Win rate with optimal strategy against limit raise bot

[pzhon]

[ QUOTE ]
Q5o should not cap, but just call one raise by the bot preflop.

[/ QUOTE ]
Great, that agrees with some heuristic calculations I did. Can you share numbers from an exact calculation or a simulation?

You can often (relative to the 50.12:49.88 preflop advantage over a random hand) find a fold with Q5o on the river, so Q5o should not win 50% of the pots when you don't cap. (Nor should it win 50% of the pots when you do cap, but that isn't as important.)

[mykey1961]

Q5o Fold = -0.5
Q5o Call = +2.8903262018
Q5o Cap = +2.8673163177

This is using an exact calculation.

It checked every possible flop
fold, call once, cap for each flop
every possible turn
fold, call once, cap for each turn
every possible river
fold, call once, cap for each river

[Ludanto]

NUMBERS! [img]/images/graemlins/smile.gif[/img]

mykey1961, I would be curious what the calculation looks like. I guess you have written some small application. If you don't mind I would like to see the code. With this app it seems one can determine the EXACT maximum BB/100 against this bot.

[mykey1961]

With Q6o

Fold -0.5
Call +3.1655971042
Cap4 +3.1934903560


Yeah, you could get the exact max, but it would take quite a while.

[mykey1961]

This could be solved much like checkers has been solved, It might take a while, but not anything like U of A did, since you know the bot will only take 1 of the many possible branches.

More interesting would be to make this optimizing for both players.

I see that as being quite the recursive problem.

Pick a strategy for SB, find BB's best response, allow SB to adjust for that, then allow the BB to adjust until both strategies are stable.

Then add in the flop, and adjust away. That might cause adjustments in the preflop rounds, and we're back to square 1.

Etc. Etc. Etc.

I'll get started on that right away.

I expect to have the answer by next never.

[RobNottsUk]

My initial optimal strategy idea is to play it in a FLHE game where the betting is not capped in Heads Up pots.

Then my strategy, is to play hands with nut potential, make the nuts on the river, then just raise the bot until whole stack is in the pot.

Obviously I may make a strong hand that's not quite the nuts, but I wouldn't 'overplay' it, knowing I can have a sure fire spot later.

This will only work if, the stacks are deep enough in relation to the blinds. Other wise I'll go the way of Broomcorn's Uncle [img]/images/graemlins/smile.gif[/img]

[mykey1961]

If there isn't a cap, I don't think this would be very interesting at all.

If you got AA preflop, the only reason to stop raising is due to Kelly, and your bankroll.

Having 85% equity on an even money bet would allow you to put your whole stack into the pot as long as your stack isn't more than 70% of your bankroll.

[RobNottsUk]

In my games AA loses sometimes, and why back a 85% shot, if you have a 100% certain winning strategy?

[mykey1961]

If you want to earn 2% on your money, put it in a bank, if you want to make some real ROI, you need to take some risks.

You don't have a 100% certain strategy, what you have is some situations that can come up where you have a 100% chance of winning.

There is no guarentee that those situations will come up while you are at the table.

I'd put 70% of my bankroll on an 85% shot paying even money, every day of week, and twice on sundays, unless I think the game isn't conducted fairly.

[RobNottsUk]

If you're thinking of a mixed game with Raise-bot as one of the players, I agree with you.

But if it's a HU match, for the bot's stack then I can't see the point of investing too heavily in 'marginal' hands like 1 pair pre-flop; when you can have a much better spot by being more patient.

You know it's going to raise all the time, so take advantage of it, when you have a winner.