Two Plus Two Publishing LLC Two Plus Two Publishing LLC
 

Go Back   Two Plus Two Poker Forums > >

Notices

Probability Discussions of probability theory

Reply
 
Thread Tools Display Modes
Old 10-02-2017, 12:06 PM   #1
whosnext
Pooh-Bah
 
whosnext's Avatar
 
Join Date: Mar 2009
Location: California
Posts: 4,031
winning hands distribution for 2-10 player nlhe

Everyone knows that heads-up poker is different from full-ring poker. Clearly, in general, you should play tighter the more players are at the table.

It is fairly obvious that it would typically take a better hand to win a pot in a 10-handed game than in a 2-handed game.

Over the weekend I ran a set of simulations to try to answer how large this effect is.

I simulated 1,000,000 deals for each of 2-handed up to 10-handed NLHE and kept track of the category (royal flush, straight flush, four of a kind, full house, etc.) of the winning hands. Of course, the simulation had all players going to showdown on each deal.

Distribution of Winning Hands

Here is a table of the percentages of the distribution over the ten poker categories of the 1 million winning hands.

Category2-Handed3-Handed4-Handed5-Handed6-Handed7-Handed8-Handed9-Handed10-Handed
ROYAL FLUSH
0.007%
0.008%
0.014%
0.015%
0.017%
0.022%
0.024%
0.026%
0.028%
STRAIGHT FLUSH
0.053%
0.077%
0.110%
0.131%
0.160%
0.185%
0.205%
0.225%
0.261%
FOUR OF A KIND
0.312%
0.458%
0.611%
0.747%
0.909%
1.031%
1.166%
1.318%
1.494%
FULL HOUSE
4.703%
6.556%
8.178%
9.581%
10.904%
12.135%
13.227%
14.245%
15.177%
FLUSH
5.248%
7.019%
8.530%
9.732%
10.805%
11.775%
12.657%
13.490%
14.215%
STRAIGHT
8.013%
10.820%
13.039%
14.977%
16.559%
17.917%
19.059%
20.013%
20.847%
THREE OF A KIND
7.195%
9.268%
11.054%
12.589%
13.893%
15.081%
15.985%
16.719%
17.337%
TWO PAIR
31.407%
33.895%
33.702%
32.507%
30.534%
28.474%
26.465%
24.560%
22.731%
ONE PAIR
37.133%
29.939%
24.140%
19.527%
16.167%
13.369%
11.208%
9.402%
7.911%
HIGH CARD
5.930%
1.961%
0.622%
0.194%
0.054%
0.012%
0.003%
0.001%
0.000%

You can see that the "quality" of the winning hand significantly improves moving from 2-handed tables to 10-handed tables.

Cumulative Distribution of Winning Hands

To make it even easier to see the effect, here is the same table in terms of the "cumulative" percentages. That is, what is the percentage of deals that was won by a hand in this category or a higher category.

Category2-Handed3-Handed4-Handed5-Handed6-Handed7-Handed8-Handed9-Handed10-Handed
ROYAL FLUSH
0.007%
0.008%
0.014%
0.015%
0.017%
0.022%
0.024%
0.026%
0.028%
STRAIGHT FLUSH
0.060%
0.084%
0.123%
0.146%
0.178%
0.207%
0.229%
0.251%
0.289%
FOUR OF A KIND
0.372%
0.542%
0.734%
0.893%
1.086%
1.238%
1.395%
1.569%
1.783%
FULL HOUSE
5.075%
7.098%
8.912%
10.474%
11.990%
13.373%
14.622%
15.814%
16.960%
FLUSH
10.323%
14.117%
17.442%
20.206%
22.795%
25.148%
27.280%
29.304%
31.174%
STRAIGHT
18.335%
24.938%
30.481%
35.183%
39.354%
43.065%
46.339%
49.318%
52.021%
THREE OF A KIND
25.530%
34.206%
41.535%
47.772%
53.246%
58.146%
62.324%
66.037%
69.358%
TWO PAIR
56.937%
68.101%
75.237%
80.279%
83.780%
86.620%
88.789%
90.597%
92.089%
ONE PAIR
94.070%
98.040%
99.378%
99.806%
99.947%
99.988%
99.997%
99.999%
100.000%
HIGH CARD
100.000%
100.000%
100.000%
100.000%
100.000%
100.000%
100.000%
100.000%
100.000%
whosnext is online now   Reply With Quote
Old 10-03-2017, 08:45 AM   #2
heehaww
Pooh-Bah
 
heehaww's Avatar
 
Join Date: Aug 2011
Location: Tacooos!!!!
Posts: 4,220
Re: winning hands distribution for 2-10 player nlhe

Thanks, good idea generating those.

I'm too lazy to calculate now, but I think most of the two-pairs use a pair on the board, even when 9-handed. So one pair is stronger than the chart might suggest.
heehaww is offline   Reply With Quote

Reply
      

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


Forum Jump


All times are GMT -4. The time now is 01:53 PM.


Powered by vBulletin®
Copyright ©2000 - 2017, Jelsoft Enterprises Ltd.
Copyright © 2008-2017, Two Plus Two Interactive
 
 
Poker Players - Streaming Live Online