Results of flop analysis over Paradise Poker hands

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):


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

it's been done before with the same results. GREAT work and I'm sure it helps SOME people. However, the conspiracy people are pretty close minded and do not see facts.


Being a number cruncher myself I can understand the amount of work that went into this (espicially if you did it by hand).


job well done.

I'm just curious why you undertook this, it's alot of work! If you were trying to help improve your play then the expected numbers would have done just fine, unless the issue is that you doubt the integrity of paradise?

I have only been on paradise for 4 months and I don't really suspect any "foul play", but I have seen a number of posts that seem to talk about the subject. Is this a wide spread belief? And if so, in which games? I only play the lower limits so perhaps I have missed the evidence?

In any case nice job on the numbers, really an impressive undertaking whatever your reasons.

With an analyser program (he definedly uses one) it's pretty easy to get those number. The program does the work.


Regards

Numbers without methodology mean little. Please enlighten us. A little history would be nice too.

Tony,


Great job.


If you look in the archives, you'll find some posts from me and others who analysed the 25 million hands they posts to their ftp site. Pretty much showed that the hands were random too.


Mark

I think you had enough hands for a statistical sample...not a lot in comparison to the 150,000,000 - but I'd say pretty darned close to good enough


(I forgot what the preferred number is for samples - I want to say 4000 - that's how they predict presidental winners with only 1% of the vote...after a certain point, it's just a given that the numbers don't change much)


clearly 39000 hands is good enough to get an accurate poll, if with a slightly higher SD for some of the rarer occurances.


Great work...maybe this will put a couple of naysayers to bed for awhile..


Of course, expect to have your character tarnished, reputation sullied, and expect to be accused of working covertly for Paradise...but it's good work, and seeing those numbers makes me a lot more comfortable on the randomness of their cards.


RB

Well, I used an analysis program of course. No way you can analyze this many hands manually as Ikke said!


The "work" involved setting this up (programming), and figuring out the "expected" numbers. To figure out the "expected" numbers, I calculated some of them, and I simulated the others (the ones that were too hard to calculate).


The hands are in my database already, so it wasn't like I started this from scratch, part of this work was already done.


I know 38,000 hands isn't enough for some of the rarer occurances, but that's all the hands I have. This has been something that I've wanted to do recently especially after seeing all the "conspiracy" postings. Personally, I think the deal is not rigged, and saw a lot of people mention a board analysis, and realized this was something I could "easily" do!


- Tony

But the results from 24 million hands which Paradise posted to their ftp/website showed the same. See the archives. I used a pretty big Sun server to get those results, would have been hard to do by hand (LOL).


Mark

Disclaimer. I don't think Paradise is cheating. Much as I hate to give the conspiracy theorists fuel, I would like to point out, as I have before, that an internet poker site that wanted to cheat could do so with completely random card distribution, by having its house players bet with full knowledge of all cards to be dealt in a hand. Regardless of the method, any poker site that wanted to cheat would have to have some of the players, be they human or software, actually "playing for the house". If they were smart, they would do just enough of this to create a "hidden rake", making the game just a little bit harder to beat.

In fact it is the conspiracy theorists' focus on card distribution and post-cashout losing streaks that make me think they're full of crap. It just wouldn't make sense for a poker site -- even a dishonest one -- to do the things that they accuse Paradise of doing.


In fact, if there is a conspiracy anywhere, it seems more likely to be a conspiracy to smear Paradise. Perhaps there is a secret cabal of sore losers, competitors, and people with a political agenda against internet gambling conspiring to discredit a successful internet gambling business. I think the Illuminati, the Tri-lateral commission and the Elders of Zion might be involved.

I think more than a conspiracy, it's just a matter of simple jealousy.


Losing players are jealous of winning players because the ability to sit at your computer and any time of the day and make money at something that's also fun.... is something everyone would like to be able to do. To see others do it and not be able to participate (due to lack of skill/knowledge/experience/intelligence/etc) must be very frustrating. Rather than blame their shortcomings on themselves and attempt to address the problem (which often has a solution if people weren't so much in denial and actually willing to face the possibility that maybe THEY are the problem), people would rather lash out and blame anything else.


The other jealousy comes from operators of other online poker rooms who see the voluminous amounts of money being raked in by Paradise and can't think of a better strategy to attract business than to try to discredit the market leader.

He's biased. His business is based on Paradise's survival. His methodology isn't published. This is just more propaganda without all the data and the methodology. Behavioral scientists would call it a little less than voodoo statistics.

It would be SO MUCH easier to cheat by having house players, than it would be to modify the flops to benefit losing players, and players who just bought in, and hurt players who cash out, and YET, keep the flop random.


Of course, you'd need those house players to play just a little bit better than they would if they didn't know what the cards were in order to go undetected. If they raised with 82o when the flop comes 228 from early position, that'll be a little suspicious. /images/smile.gif Though some maniacal players DO play like that normally!


- Tony

What is your real name?


I post using my real name. Why do the conspiracy theorists always remain anonymous? Why do they keep switching names?


First, I pay my taxes. I do not cheat the IRS. Second, I'm a patriot, I am not a traitor. How did you get those two accusations from my post? Oh, my mistake, you're just a net kook making random accusations, which is all you can do. /images/smile.gif About being biased, how is presenting facts being biased? I admit my motivation is biased, but how does that change the facts?


Where is your evidence the flop and card distribution isn't random? What analysis have you done?


About "methodology", I am not about to give out my hand histories, and even if I did, you'd accuse me of "modifying" the hands to be statistically random. Look in my response to Doug Duke's intelligent post for more about the way I analyzed the hands.


- Tony

Of course you won't expose your voodoo to scientific investigation. It's all bunk. You are just a Paradise shill.

So how long have you played at Paradise? What portion of your play is in the sample? Recent or old? What limits are here? Are all these hands consecutive? What dates are involved? Get specific, it adds a lot to the value of your work.


Lastly, Do you beat the games and if so for how much?

I will expose the method I use, but not my hand histories, since they have a record of how I played. If you want to know how I calculated these statistics (I went through records in a database, basically), email me at tony@junk-jungle.com, and I will send it to you.


- Tony

Recreational player, mostly micro-limits (.50-1 to 1-2, sometimes 3-6).


I've only started saving hand histories last year, so these are from sometime last year to now. I've missed requesting some hands here and there, but for the most part, it's consecutive and is a record of almost every hand I've played at Paradise since May of last year.


I don't want to reveal my win rate, but it's nothing to get excited about. I think that people who feel you get pairs more than you should, or that you don't get flushes as often as you should, are wrong. It's not difficult to prove this.


About whether there's actual cheating of another form going on, I can't say, but I'm pretty confident the cards being dealt will be random when a user compares hole cards to the boards they saw with those hole cards. There may be cheating going on, but it's not of the "flushes come too often" variety.


- Tony

For the most part, I agree.


If I were to list my suspicions about Paradise in order of probaqbility it would look like this:


Most likely: New players get a few helpful river cards turning poor players into break even and marginal players into winners. The number of cards needed to do this is tiny and undectable. The experiment needed to prove it is daunting indeed, requiring several new accounts and someone monitering their play.


Somewhat likely: As above, the habitual pigeons are treated to some good fortune at the expense of the other players. Similarly difficult to run the experiment.


Almost guaranteed: Independent individuals cheating collusively. Count on it. Directly proportional to the limit played.


No idea: Bots and house players. I haven't formed an opinion on this but the money involved is so big I wouldn't rule out anything. This may have been what happened in May 1999, Myself, Ed Hill, Angelina and others got bombed, no way to win. Whatever it was, Paradise realized it had gone too far. They never got me back for serious play after that.


Probable not: Cash out jinx is likely imaginary. Given the other possible handicaps, the paranoids here do, in fact, have reason to worry. It's just for the other reasons above.


Note that even if several of these enhancements were in place winning would still be possible but at some fraction of your fair share.

or keep your biased mouth shut.

That's fine. I'm not sure why you won't email me, and I don't know why you choose to remain anonymous. And I'll post what I want, as I'm sure you'll post what you want.


- Tony


P.S. Anyone notice the most extreme "conspiracy theorists" always remain anonymous and keep changing names, and always choose the wierdest names? Whatever happened to the login system?

P.S. Anyone notice the most extreme "conspiracy theorists" always remain anonymous and keep changing names, and always choose the wierdest names? Whatever happened to the login system?


The login system, such as it is, only prevents someone else from posting as you, and only if you set up a profile.