Win rate with optimal strategy against limit raise bot

[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.

[pzhon]

As I pointed out, you may not want to put in 4 bets when you have a tiny advantage over a random hand, but will not win the pot 50% of the time because you will sometimes fold before showdown, or would be better off folding after not bloating the pot.

[mykey1961]

If you have a hand that at one point has atleast .50 Pot equity against a random hand, what could possibly flop, turn, or river that would cause you to not have enough equity to even call one more bet?

[Ludanto]

[ QUOTE ]
As I pointed out, you may not want to put in 4 bets when you have a tiny advantage over a random hand, but will not win the pot 50% of the time because you will sometimes fold before showdown, or would be better off folding after not bloating the pot.

[/ QUOTE ]

Game: $1/$2 Limit Texas Hold'em Heads-up

Hero = SB
Bot = BB


I get dealt 9c8d

Equity evaluation:
---
2,097,572,400 games 0.266 secs 7,885,610,526 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 51.903% 49.87% 02.03% 1046148851 42553464.50 { random }
Hand 1: 48.097% 46.07% 02.03% 966316620 42553464.50 { 9c8d }


---


Preflop action: Hero calls, Bot raises, Hero calls.


Pot: $4
Flop: JhTs2c

Equity evaluation:
---
1,070,190 games 0.062 secs 17,261,129 games/sec

Board: Jh Ts 2c
Dead:

equity win tie pots won pots tied
Hand 0: 49.600% 47.65% 01.95% 509986 20828.00 { random }
Hand 1: 50.400% 48.45% 01.95% 518548 20828.00 { 9c8d }


---

Flop action: Bot bets, Hero raises, Bot raises, Hero caps, Bot calls.

Pot: $12
Turn: 3d

Equity evaluation:
---
45,540 games 0.031 secs 1,469,032 games/sec

Board: Jh Ts 2c 3d
Dead:

equity win tie pots won pots tied
Hand 0: 63.542% 62.79% 00.75% 28595 342.00 { random }
Hand 1: 36.458% 35.71% 00.75% 16261 342.00 { 9c8d }


---

Turn action: Bot bets, Hero calls.

Pot: $16
River: one of 46 cards

River action:
Bot bets -> pot = $18 -> I would need to win one in 9 times to make a call profitable = 11.1%
There is not one single river card which would give me less than 11.1% EV.


It seems that capping the flop didn't make my EV negative in this hand. Where is my mistake?

[DarkMagus]

[ QUOTE ]

5. River play:
If my hand has 50% EV against a random I put in 4 bets. Otherwise I call if i can beat enough random hands to justify the pot odds i am getting.


[/ QUOTE ]

[Ludanto]

[ QUOTE ]
[ QUOTE ]

5. River play:
If my hand has 50% EV against a random I put in 4 bets. Otherwise I call if i can beat enough random hands to justify the pot odds i am getting.


[/ QUOTE ]

[/ QUOTE ]

Thank you DarkMagus [img]/images/graemlins/smile.gif[/img] Looks obvious but I can't think of everything [img]/images/graemlins/wink.gif[/img]


BTW, what does the expression "win hot and cold" mean?