Hey, an actual NLHE game theory question/simulation.

[Nichomacheo]

I'm trying to make a program that solves simple jam/fold situations for me. Here's the situation:

SB vs BB. Both start with stacks of 10, SB posts 0.5 and BB posts 1. SB can shove/fold and BB can fold/call.

Currently I am doing this with a deck consisting of only aces king and queens. All-ins are evaluated by a program simular to PokerStove.

My preliminary results are that the SB should push with AA,KK,AKs,AKo and the BB should call with AA and KK only.

If anyone else could verify this, I would be thankful and impressed. If not, in general, how does this sound? I can provide some numbers for people that want to help me debug it.

/\/

[HP]

I am too lazy to verify this myself, but one way to verify this is too:

Use pokerstove. Double check that KK is at least a 0 EV call for BB. You can make jacks and lower dead cards i believe. Then, double check that AKs and QQ are at most a 0 EV call

After that, double check that AKo is at least a 0 EV push (where folding is considered 0 EV) for SB given that BB calls with AA/KK. Then, double check that pushing AQs and QQ are at most 0 EV

If all of the above are true, you've got yourself a Nash Equilibrium, and both players are playing in an un-exploitable fashion. I'd define that 'perfect poker'

[ QUOTE ]
If not, in general, how does this sound?

[/ QUOTE ]
Not good. I suspect you may be wrong. I suspect the un-exploitable strategy for the BB should be something like "call AA/KK 100% of the time, call with AKs 32.83% of the time, fold everything else"

I think it's way too much of a coincidence there are no 'boderline' hands (hands where they fold some non-zero percentage of the time, but don't fold some non-zero percentage also) in either of the player's ranges.

[HP]

Alright, you are lucky I am bored

I checked the EV of the SB pushing AQs:

If called by AA/KK, we have an equity of 31.846% if I've done it right

but according to my counting, we only get called 1 out of 5 times

so if we say the EV of folding is -0.5, the EV of pushing is:

0.8 + 0.2*(20*.31846 - 10)

which equals

0.0738

So unless I've made a mistake, pushing AQs from the SB is +EV if the BB is only calling AA/KK

[Nichomacheo]

Yeah, I'm crunching away at this... More time!

[HP]

While in the shower I thought of a way to find a Nash Equilibrium

First, suppose BB calls with AKs some percentage of the time. Call it X
Now, write out the EV of SB pushing with AQs in terms of X
Set this EV equal to the EV of SB folding. Now you can solve for X.
So now SB is indifferent to pushing or folding AQs

After you have done this, now suppose SB pushes AQs some percentage of the time. Call it Y
Write out the EV of BB calling with AKs in terms of Y
Set this EV equal to the EV of BB folding. Now you can solve for Y.
So now BB is indifferent to calling or folding AKs

And now you have a Nash Equilibrium

[jukofyork]

Download this: http://econweb.tamu.edu/gambit/

Then goto this page and follow the flash tutorial to have some idea what you're doing.

Then download and have a good look at "4cards.efg" (at the bottom of the same page).

You should be able then to work out how to get this working for your game using equities generated in poker-stove. Atm, I'm just trying to work out how to write some code to generate the ".efg" file automatically for the full push/fold game and then adapt it to allow for limps/checks using a simple heuristic instead of real post-flop play.

Juk [img]/images/graemlins/smile.gif[/img]

[HP]

[ QUOTE ]
You should be able then to work out how to get this working for your game using equities generated in poker-stove. Atm, I'm just trying to work out how to write some code to generate the ".efg" file automatically for the full push/fold game and then adapt it to allow for limps/checks using a simple heuristic instead of real post-flop play.

Juk

[/ QUOTE ]
bump

did you ever get this going btw?

[Paxinor]

gambit is really slow though in calculating, so for games with a big gametree you propably need to solve it outside gambit...

[jukofyork]

I'd settle for knowing the if SB limping/min-raising is (essentially) dominated by pushing and/or how much EV the BB loses by just pushing anything he would have called a push with (for each effective stack upto say 15BB), but creating a good post-flop heuristic is the hard part.

Juk [img]/images/graemlins/smile.gif[/img]

[trojanrabbit]

[ QUOTE ]
I'd settle for knowing the if SB limping/min-raising is (essentially) dominated by pushing and/or how much EV the BB loses by just pushing anything he would have called a push with (for each effective stack upto say 15BB), but creating a good post-flop heuristic is the hard part.

[/ QUOTE ]
This is something I've looked into a great deal. I've run some simulations that allow limping and mini-raising in addition to pushing. The optimal play seems to limp fairly frequently, push moderately, and rarely mini-raise, however... The EV gain by allowing these additional options is very small compared to a player who is confined to jam/fold options.

Tysen