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Analysis of 100,000+ hands dealt at PokerStars


Tony H. Oct 8, 2003 11:26 AM
Posted in group: rec.gambling.poker
Hi all,

Since I've finally finished the PokerStars version of PokerStat, I had
someone send me their hand statistics. I don't have this many hand
histories, so these aren't my statistics, but the statistics are
anonymous. I also have permission to post these, so, anyways, here
they are, hopefully these, along with statistics for card
distributions from Paradise Poker and TruePoker which I've posted in
the past, will be read by some of the conspiracy theorists! Of course,
these stats doesn't mean there isn't cheating due to collusion going
on, or that there could still be situational rigging of the deal (two
strong hands against each other). It just means that people who
complain that "my four flushes don't make it" or that "Aces flop more
often than they should when I have AK" can now see that the
distribution is normal, and that players make their hands at normal
rates (expected number of pairs, 2 pairs, flushes, straights, etc).

                                                     - Tony

Starting cards:

Total hands you were dealt cards:       125852

All suited starters dealt:      29595 (23.52%)
All suited starters expected:   29612 (23.5%)

All connected starters dealt:   19493 (15.49%)
All connected starters expected:        19741 (15.7%)

Suited connector starters dealt:        4837 (3.84%)
Suited connector starters expected:     4935 (3.92%)

Paired starters dealt:  7364 (5.851%)
Paired starters expected:       7403 (5.88%)

AKo dealt:      1202 (0.955%)
AKo expected:   1139 (0.905%)

AKs dealt:      373 (0.296%)
AKs expected:   380 (0.302%)

Any AK dealt:   1575 (1.251%)
Any AK expected:        1519 (1.21%)

A's dealt:      603 (0.479%)
K's dealt:      543 (0.431%)
Q's dealt:      558 (0.443%)
J's dealt:      551 (0.438%)
T's dealt:      546 (0.434%)
9's dealt:      585 (0.465%)
8's dealt:      568 (0.451%)
7's dealt:      597 (0.474%)
6's dealt:      542 (0.431%)
5's dealt:      532 (0.423%)
4's dealt:      603 (0.479%)
3's dealt:      582 (0.462%)
2's dealt:      554 (0.440%)
Each pair expected:     569 (0.452%)

(Note that only data for hands where a flop was dealt and you
were dealt cards preflop are used. Hands where no flop was dealt
are skipped.)

Total hands you were dealt cards:       125852
Times a flop dealt when you were dealt cards:   80610 (64.05%)

When user dealt AK, flops at least one A or K: 346 (33.11%)
        expected: 339 (32.4%)

USER HAS ANY TWO SUITED CARDS (dealt 19446 times):
Using both user's hole cards, flopped a:
        3 flush:        8164 (41.98%)   expected: 8087 (41.6%)
        4 flush:        2226 (11.45%)   expected: 2128 (10.9%)
        5 flush:        147 (0.76%)     expected: 164 (0.842%)
Three cards on the flop make up a:
        3 straight:     612 (3.15%)     expected: 620 (3.18%)
        2 flush:        10728 (55.17%)  expected: 10718 (55.1%)
        3 flush:        981 (5.04%)     expected: 1015 (05.22%)
        any pair:       3303 (16.99%)   expected: 3292 (16.9%)
Hand user flops:
        High card:      10257 (52.7%)   expected: 10233 (52.6%)
        Pair:           7868 (40.5%)    expected: 7858 (40.4%)
        Two pair:               757 (3.89%)     expected: 786 (4.04%)
        3 of a kind:    302 (1.55%)     expected: 306 (1.57%)
        Straight:               97 (0.50%)      expected: 80 (0.412%)
        Flush:          147 (0.76%)     expected: 162 (0.835%)
        Full house:     15 (0.077%)     expected: 18 (0.0918%)
        Four of a kind: 3 (0.015%)      expected: 2 (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 5218 times):
Using both user's hole cards, flopped a:
        Underpair (to flop):    1224 (23.46%)   expected: 1225 (23.5%)
        Overpair (to flop):     1215 (23.28%)   expected: 1225 (23.5%)
        Set:            647 (12.40%)    expected: 601 (11.51%)
        Quads:          5 (0.096%)      expected: 13 (0.245%)
Three cards on the flop make up a:
        3 straight:     168 (3.22%)     expected: 166 (3.18%)
        2 flush:        2860 (54.81%)   expected: 2872 (55.0%)
        3 flush:        305 (5.85%)     expected: 269 (5.16%)
        any pair:       896 (17.17%)    expected: 895 (17.1%)
Hand user flops:
        High card:      0 (0.0%)                expected: 0 (0.00%)
        Pair:           3707 (71.0%)    expected: 3748 (71.8%)
        Two pair:               841 (16.12%)    expected: 843 (16.2%)
        3 of a kind:    597 (11.44%)    expected: 562 (10.8%)
        Straight:               0 (0.00%)               expected: 0
(0.00%)
        Flush:          0 (0.00%)               expected: 0 (0.00%)
        Full house:     68 (1.303%)     expected: 51 (0.980%)
        Four of a kind: 5 (0.096%)      expected: 13 (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 5026 times):
Using both user's hole cards, flopped a:
        Open ended:     414 (8.24%)     expected: 430 (8.55%)
        Double belly:   24 (0.48%)      expected: 27 (0.531%)
        Straight:               70 (1.39%)      expected: 63 (1.26%)
Three cards on the flop make up a:
        3 straight:     180 (3.58%)     expected: 158 (3.15%)
        2 flush:        2804 (55.79%)   expected: 2766 (55.0%)
        3 flush:        259 (5.15%)     expected: 260 (5.16%)
        any pair:       852 (16.95%)    expected: 851 (16.9%)
Hand user flops:
        High card:      2641 (52.5%)    expected: 2646 (52.6%)
        Pair:           2025 (40.3%)    expected: 2031 (40.4%)
        Two pair:               200 (3.98%)     expected: 203 (4.04%)
        3 of a kind:    87 (1.73%)      expected: 79 (1.57%)
        Straight:               72 (1.43%)      expected: 62 (1.23%)
        Flush:          0 (0.00%)               expected: 0 (0.00%)
        Full house:     1 (0.020%)      expected: 5 (0.0918%)
        Four of a kind: 0 (0.000%)      expected: 1 (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:     2630 (3.26%)    expected: 2568 (3.19%)
        2 flush:        44329 (54.99%)  expected: 44383 (55.1%)
        3 flush:        4176 (5.18%)    expected: 4173 (5.18%)
        any pair:       13699 (16.99%)  expected: 13656 (16.9%)
Hand user flops:
        High card:      40153 (49.8%)   expected: 40400 (50.1%)
        Pair:           34179 (42.4%)   expected: 34063 (42.3%)
        Two pair:               3863 (4.79%)    expected: 3832 (4.75%)
        3 of a kind:    1770 (2.20%)    expected: 1703 (2.11%)
        Straight:               357 (0.44%)     expected: 316 (0.392%)
        Flush:          147 (0.18%)     expected: 158 (0.197%)
        Full house:     131 (0.163%)    expected: 116 (0.144%)
        Four of a kind: 10 (0.012%)     expected: 19 (0.0240%)
        Straight flush: 0 (0.000%)      expected: 1 (0.00139%)
        Royal flush:    0 (0.000%)      expected: 0 (0.000154%)

(Note that only data for hands where a river was dealt and you
were dealt cards preflop are used. Hands where no river was dealt
are skipped.)

Total hands you were dealt cards:       125852

Total final boards seen when you were dealt cards:      44325

USER HAS ANY TWO SUITED CARDS (dealt 10628 times):
Four flushes flopped:           1262 (11.87%)
        expected:                       1163 (10.9%)
When flop four flush, got flush:        464 (36.77%)
        expected:                       441 (35.0%)
Hand user has at river:
        High card:      1871 (17.6%)    expected: 1852 (17.4%)
        Pair:           4465 (42.0%)    expected: 4532 (42.6%)
        Two pair:               2290 (21.55%)   expected: 2349 (22.1%)
        3 of a kind:    463 (4.36%)     expected: 461 (4.33%)
        Straight:               494 (4.65%)     expected: 484 (4.56%)
        Flush:          786 (7.40%)     expected: 692 (6.51%)
        Full house:     236 (2.221%)    expected: 236 (2.22%)
        Four of a kind: 15 (0.141%)     expected: 13 (0.126%)
        Straight flush: 7 (0.066%)      expected: 7 (0.0663%)
        Royal flush:    1 (0.009%)      expected: 1 (0.00781%)

USER HAS ANY PAIR (dealt 3264 times):
A set flopped:          470 (14.40%)
        expected:                       368 (11.3%)
When flop set, got boat or quads:       153 (32.55%)
        expected:                       157 (33.4%)
Hand user has at river:
        High card:      0 (0.0%)                expected: 0 (0.00%)
        Pair:           1126 (34.5%)    expected: 1158 (35.5%)
        Two pair:               1253 (38.39%)   expected: 1290 (39.5%)
        3 of a kind:    435 (13.33%)    expected: 383 (11.7%)
        Straight:               45 (1.38%)      expected: 62 (1.90%)
        Flush:          63 (1.93%)      expected: 64 (1.95%)
        Full house:     316 (9.681%)    expected: 279 (8.54%)
        Four of a kind: 26 (0.797%)     expected: 27 (0.842%)
        Straight flush: 0 (0.000%)      expected: 1 (0.0160%)
        Royal flush:    0 (0.000%)      expected: 0 (0.00182%)

USER HAS OFFSUIT CONNECTORS FROM 54o to JTo (dealt 2655 times):
Flopped open ended:             244 (9.19%)
        expected:                       227 (8.55%)
When open ended, got straight:  69 (28.28%)
        expected:                       75 (30.7%)
Hand user has at river:
        High card:      445 (16.8%)     expected: 457 (17.2%)
        Pair:           1140 (42.9%)    expected: 1135 (42.7%)
       Two pair:               561 (21.13%)    expected: 591 (22.3%)
        3 of a kind:    112 (4.22%)     expected: 115 (4.35%)
        Straight:               259 (9.76%)     expected: 242 (9.12%)
        Flush:          60 (2.26%)      expected: 52 (1.95%)
        Full house:     72 (2.712%)     expected: 59 (2.22%)
        Four of a kind: 5 (0.188%)      expected: 3 (0.126%)
        Straight flush: 1 (0.038%)      expected: 1 (0.0209%)
        Royal flush:    0 (0.000%)      expected: 0 (0.00110%)

ALL RIVERS SEEN BY THE USER:
Hand user has at river:
        High card:      7614 (17.2%)    expected: 7718 (17.4%)
        Pair:           19268 (43.5%)   expected: 19424 (43.8%)
        Two pair:               10327 (23.30%)  expected: 10414
(23.5%)
        3 of a kind:    2271 (5.12%)    expected: 2141 (4.83%)
        Straight:               2095 (4.73%)    expected: 2048 (4.62%)
        Flush:          1468 (3.31%)    expected: 1341 (3.03%)
        Full house:     1195 (2.696%)   expected: 1151 (2.60%)
        Four of a kind: 74 (0.167%)     expected: 74 (0.168%)
        Straight flush: 12 (0.027%)     expected: 12 (0.0279%)
        Royal flush:    1 (0.002%)      expected: 1 (0.00323%)

Four to a flush on board 2042 (4.607%)
        expected: 1902 (4.29%)