Party flop distribution

[Jim Easton]

The code option is the only way I can see to make a table. This is from 164182 flops. The far left is the card, the Flop 1, Flop 2 and Flop 3 columns are the number of times that card appeared in that position. The other columns are the difference between the actual number and the expected number of 3157. I'm no statistician, so I'm just putting up the raw data.

<font class="small">Code:</font><hr /><pre> Flop 1 Flop 2 Flop 3
As 3111 -46 3169 12 3072 -85
Ah 3174 17 3157 0 3175 18
Ad 3126 -31 3144 -13 3107 -50
Ac 2994 -163 3060 -97 3261 104
Ks 3000 -157 3158 1 3059 -98
Kh 3148 -9 3183 26 3203 46
Kd 3234 77 3097 -60 3161 4
Kc 3222 65 3111 -46 3132 -25
Qs 3255 98 3136 -21 3177 20
Qh 3240 83 3149 -8 3154 -3
Qd 3142 -15 3154 -3 3224 67
Qc 3162 5 3067 -90 3118 -39
Js 3185 28 3176 19 3068 -89
Jh 3155 -2 3091 -66 3036 -121
Jd 3065 -92 3167 10 3068 -89
Jc 3108 -49 3038 -119 3126 -31
Ts 3049 -108 3147 -10 3087 -70
Th 3236 79 3095 -62 3147 -10
Td 3195 38 3262 105 3122 -35
Tc 3143 -14 3103 -54 3250 93
9s 3115 -42 3161 4 3202 45
9h 3128 -29 3187 30 3158 1
9d 3077 -80 3190 33 3144 -13
9c 3189 32 3158 1 3153 -4
8s 3199 42 3249 92 3134 -23
8h 3237 80 3182 25 3126 -31
8d 3138 -19 3126 -31 3155 -2
8c 3136 -21 3252 95 3115 -42
7s 3123 -34 3097 -60 3102 -55
7h 2993 -164 3058 -99 3133 -24
7d 3172 15 3218 61 3112 -45
7c 3203 46 3239 82 3196 39
6s 3123 -34 3209 52 3242 85
6h 3138 -19 3164 7 3223 66
6d 3118 -39 3101 -56 3174 17
6c 3191 34 3240 83 3270 113
5s 3158 1 3193 36 3186 29
5h 3262 105 3255 98 3213 56
5d 3123 -34 3175 18 3086 -71
5c 3138 -19 3131 -26 3147 -10
4s 3154 -3 3168 11 3135 -22
4h 3088 -69 3168 11 3207 50
4d 3239 82 3164 7 3269 112
4c 3219 62 3187 30 3235 78
3s 3185 28 3063 -94 3183 26
3h 3206 49 3177 20 3120 -37
3d 3307 150 3094 -63 3222 65
3c 3156 -1 3194 37 3152 -5
2s 3142 -15 3168 11 3161 4
2h 3219 62 3201 44 3159 2
2d 3215 58 3148 -9 3090 -67
2c 3147 -10 3201 44 3231 74
</pre><hr />

[Lori]

Jim, just to clarify, is this all flops, or flops where you still had cards?

Thanks,

Lori

[Jim Easton]

All flops.

[Thythe]

I think its somewhat interesting to note the higher amount of negatives on the "better" cards such as jacks through aces. I guess this is because when there is a flop, its more likely that people are holding these cards and less likely that the flop will contain them, since they are in people's hands. The times when there is no flop would tend to be when only one person has a good hand.

[Lori]

Thanks.

The reason I asked is that at a very casual first glance, it appears there are slightly less higher cards.

Before any statistitians give a more meaningful response, could I ask if you are playing at a level where, from time to time, a raise can actually take a pot down.

Thanks.

Lori

[Lori]

Mongeron published a similar list from stars, with similar findings here.

Thanks for the data Jim, hopefully someone like Homer or BruceZ can tell us what it means [img]/images/graemlins/smile.gif[/img]

Lori

[Jim Easton]

[ QUOTE ]
The reason I asked is that at a very casual first glance, it appears there are slightly less higher cards.


[/ QUOTE ]

Yes. Maybe one of the statistician types could provide some sort of "correction" for that.

Question for the statisticians - would knowledge of the known hole cards (mine and whoever went to a showdown) help with this?

Question for DB people - if the statisticians say yes, is anybody really good with Access 2002/SQL? I brute forced these numbers, but I think it would be very difficult to do the same for the hole cards.

[ QUOTE ]
could I ask if you are playing at a level where, from time to time, a raise can actually take a pot down.


[/ QUOTE ]

That doesn't happen much at any level at Party.

26,000 15/30
1,500 10/20
27,000 5/10
the rest 3/6

I had about 185k hands in the DB, there were 164182 flops, 134,882 turns and 108697 rivers. I'll be putting up the distributions for the turn and river in the next couple of days.

[Jim Easton]

[ QUOTE ]
Mongeron published a similar list from stars, with similar findings here.


[/ QUOTE ]

Thanks for the link. I remembered this post, but I'm not nearly as good with the search function as you are.


[ QUOTE ]
Thanks for the data Jim, hopefully someone like Homer or BruceZ can tell us what it means

[/ QUOTE ]

You're welcome, I'm hoping for the same thing.

[aces961]

Well assuming each card has a 1/52 chance of being in each position on the flop we have for a sample of 164182 a standard deviation of sqrt(164182*1/52*51/52) or 55.6. Now the sample size here is very large so this should act like a normal distribution, in such a distribution 99.73 percent of the data would lie within 3 standard deviations of the mean. From the data provided it doesn't appear as if any of the cards have surpassed this 3 standard deviations, away from the expected value of 3157, mark for any position though a few have come close.

[RollaJ]

Call Support, they owe you ACES!