 153 (9.12%)
Flush: 31 (1.85%) expected: 33 (1.95%)
Full house:33 (1.967%) expected: 37 (2.22%)
Four of a kind: 5 (0.298%)expected: 2 (0.126%)
Straight flush: 0 (0.000%)expected: 0 (0.0209%)
Royal flush:0 (0.000%) expected: 0 (0.00110%)
ALL RIVERS SEEN BY THE USER:
Hand user rivers:
High card:4686 (17.9%) expected: 4565 (17.4%)
Pair: 11522 (44.0%) expected: 11489 (43.8%)
Two pair:6039 (23.04%) expected: 6160 (23.5%)
3 of a kind:1198 (4.57%)expected: 1266 (4.83%)
Straight:1237 (4.72%) expected: 1211 (4.62%)
Flush: 806 (3.07%) expected: 793 (3.03%)
Full house:675 (2.575%) expected: 681 (2.60%)
Four of a kind: 48 (0.183%)expected: 44 (0.168%)
Straight flush: 4 (0.015%)expected: 7 (0.0279%)
Royal flush:1 (0.004%) expected: 1 (0.00323%)
- Tony
RMITCHCOLL
> Hi all,
>
> I've just completed a starting cards, flop, and board analysis over 37,867
>hands I've played at low limits on Paradise Poker. There may be errors in
>the calculations here, but I've tried to make it as accurate as possible. If
>someone could check the "expected" numbers I've posted, that would be great.
>This took a lot of work to finish, and it's been something I've been working
>on over the past 1-2 weeks! Hope this is helpful. Here are the results
>(warning, lengthy post):
>
snip rest of post
The expected results and the actual results seem to be very close. But is that
a good thing? This is a serious question.... Isnt the number of tests (37867)
really too small for the numbers to be so close? I havent messed with
probablities since college, but my gut tells me the number of hands should be
much higher before the actual approached the expected.
Thanks for all the efforts.
Randy Collack
p.s. any chance of an analysis program that works with Pokerstars?
Bad Bob the Albino
about Paradise cards being manipulated by the software is just that... bullshit. Not that I doubted
it anyway. It will sure be interesting how this comes out when you get to 100,000 hands. (I can hear
you groaning.)
Looks also like a hell of a lot of hard work Tony. I appreciate your effort on everyone else's
behalf. Take a bow.
On Wed, 23 Jan 2002 18:09:34 GMT, "Tony H" <to...@thsoftware.com> wrote:
> Hi all,
>
> I've just completed a starting cards, flop, and board analysis over 37,867
>hands I've played at low limits on Paradise Poker. There may be errors in
>the calculations here, but I've tried to make it as accurate as possible. If
>someone could check the "expected" numbers I've posted, that would be great.
>This took a lot of work to finish, and it's been something I've been working
>on over the past 1-2 weeks! Hope this is helpful. Here are the results
>(warning, lengthy post):
>
"Big, big snip"
Bad Bob the Albino
[Cook him till he's blue and smother him in onions!]
Steve Badger
Will the conspiratorialists spend one second to think about any of this?
"Tony H" <to...@thsoftware.com> wrote ...
Steve Badger
> Finally, some real proof. These figures seem to me to make it very evident
that all the rhetoric
> about Paradise cards being manipulated by the software is just that...
bullshit. Not that I doubted
> it anyway. It will sure be interesting how this comes out when you get to
100,000 hands. (I can hear
> you groaning.)
>
> Looks also like a hell of a lot of hard work Tony. I appreciate your
effort on everyone else's
> behalf. Take a bow.
It's not "proof" really, but it is data. Do you think one of the
conspiracyites could post similar data? Of course not, mostly because they
don't make the effort to learn about their situations. We've see the
conspiracyites waving their arms for a couple years, but they never post
anything from even 1000 hands, let alone 37,000.
People can either live in the dark and conjure up imaginary monsters, or get
Tony's program (www.pokerstat.com) or manually do the work from hand
histories. In any case, the last two groups will win money from the first
group while the first group just waves their arms.
--
Steve Badger
http://www.playwinningpoker.com
danny
>Finally, some real proof. These figures seem to me to make it very
evident >that all the rhetoric about Paradise cards being manipulated
by the software >is just that... bullshit. Not that I doubted it
anyway. It will sure be >interesting how this comes out when you get
to 100,000 hands. (I can hear
>you groaning.)
If you did the same analysis of cards at a B&M game where cheating was
KNOWN to occur (marked cards, electronic means, etc), you'd also get a
random analysis of the cards.
The complaints I've read about cite very unlikely multiple bad beats -
which the analysis doesn't include, i.e. you may have had the correct
% of full houses, but a higher % than expected were beat (in the most
bizarre ways). Also 10 scripted bad beat hands (out of 37,000), while
statistically insignificant, could wipe out your backroll in a few
hours.
Aug
> Hi all,
>
> I've just completed a starting cards, flop, and board analysis over 37,867
> hands I've played at low limits on Paradise Poker. There may be errors in
> the calculations here, but I've tried to make it as accurate as possible. If
> someone could check the "expected" numbers I've posted, that would be great.
> This took a lot of work to finish, and it's been something I've been working
> on over the past 1-2 weeks! Hope this is helpful. Here are the results
> (warning, lengthy post):
>
>
Great work!!!! Now all the losers will just have accept the fact that
they've been outplayed.
Tony, tell us a bit about the tools you used. Would you be willing to
share them?
MGuzz55625
>
>Post of the decade.
>
>Will the conspiratorialists spend one second to think about any of this?
No, of course not. They're too busy making websites about "Badge Man" on the
Grassy Knoll and The Moon Landing being fake. I was in the process of
gathering this kind of data about another website, but mine post wouldn't of
been nowhere near as good as this one. Great post Tony.
Nick
Bad Bob the Albino
wrote:
I didn't mean proof in the sense of scientific or legal proof. I should have used the word evidence
instead I suppose. My point being that, as we have all suspected, there will be no great variance
between the actual numbers and the expected. Although 37,000 hand histories are not a nearly enough
of a sample, it is still 37,000 more examples than anyone from the other side of the argument has
provided. I don't play on Paradise anymore, not because I think there is anything funky about the
site. Just because I can't win there. I don't play at the local Eagles lodge anymore for the same
reason. Most of the time the question "Why?" does not need to be asked or answered....just dealt
with!
MGuzz55625
You're right. This analysis doesn't prove people are not colluding or hacking
etc, but I've heard alot people claim that Poker Paradise and other websites
don't have a true randomize deck. This kind of analysis shows a real good
indiction that they do.
"That's just my opinion, I could be wrong." -- DM
Nick
Asha34
recalculate all of this and get back to me on it.
Thanks.
Ashley
Just kidding. Seems about right all around. Thanks for your hard work.
Mike Benveniste
> The expected results and the actual results seem to be very close. But is that
> a good thing? This is a serious question.... Isnt the number of tests (37867)
> really too small for the numbers to be so close? I havent messed with
> probablities since college, but my gut tells me the number of hands should be
> much higher before the actual approached the expected.
I ran a Chi-Squared test on the pair and suited starting hand distribution
and came up with a tail of 33.6%. In other words, there is just about a
two-thirds chance that this distribution was due to some bias in Paradise's
algorithm. To establish statistical significance one way or another, you'd
need considerably more samples.
> Thanks for all the efforts.
Indeed.
--
Michael Benveniste -- m...@clearether.com
Any comments or statements made are not necessarily those of any
employer or client, their subsidiaries, or affiliates.
Harry 026
(RMITCHCOLL) writes:
> The expected results and the actual results seem to be very close
> But is that a good thing? This is a serious question.... Isnt the number
> of tests (37867) really too small for the numbers to be so close? I
> havent messed with probablities since college, but my gut tells me
> the number of hands should be much higher before the actual
> approached the expected.
I didn't check them all, but the few (towards the beginning) that I
checked all fell within one standard deviation of the expected. I
then looked for an observed value that seemed to miss the expected
by quite a bit, and the KK case seemed to qualify. The low number
of observed KK (140) missed the expected number (171) by 2.4
standard deviations. In the pairs group, having (only) one out of
13 pairs fall outside the 2-sigma range seems reasonable.
Harry
tells
> You're right. This analysis doesn't prove people are not colluding or hacking
> etc, but I've heard alot people claim that Poker Paradise and other websites
> don't have a true randomize deck. This kind of analysis shows a real good
> indiction that they do.
Yes and no. I know that many of the pokersites barely manage to keep
their software running, but with the right people doing the coding and
designing it is possible to maximize their profit without it showing in
such a relativly basic "test".
On way to do it would be to have a few accounts of their own that are
playing a basic break even game most of the time, but that every now and
then will get the upper hand in a bad beat-like situation. Then their
extra "luck" would be hidden with the help of some other player getting
"bad luck"; or their own accounts getting "bad luck" when there's less
money involved.
We're not talking anything that would show up easily when looking at
expected data, but by picking the right time to do it (ignoring the
profit from the extra rake), as well as the right game/limit, it could
mean a lot of money.
Let's play with some numbers...
The online site Really Greedy Poker always have 3-5 of these extra
accounts in action (more if more tables open up), and they are playing
at higher limits and/or pot limit tables.
The average pot in these fixed hands is 340 USD (easily reached when
more than one great hand, esp. in PL), where 70 USD is by their own
account.
These fixed hands happens only two times per account per day.
Ignoring the extra rake Really Greedy Poker will then make an extra:
270 * 4 * 2 * 30 * 12 = 777'600 USD each year.
(Make it a successfull site with lots of tables going, so that they can
have an average of 10 of these accounts going, and it's close to two
million USD per year.)
Now let's say that they have a bad beat-jackpot, and that 30% of the
time their own accounts will win, and that the ones working for the site
are acting as shills 3 hours a day...
Nah, I don't think that there's any real non-beatable cheating going on
at the owners end of these casinos, I just wanted to give the paranoid
people something to worry about. ;-)
/t
Bennett Niizawa
wrote:
> Hi all,
>
<snip of excellent card distribution analysis>
Great work, Tony. Of course, for the people who feel Paradise's deal
is legit, it's evidence of what we're reasonably sure is the truth.
It is with great eagerness that I click over to the IG forum on 2+2
and see how much of a subversive and organized crime supporter you're
being labelled right now...
:-D
Patti Beadles
>conspiracyites could post similar data? Of course not,
On FIBS, the backgammon server that I maintain, you can type "dicetest"
and get a statistical analysis of every single roll that has occurred
since the last server restart, which often means several million rolls
are being analyzed.
It hasn't stopped the complaints.
-Patti
--
Patti Beadles | Not just your average
pat...@gammon.com | degenerate gambling adrenaline
http://www.gammon.com/ | junkie software geek leatherbyke
or just yell, "Hey, Patti!" | nethead biker.
Tony H
news:e97d05e6.02012...@posting.google.com...
Well, the losers will still complain, but at least now, there's some actual
statistical "evidence" of the deal being truely random. Though I'll admit,
38,000 hands isn't enough! Maybe someone with 100,000+ hands in their
PokerStat database will run these calculations and post their results here.
About the tools I used, I used http://www.pokerstat.com, which is a tool I
wrote and sell online. So, my motivation for creating this is biased, in
that it is like "free advertising", but it's not really free, since I spent
a little more than one week writing the code that does all this!
Anyone who has hand histories can run them through the "Tools->Card
Analysis" database query feature of PokerStat to get these statistics.
Hopefully the "losing" conspiracy players will do this, gain more trust in
online poker in general, and keep losing to winning players. ;) So, I feel
that this analysis is good for online poker in general (helps keep fish in
the game). In general, I find that conspiracy theorists are losing players,
while winning players usually keep silent. I wish the winning players
stopped playing instead of the other way around!
- Tony
Tony H
are losing ammo. ;)
- Tony
"Bennett Niizawa" <beando...@yahoo.com> wrote in message
news:3c4fabdc...@news.cis.dfn.de...
Tony H
mind no matter what evidence is produced. Stupid people. ;)
- Tony
"Patti Beadles" <pat...@rahul.net> wrote in message
news:a2ofa6$a4t$1...@samba.rahul.net...
Aug
> Post of the decade.
>
> Will the conspiratorialists spend one second to think about any of this?
>
The first rule of conspiracism:
"When presented with contrary information, cite it as proof of a
cover-up and a larger plot." Gotta keep those black helicoptors in
the air.
Bad Bob the Albino
Somehow Tony I got the feelin' if Paradise posted 10,000,000 hand histories and the stats came out
the same as yours it wouldn't matter to some people. Probably better to spend your time workin' on
your game. Not that many of us don't appreciate your efforts....but don't cast pearls among the
swine.