Statistical analysis of board cards.

[mongeron]

Hello,

Since the discussion about rigged dealing and such has arisen again, I got the incentive to do some programming for a change. The result was a hand history analyzer program, which calculates the number of different cards occuring at boards.

I have not included the calculation of hole cards, because there are either two or four cards, and I went the easy way in the first step.

The hand histories include all my hands played at PokerStars, from 11/23/2001 to 05/15/2003. The data contains 168532 flops, 128405 turns and 104586 rivers. The games are Hold'em, Omaha and Omaha Hi/lo, all added together.

The results look like this:

Flop statistics:
Three-flushes: 8777 Two-flushes: 92599 Rainbows: 67156

Card counts on Flop (168532 flops):
Ad: 9369 Ac: 9735 As: 9600 Ah: 9414
2d: 9758 2c: 9815 2s: 9830 2h: 9889
3d: 9803 3c: 9896 3s: 9583 3h: 9784
4d: 9852 4c: 9922 4s: 9825 4h: 9742
5d: 9744 5c: 9634 5s: 9681 5h: 9753
6d: 9663 6c: 9692 6s: 9631 6h: 9805
7d: 9668 7c: 9900 7s: 9659 7h: 9725
8d: 9790 8c: 9825 8s: 9677 8h: 9972
9d: 9536 9c: 9758 9s: 9917 9h: 9813
Td: 9532 Tc: 9636 Ts: 9793 Th: 9650
Jd: 9767 Jc: 9714 Js: 9708 Jh: 9726
Qd: 9695 Qc: 9757 Qs: 9833 Qh: 9530
Kd: 9736 Kc: 9762 Ks: 9489 Kh: 9608

Card counts on Turn (128405 turns):
Ad: 2459 Ac: 2370 As: 2402 Ah: 2322
2d: 2558 2c: 2493 2s: 2524 2h: 2535
3d: 2514 3c: 2513 3s: 2490 3h: 2491
4d: 2477 4c: 2526 4s: 2486 4h: 2505
5d: 2363 5c: 2497 5s: 2473 5h: 2495
6d: 2448 6c: 2417 6s: 2505 6h: 2479
7d: 2483 7c: 2519 7s: 2452 7h: 2530
8d: 2480 8c: 2539 8s: 2471 8h: 2484
9d: 2417 9c: 2463 9s: 2439 9h: 2501
Td: 2461 Tc: 2487 Ts: 2401 Th: 2461
Jd: 2447 Jc: 2449 Js: 2492 Jh: 2488
Qd: 2439 Qc: 2405 Qs: 2499 Qh: 2418
Kd: 2429 Kc: 2428 Ks: 2522 Kh: 2459

Card counts on River (104586 rivers):
Ad: 1891 Ac: 2022 As: 2033 Ah: 1994
2d: 2092 2c: 2056 2s: 2017 2h: 2047
3d: 2031 3c: 1981 3s: 1945 3h: 2020
4d: 2007 4c: 2034 4s: 2043 4h: 2037
5d: 2015 5c: 2045 5s: 1977 5h: 1957
6d: 2072 6c: 1980 6s: 2024 6h: 1964
7d: 2011 7c: 1981 7s: 1995 7h: 1978
8d: 2025 8c: 2024 8s: 2039 8h: 1972

9d: 2050 9c: 1967 9s: 2052 9h: 2020
Td: 2021 Tc: 1993 Ts: 2077 Th: 2003
Jd: 1997 Jc: 2029 Js: 2003 Jh: 2006
Qd: 2058 Qc: 1956 Qs: 2004 Qh: 1988
Kd: 1971 Kc: 2038 Ks: 2058 Kh: 1986

I will include the calculation of hole cards later.

What other kind of data would be nice to know in addition to these?

I hope at least someone finds this data interesting. All comments are welcome!

- Tero

[lorinda]

I always did like you mongeron, but you are now officially my new hero...didn't know you read this site though! /forums/images/icons/blush.gif

Lori

[lorinda]

At a glance, it appears there are more 7,8 and 9 appearing on the flop than anything else... do you play hi lo quite a lot?

(I haven't totalled the columns (perhaps you could add that) but it seems like there are slightly less aces too, this is because, as a strong player, these will be a flop very slightly more often when you hold an ace compared to when you dont, Im actually surprised that it comes out in the data!)

Lori

[Terry]

Nice work. Want to bet that the "hystericals" won't get anywhere near this post. /forums/images/icons/wink.gif

[mongeron]

</font><blockquote><font class="small">In reply to:</font><hr />
At a glance, it appears there are more 7,8 and 9 appearing on the flop than anything else... do you play hi lo quite a lot?

[/ QUOTE ]

I just calculated the number of different games in the data in a quick &amp; dirty way, there could be some errors, but the numbers should be quite near what they should be:

Hold'em: 89262 hands
Omaha Hi: 63612 hands
Omaha Hi/Lo: 56237 hands

So, it seems that I have played Hi/Lo less than the other two. Regarding the question of 7, 8 and 9 appearing more than other cards, I really can't see that in the data. I think the difference could be just statistical error.

However, I am planning to make separate statistics for each of these game types. I'll also add the calculation of totals for each suit / rank. I will also add the distribution of hole cards.

After all, it's really fun to code something after a long time /forums/images/icons/smile.gif

And yes, I've been reading this forum for quite a while, but I don't have so much to say often, so I've been a bit quiet /forums/images/icons/smile.gif

- mongeron

[mbpoker]

nice analysis.