Party Board Cards

[Jim Easton]

Here is some raw data. It is about 230k hands (about 50k more hands than the other data).

<font class="small">Code:</font><hr /><pre>card count_flop1 count_flop2 count_flop3 count_turn count_river
2c 4051 4076 4105 3401 2810
2d 4131 4054 3935 3382 2851
2h 4081 4022 4055 3445 2816
2s 3946 4006 4057 3246 2754
3c 4063 4099 4001 3349 2764
3d 4148 3965 4114 3364 2659
3h 4081 4045 3967 3257 2673
3s 4066 3916 3999 3445 2598
4c 4076 4041 4138 3402 2767
4d 4063 4064 4164 3369 2642
4h 3965 4029 4096 3400 2666
4s 4056 4022 4052 3407 2731
5c 4019 3990 3974 3301 2601
5d 3997 4029 3943 3398 2743
5h 4094 4070 4069 3273 2683
5s 4019 4131 4107 3355 2736
6c 4015 3947 4162 3356 2787
6d 4033 4105 4028 3272 2651
6h 3970 3990 4045 3413 2731
6s 4061 4073 4083 3361 2722
7c 4045 4087 4058 3341 2793
7d 4052 4095 3999 3359 2664
7h 3860 3927 3982 3435 2644
7s 4010 3941 3953 3369 2643
8c 4012 4136 4009 3327 2731
8d 3973 4008 4021 3380 2803
8h 4110 4061 3967 3349 2645
8s 4063 4062 4054 3386 2672
9c 4075 4061 4036 3330 2675
9d 4012 4042 4031 3297 2699
9h 3999 4009 4022 3237 2744
9s 3965 4093 4038 3284 2706
Tc 3975 3984 4086 3263 2571
Td 4091 4160 3999 3251 2628
Th 4158 4042 3998 3386 2665
Ts 3938 4031 3913 3389 2702
Jc 3938 3952 3981 3363 2721
Jd 3915 4055 3996 3234 2665
Jh 4028 3979 3943 3227 2656
Js 4053 4050 3884 3319 2681
Qc 4089 3944 3955 3255 2621
Qd 3976 3987 4084 3218 2666
Qh 4092 4056 4062 3292 2649
Qs 4111 3971 4068 3281 2735
Kc 4049 3976 3961 3342 2587
Kd 4108 3978 3982 3354 2704
Kh 3992 4039 4116 3346 2688
Ks 3888 4025 3950 3335 2714
Ac 3895 3899 4119 3325 2589
Ad 4008 4004 4022 3213 2624
Ah 4007 4023 4089 3229 2641
As 3969 4040 3919 3154 2517
</pre><hr />

*Special thanks to Rharless for helping with the SQL.

[Alobar]

is that how its supposed to look???

[Jim Easton]

[ QUOTE ]
is that how its supposed to look???

[/ QUOTE ]

I'll let the statistics experts (Homer?) evaluate that, I just posted the numbers.

[GrannyMae]

is that how its supposed to look???

i have not looked too closely (also waiting for homer), but i sure don't see any 2.5+ SD

[harboral]

numbers should be +/- 100 at this 250K total? - looks right to me. Still won't stop the "losers" from saying this does not prove anything. AL

[uuDevil]

Very interesting.

Looks like the single largest deviation is for the As on the river (-2.57 SD from mean of 2689 for the 52 possible cards). This is fine. You expect some relatively large deviations if the distribution is "normal". What's important is that the number of points that deviate by a given amount should decrease as the deviation increases.

When I plot the deviation from the mean (in units of SD) for the occurance of each card (using a different series for [edit]flop_card_1, flop_card_2, etc.[/edit]), I get a plot that definitely looks normal to me. There are standard tests for this and I'd like to see someone post an Excel chart (or equivalent) showing one.

I'm not a statistician, but if Homer or someone else doesn't have time in the near future, I'll give it a shot.

Testing for normality, however, is different from a test of randomness. For instance, you could obtain this same set of numbers if the As fell on the river 2517 consecutive times. So the kooks still have outs....

[uuDevil]

Disclaimer (a la G.W.B.): I'm not a statistician.

The plot below is a "probability plot." This type of plot is used to graphically determine whether sample data are consistent with a population that is normally distributed. If the points fall on a straight line, the hypothesis of normality is justified. This method is subjective since it requires some judgement as to the of the goodness of fit. There are more formal, analytical methods for evaluating this question, but someone else would have to tackle those.

In the plot below, the data for the three flop cards pretty much fall on top of each other (as expected). Since the turn and river cards don't get dealt out as frequently, these show up as separate groups of points.

I am satisfied that the distribution is normal. However, this is not the same as proving that the deal is random. I think normality is a necessary, but not sufficient condition.

Reference: Introduction to Statistical Quality Control, by Douglas Montgomery, pp. 110-114.