Analysing An All In Preflop Play

[David Sklansky]

The game is nine handed. Not a tournament. Blinds are 1 and 2. You have 20 in front of you and are under the gun. What are the minimum hands that will show a profit by moving in? (That doesn't mean you should move in, as a call or smaller raise might make more).

To turn this into a pure math problem lets make some simplifying assumptions. Your hand is face up. The first caller will always call if he is favored or a tiny dog (meanig tewo overcards). Any overcaller needs a pair of queens, kings, or aces. These assumptions have the effect of requiring a better hand to move in than if your hand was hidden but only, I think, by a little bit. I'm making these assumptions so that someone can more easily calculate or have a computer simulate to the right answer. Or you can guess. My guess would be AQ or two nines.

[Don Olney]

I have not run a simulation yet-- but my quess is 9-8 suited

I remember reading that when Diamond Jim Brady was asked about his biggest bet, he would say "My last two dollars."

Going All-In against an opponent with a bigger stack is for all intents and purposes the Hold'm version of betting your last deuce.

That said, should you let the situation influence you, or is a profitable bet just that regardless of any other factor?

Sorry to change the subject.

[David Sklansky]

Assume no one but the blinds will call with an overcard and an undercard. Otherwise hands like nine eight suited would be close because the next guy would call with J3 and everybody else would fold.

[NMcNasty]

I made some super rough calculations for just pairs that show its 99, although 88 is right behind and if a complicated factor that I didn't calculate was calculated I think 88 and possibly 77 might be correct.

One person has a hand better than 99 (all the other pairs) 15/663 of the time which is .023%. So the probability that no one has a better hand than 99 with 9 players left at a table is (.977)^9 = .81. So 99 takes the blinds 81% of the time and is a huge dog 19% of the time. Coincidentally when 99 is a huge dog there's a 19% chance it will win. I just got this number by casually fooling around with the cardplayer calculator and using QQ sharing one suit as the average dominating hand. You get 23 when you win (your opponents matching stack plus the blinds) and you lose your 20 when you lose. So the EV when up against a pair is roughly .19(23)+.81(-20) = -11.83. So we then plug that in to get our final EV .81(3)+.19(-11.83) = .18.
With 88 our chance that we are beat preflop rises from a 19% to a 22% chance.
So its the EV is .78(3)+.22(-11.83) = -.2626

There are two factors I did not calculate though. One is that you don't always win 23 when you win because sometimes your caller is in the blinds, so you'll only win 22 or 21. This factor would lower your EVs a little. The huge factor I'm not calculating though is when there's a second or third caller. When you get called by JJ and then QQ, your chance to win is only reduced by a few percentage points although the money in the pot is almost doubled. I think that factor would be enough to put 88 in the +EV range and possibly even 77.

Again these numbers are all super rough estimates with all sorts of rounding errors and I also completely ignored the possibility of split pots.

[yellowjack]

Whoa, -the- Newbie McNasty.

[Borodog]

McNasty,

Nice work, although I haven't reproduced it to check it.

A followup question. How does your answer change as you position becomes better and better, assuming that it is folded to you?

[NMcNasty]

[ QUOTE ]
McNasty,

Nice work, although I haven't reproduced it to check it.

A followup question. How does your answer change as you position becomes better and better, assuming that it is folded to you?

[/ QUOTE ]

I'm too lazy to do more calculations, but if you wanted to figure it out for yourself just use the same numbers except take the chance one player would have you beat to the 8th power instead of the ninth for second position, and seventh power for 3rd position, etc. One big problem though is calculating for pairs 66 and lower, since they are actually slight dogs to the big suited connectors.