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. http://home.earthlink.net/~craighowald/images/aa.gif

[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.

[Bozeman]

Yeah, you are right. For 10 players, 10M trials gives better than 3 significant figures. It helps to do AA, because there is less variance among win prob. depending on what it faces, since it dominates everything; other hands have moe than twice the uncertainty for this simulation.

Craig

[Nottom]

I'd like to see a similar situation with the change that instead of random hands they are randomly selected from playable hands (or at least stuff people think are playable).

Basically any pair, any unsuited connector, any straight-flush combo, Ax, or any two broadway cards. This should give a slightly more realistic output since even the biggest fishies aren't going to be calling big preflop bets with 36o.

[Bozeman]

Against 9 random hands, AA wins 31.1%, while against 9 Group 5 or better hands, AA wins 18.8%. However, you are very unlikely to ever face this many decent hands. Poker calculator allows you to pick ranges for hands, and is overall quite a nice simulator/enumerator.

Craig

[ZeeJustin]

Where would one find this alleged poker calculator you speak of?

[ZeeJustin]

[ QUOTE ]
Against 9 random hands, AA wins 31.1%, while against 9 Group 5 or better hands, AA wins 18.8%.

[/ QUOTE ]

I have a suspicion that the reason why the difference here is so big, is because your aces are likely to be taken by another hand, rather than remaining in the deck.

The reason I didn't mind asking for random hands for this example was because I figured that an overpair is an overpair. 54s and 98s have almost the same odds against AA. 22 and KK have almost the same odds against AA.

[Bozeman]

This is a large part of it. Against 8 Sklansky 1-8 hands, AA wins about 16%, but against 8 Sklansky 1-8 hands that contain no aces, it wins ~30%. The remaining 5% is from pairs, flushes, and straights.