Game theory for the end of a SnG

[bigg_nate]

From a game-theoretic point of view, NL holdem is a very complicated game. You're typically up against many opponents with different playing styles, there are several rounds of action, and in each round you have many different possible strategies. From a practical point of view, I doubt that most players could improve their play by using game theory.

However, heads-up play at the end of a SnG tournament is much simpler. You're only up against a single opponent, and often the blinds are so high that you really only have two options: fold preflop or push all-in. Because of this, I think it might be possible to use game theory to come up with a decent strategy.

Before solving for an optimal strategy, I first simplified the game even more by splitting the starting hands into 3 categories:

Great hand: QJs or better (about 15% of hands)
Good hand: Q5o or better (about 35% of hands)
Bad hand: everything else (about 50% of hands)

I then solved for both players' Nash Equilibrium strategies:

If you are the small blind:
- Always push with a great hand.
- Push 60% of the time with a good hand.
- Push 20% of the time with a bad hand.

If you are the big blind and the small blind pushes:
- Always call with a great or good hand.
- Call 15% of the time with a bad hand.

This is really just a "very rough draft" of the strategy -- I'm planning to try it out a couple of times and then think about it some more. One of the things I plan to rethink is the categorization of starting hands ... which categories would you use?

- Nate

[Alibi]

Well I think it should be more based on your read of your opponent at this point than determining whether or not a hand is "good" or "poor." Reads are much more important HU than they are at any other point in the SnG

[PocketAces]

yeh deffintly tells b/c then you can know if you beaten or not before you push them all

[bigg_nate]

Really? I find it difficult to get reads this late in a tournament. People tend to change their playing style when it gets heads-up, so you can't really rely on previous hands. And the tournament always seems to be over before I can get a good read on their new style.

- Nate

[gabe]

i think the theory works well for pushing, but calling allins really depends on what your opponent is pushing with.

[ensign_lee]

Wait; Q 5 off is good? I'd consider that in the trash category, right?

[Iconoclastic]

What about pot odds

[bigg_nate]

Wait; Q 5 off is good? I'd consider that in the trash category, right?

Q5o is barely over 50% against a random hand, which makes it the worst hand in the "good" category. Maybe "mediocre" would be a better name than "good".

- Nate

[bigg_nate]

What about pot odds

They're taken into account. The numbers are based on the assumption that the small stack has 7.5 BB.

- Nate

[drmcboy]

Any way to account for the action in a previous hand - i.e. you've pushed three hands in a row, you should be more likely to push a quality hand, but less likely to push a marginal one?

[ihategnomes]

I know when I play HU in SnG's a lot I have two different base strategies. First is for aggressive players, then another for passive players. Since the hands you play can drastically change what hands you play. IE. You more apt for fold a marginal hand to raise against a tight/passive player than you would be against an aggressive player.

When playing aggressive players, I like to let them hang themself. If we start out close to equal chips, I will let him think he is boss, as he speeds up I start catching him in hands, slowly grinding up until I hit "the" hand. A lot of players are unable to change gears, so as you speed up, you will pick up plenty of dead money.

With passive players, play the table captain. You should be the one raising, not calling raises. This is one of the most important aspects of HU. Eventually via betting pattern or what not you should be able to take advantage of this situation, a lot of times passive players tilt when they can't see a flop

So without being much of a math geek, you should probably have to basic strategies, then deviate from them as needed. What do you guys think?

[drmcboy]

I think he's trying to look a little deeper than - if they play loose, you play tight, vice versa.