Win rate with optimal strategy against limit raise bot

[Ludanto]

rufus, I am not sure if I understand what you mean by "work backward from the river". Can you please give one specific example for this?

What would be your calling, raising ranges?

[creedofhubris]

Does the casino have a cap on HU betting? Hitting the nuts would complicate calculations if there were no cap.

[KeathCole]

If there is no cap on HU betting, wouldn't it be as simple as:

1. Play any two cards.
2. Check-call each street if a nut hand is possible for your hole cards.
3. Check-fold once your hand can no longer make a nut hand.
4. When you make the nuts, keep re-raising the river until you bankrupt the casino.

You will lose money in the short run when you check-call hoping to make the nuts but end up check-folding the river, but you have implied odds on the river as large as the casino's bankroll.

[creedofhubris]

[ QUOTE ]
If there is no cap on HU betting, wouldn't it be as simple as:

1. Play any two cards.
2. Check-call each street if a nut hand is possible for your hole cards.
3. Check-fold once your hand can no longer make a nut hand.
4. When you make the nuts, keep re-raising the river until you bankrupt the casino.

You will lose money in the short run when you check-call hoping to make the nuts but end up check-folding the river, but you have implied odds on the river as large as the casino's bankroll.

[/ QUOTE ]

While that's a strategy that will eventually lead to you winning all the money, (assuming you start with a decent-sized bankroll), it's certainly not the strategy wth the highest BB/100, since you will be folding in a lot of +EV spots.

[rufus]

[ QUOTE ]
rufus, I am not sure if I understand what you mean by "work backward from the river". Can you please give one specific example for this?

What would be your calling, raising ranges?

[/ QUOTE ]

I don't know what the specific ranges would be. Basically what I'm saying is the following:

There are about 175,000 equivalent 5-card boards, so for every possible pot size, and holding, it's possible to calculate the river equity that such a situation represents.

Having calculated that, it's similarly possible to work out the value for each possible pot size and holding for each possible river situation - by maximizing the expected EV using the table of river situations.

Having done that, you can address the flop round, and then the pre-flop rounds.

[Beanos]

If there was no cap on the betting, the variance for max ev strategy would be too big for any bankroll. Surely you would have to keep betting (your entire roll) on whichever street provides the best equity vs a random hand. This way, you will maximise your ev on every hand.

Its a strange problem because your implied odds are infinite. I think what you would have to do, is calculate the probability of whether your currents hands equity vs random will rise or decline over further streets.

I dunno bout what i just wrote and cant be bothered to read it. Calling until you find a street where your quity is 50%+ and then jamming the pot might work.

I knew where i was going with this when i started, now im too tired, give up

[creedofhubris]

[ QUOTE ]
If there was no cap on the betting, the variance for max ev strategy would be too big for any bankroll. Surely you would have to keep betting (your entire roll) on whichever street provides the best equity vs a random hand. This way, you will maximise your ev on every hand.

Its a strange problem because your implied odds are infinite. I think what you would have to do, is calculate the probability of whether your currents hands equity vs random will rise or decline over further streets.

I dunno bout what i just wrote and cant be bothered to read it. Calling until you find a street where your quity is 50%+ and then jamming the pot might work.



[/ QUOTE ]

The catastrophic scenario is to bust out before you hit the nuts and get either a guaranteed double-up or a freeroll with an extremely likely double-up. So you'd want to calculate how often you hit the nuts playing super passive (wait for nuts, otherwise checkfold), how much you would lose getting there and therefore how big on average your stack would be once you hit the double-up opportunity, and then use that as a baseline to compare to some form of kelly betting as an alternative plan.

[MrBatman]

Assuming:
- Unlimited betting HU
- Finite sized bankroll
- each bet is (very?) small compared to bankroll

Under the above assumptions maximizing the winrate should be very close to applying the Kelly criterion to each street independently.

1. Pit holecards against random hand and evaluate edge.
2. Calculate bet size for maximal growth of bank.

If the bets (increments) are small compared to the total bankroll, then it shouldn't matter *much* wether you call down or fold.

[Dalek]

If there is no cap to the betting and you have enough money, see every flop. If you have a draw to the nuts stick around. If you hit the nuts you win as much money as you have on the table. If you have a good hand stick around anyway because it is probably the best hand.

[Ludanto]

I am assuming that there is a cap of 4 bets per player per betting round.

1. VP$IP:
I would play every hand because the calculatable implied odds make every single hand +EV if played correctly.

2. Preflop ranges:
I put in 4 bet PF with hands that have 50% and above EV against a random hand heads-up. I call/check PF with hands that have less than 50% EV against a random hand heads-up.

3. Flop play:
If I have 50% EV or more against a random hand I put in 4 bets.

IF my EV is LESS than 50%:
1. I would need to find out the 'turn range' AND 'river range' which would make my hand +EV on the river against a random hand.
2. I would need to translate those ranges into outs and considering my exactly defined implied odds I would call or fold.

4. Turn play:
If I have 50% EV or more against a random hand I put in 4 bets.

IF my EV is LESS than 50%:
1. I would need to find out the 'river range' which would make my hand +EV on the river against a random hand.
2. I would need to translate this range into outs and call or fold according to my implied odds.

5. River play:
If my hand has 50% EV against a random I put in 4 bets. Otherwise I fold.


Please comment on where you think my play would be improvable and why.