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.
| Category | 2-Handed | 3-Handed | 4-Handed | 5-Handed | 6-Handed | 7-Handed | 8-Handed | 9-Handed | 10-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.
| Category | 2-Handed | 3-Handed | 4-Handed | 5-Handed | 6-Handed | 7-Handed | 8-Handed | 9-Handed | 10-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% |
