Win rate with optimal strategy against limit raise bot

[Ludanto]

Imagine you are at the casino and they have new game there (disregard that it would be -EV for the casino).

You are playing limit Texas Hold'em against a computer and all the computer does is just raising every hand until showdown.

Questions:
1. What's the optimal preflop raise range?
2. What's the optimal postflop strategy?
3. How many BB/100 do you win with the optimal strategy?

The opponent (computer) is absolutely predictable so an optimal strategy must be calculatable. If this is doable then one must also be able to calculate the exact win rate with this strategy.

I hope there is somebody out there who is able to calculate those things and maybe even explain a little bit how they do it. AaronBrwon, pzhon?

Is this maybe a lot harder to calculate than it seems?

[Thremp]

[ QUOTE ]
Imagine you are at the casino and they have new game there (disregard that it would be -EV for the casino).

You are playing limit Texas Hold'em against a computer and all the computer does is just raising every hand until showdown.

Questions:
1. What's the optimal preflop raise range?
2. What's the optimal postflop strategy?
3. How many BB/100 do you win with the optimal strategy?

The opponent (computer) is absolutely predictable so an optimal strategy must be calculatable. If this is doable then one must also be able to calculate the exact win rate with this strategy.

I hope there is somebody out there who is able to calculate those things and maybe even explain a little bit how they do it. AaronBrwon, pzhon?

Is this maybe a lot harder to calculate than it seems?

[/ QUOTE ]

This is harder than it seems and you have very solid implied odds if he is raising every hand every street.

[jay_shark]

The optimal strategy will depend on many things like the flop texture . Whether or not you should call a person down .

[Flip-Flop]

The winning strategy is very obvious.
Only thing that matters is that the bot is playing every hand so all you have to do is play every hand that has over 50% pre-flop equity against a random hand heads-up followed by putting max possible money in the pot on every street.

As for calculating your win rate, I`ll leave that for others.

[Poker_is_Hard]

[ QUOTE ]
Imagine you are at the casino and they have new game there (disregard that it would be -EV for the casino).

You are playing limit Texas Hold'em against a computer and all the computer does is just raising every hand until showdown.

Questions:
1. What's the optimal preflop raise range?
2. What's the optimal postflop strategy?
3. How many BB/100 do you win with the optimal strategy?

The opponent (computer) is absolutely predictable so an optimal strategy must be calculatable. If this is doable then one must also be able to calculate the exact win rate with this strategy.

I hope there is somebody out there who is able to calculate those things and maybe even explain a little bit how they do it. AaronBrwon, pzhon?

Is this maybe a lot harder to calculate than it seems?

[/ QUOTE ]

Well at first glance I would think the best approach would be to play the upper 50% range of starting hands and max out betting in each round regardless of board. High variance, but it should be +EV.

~K9o+

[DarkMagus]

Always raise with anything where you have more than 50% equity vs. random cards, and call down with anything where you have less than 50% equity but enough equity to continue given the pot odds and implied odds. Preflop you can pretty much call with ATC since your implied odds will be so huge.

Obviously it would be hard to grind out an exact strategy, but play around with PokerStove a bunch and you should be able to gauge how much equity you have in various common situations.

Obviously you'll always want to call down with any pair, and probably ace and king high as well. Remember that when there's a pair on board, high card gains a lot more equity since it's so much less likely that he has a pair. With paired boards it may even be worth it to call down with queen and jack high, and maybe even raise with king high.

[pzhon]

[ QUOTE ]
The winning strategy is very obvious.

[/ QUOTE ]
No, it isn't. Maybe you should think about it some more.

[ QUOTE ]
Only thing that matters is that the bot is playing every hand so all you have to do is play every hand that has over 50% pre-flop equity against a random hand heads-up followed by putting max possible money in the pot on every street.

[/ QUOTE ]
This is wrong in several ways.

[img]/images/graemlins/diamond.gif[/img] That you were ahead of a random hand preflop does not mean you are ahead of a random hand once you get more information. 33 isn't so good on a KKTT4 board. QJo is ok on a board of AAK97r (51% against a random hand), but not 97653 with 3 to a suit (6% against a random hand).
[img]/images/graemlins/diamond.gif[/img]If your hand is worse than a random hand, you may be better off calling down rather than folding.
[img]/images/graemlins/diamond.gif[/img]If your hand is worse than a random hand, you may be happy to call and see if your hand improves. Even without the ability to raise the bot, you would come out ahead with many hands by doing this.

Less obviously, if you win slightly more than 50% of the time hot and cold, say with 98o on a JT2r board, where you win 50.4% against a random hand, you might not want to raise back and forth. You do not win the pot over 50% of the time when you sometimes fold unimproved, and you don't want to bloat the pot so that folding with 98o unimproved is a close decision.

[jay_shark]

There are many situations where folding your unimproved hands is a mistake . If most streets are getting capped , then it may actually be correct , depending on the flop texture, to call down without having paired the board . If the decision to raise or call is close , then it may be correct to just call since there are times when you may fold unimproved .

The winning strategy is very complex and will have to be adjusted for every unique flop combination that comes out . Pre-flop is where it can get tricky . Since you're getting wonderful implied odds , it's often times correct to just call with inferior hands rather than fold . Hands that are close to 50% equity against a random hand have to be looked at and analyzed carefully .

Something like q-5 o wins slightly more than 50% of the time when you get to see all 5 cards . If you cap it pre-flop and hit a pair on the flop then you may actually be reducing your EV if your opponent has 5+ outs with good implied odds . This positive EV situation may offset the EV you will have earned by raising him pre-flop .

A question of interest is whether or not it's ever correct to fold before the flop .

Folding is always 0 EV . On the other hand , you may call with a hand like 3-2 o knowing that if you hit a 2 or a 3 , then all streets will ( usually) be capped . This is actually a good thing as you gain some of the EV that you would have lost by calling with this hand btf .

[DarkMagus]

[ QUOTE ]
There are many situations where folding your unimproved hands is a mistake . If most streets are getting capped , then it may actually be correct , depending on the flop texture, to call down without having paired the board . If the decision to raise or call is close , then it may be correct to just call since there are times when you may fold unimproved .

The winning strategy is very complex and will have to be adjusted for every unique flop combination that comes out . Pre-flop is where it can get tricky . Since you're getting wonderful implied odds , it's often times correct to just call with inferior hands rather than fold . Hands that are close to 50% equity against a random hand have to be looked at and analyzed carefully .

Something like q-5 o wins slightly more than 50% of the time when you get to see all 5 cards . If you cap it pre-flop and hit a pair on the flop then you may actually be reducing your EV if your opponent has 5+ outs with good implied odds . This positive EV situation may offset the EV you will have earned by raising him pre-flop .

A question of interest is whether or not it's ever correct to fold before the flop .

Folding is always 0 EV . On the other hand , you may call with a hand like 3-2 o knowing that if you hit a 2 or a 3 , then all streets will ( usually) be capped . This is actually a good thing as you gain some of the EV that you would have lost by calling with this hand btf .

[/ QUOTE ]

I'd say it's probably worth it to call preflop even with 32o. The times that you hit only 1 pair, you'll probably be good more than 50% of the time, and when you hit 2pair/trips/straight then you can cap it every street, and you end up getting 23:1 implied odds on your preflop call.

[rufus]

[ QUOTE ]
Is this maybe a lot harder to calculate than it seems?

[/ QUOTE ]

It's not theoretically difficult, but it involves a lot of calculation. Your opponent's actions give you *no* information about his hand, so it's possible to work backward from the river.

It's also quite clear that there are only 3 plausible choices of betting strategy for each round: fold, minimal call, and 4-bet.

This simplifies analysis greatly, and the problem is probably small enough to computer solve by working out the value for each possible final round state, and then working backwards round-by-round for a complete solution. (Although it might take months to do so on a single computer.)

With such a solution, this could easily be turned into a casino game by simply charging more than the value/hand to play, although this sort of structure has psychological drawbacks that probably make it unsuitable to be a floor game.