AA at a NL table. How many callers do you want?

[ZeeJustin]

.50/1 NL against 9 drunken monkeys. Everyone has a stack of $100.

You are utg with AA. You look around, see the mounds of budweisers and soiled daipers and decide to shove for $100. How many callers do you want for maximum EV? Those monkeys aren't sobering up any time soon, so ignore variance. Also, assume random holdings for all callers.

My instinct tells me you would want the whole table to call, however, I could see how this would be incorrect. The probability of your pair holding up unimproved would be negligible, and you are much less likely to improve than the rest of the table.

[Bozeman]

From the numbers at http://www.gocee.com/poker/HE_Val_Sort.htm, 8, although 7, 8, and 9 are quite close, so simulation uncertainties might change the answer.

[ZeeJustin]

Wow, this is exactly what I wanted. Thanks!

[squiffy]

Why would the optimal number of callers differ in NL vs. a ring game? I thought that at a ring game, you always want the maximum number of callers, 9 without question????

[Bozeman]

The peculiarity of this situation is that all the money goes in preflop. If there was more to bet, things would change.

[Nottom]

[ QUOTE ]
I thought that at a ring game, you always want the maximum number of callers, 9 without question????


[/ QUOTE ]

According to that chart ... the answer is 8 instead of 9. I think thats quite interesting.

[thylacine]

Why stop your graph at 9 opponents??! There are enough cards in the decks for up to 22 opponents! Could you do the same chart for up to 22 random hands? I think it would be interesting!

[Bozeman]

Because I didn't generate the data from which the graph is made, I borrowed it. In addition, I don't see any way to generate this data without simulation, and either the uncertainty or the computing overhead will get large for many opps. Would be nice though.

Craig

[thylacine]

Anyone know how to do this? It would be nice to see!

I agree it would have to be a simulation result. I don't know how to do it. I looked at http://www.twodimes.net/poker/ but I don't see how to do AA vs n random hands.

The sampling error need not be huge, say if you did N=1000000 trials. If the actual win probability is p, then I think the variance in the estimate is something like p(1-p)/N. It may not be good enough,though,to see where the graph truly peaks and troughs.

Still hoping I can persuade someone to do it. It comes down to doing AA vs n random hands, for n=1,...,22. Anyone know of software for this kind of question?

It just occurred to me that a related problem would be the probability distribution of the ranking (1st to 23rd) of AA vs 22 random hands. From those numbers you could deduce the other numbers we want. (see how?)

[Bozeman]

poker calculator could probably do it, but maxes out at ten hands.