Win rate with optimal strategy against limit raise bot

[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?

[pzhon]

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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?

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Did you look at the 98o with a JT2r board example I gave earlier in this thread?

Let's suppose that you win 50.5% of the time hot and cold. Every dollar you put in with a strategy now combined with calling down, or raising when you have an advantage, will return $1.01. However, you may be hurting yourself, since you have the option of folding, and if you pump up the pot now you may lose some of your ability to make good folds later.

Your 50.5% chance to win hot and cold may come from ending up with 10% equity 10% of the time, in which case you will fold even if you pump up the pot now, and a greater equity (averaging 55%) 90% of the time, when you won't fold. This means you actually win 49.5% of the pots, and every extra dollar you put in now returns only $0.99, and is a mistake. When you pump up the pot on the flop, you decrease the value you get from your ability to fold when you end up with a hand like 98 unimproved.

[DarkMagus]

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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.


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[Ludanto]

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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.


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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?

[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.

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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:
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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 }


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

Pot: $12
Turn: 3d

Equity evaluation:
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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?

[pzhon]

[ QUOTE ]
[ 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.

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Where is my mistake?

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The major point you are missing is that not being able to fold (or not having an easy fold) because you have bloated the pot hurts you. Putting in an extra $3 gave you and extra $0.02 worth of hot and cold equity from the flop action, but it gave up chances to fold with as low as 10.1% equity getting $12:$2 on the river. That would save you $0.46-$0.59 on the 96 out of 1081 turn and river combinations where the board stays unpaired and both the turn and river are below a 7. That is worth over 4 cents, more than the value you obtained on the flop.

I don't like having to make the same point 4 times in a thread. I'm not going to make it a 5th time.

[mykey1961]

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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?

[/ QUOTE ]
Did you look at the 98o with a JT2r board example I gave earlier in this thread?

Let's suppose that you win 50.5% of the time hot and cold. Every dollar you put in with a strategy now combined with calling down, or raising when you have an advantage, will return $1.01. However, you may be hurting yourself, since you have the option of folding, and if you pump up the pot now you may lose some of your ability to make good folds later.

Your 50.5% chance to win hot and cold may come from ending up with 10% equity 10% of the time, in which case you will fold even if you pump up the pot now, and a greater equity (averaging 55%) 90% of the time, when you won't fold. This means you actually win 49.5% of the pots, and every extra dollar you put in now returns only $0.99, and is a mistake. When you pump up the pot on the flop, you decrease the value you get from your ability to fold when you end up with a hand like 98 unimproved.

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Yes I looked at it, but obviously not close enough.

The part that stood out to me was:

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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.

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If folding unimproved is a close decision, then making the wrong decision isn't going to have much effect on your EV.

[pzhon]

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Yes I looked at it, but obviously not close enough.

The part that stood out to me was:

[ QUOTE ]
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.

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If folding unimproved is a close decision, then making the wrong decision isn't going to have much effect on your EV.

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Well, do you agree now? Getting a close decision right once you get there is not important, but this says nothing about how much it costs you to put yourself into that situation.

I know my point was subtle. That's part of why it was worth stating it here. This is an esoteric hypothetical, but the same idea shows up in real poker, both limit and NL, and it's worth a lot more than a few pennies. Raising with a hand that is ahead hot and cold does not necessarily gain value for you if you win less than your share of the pots. Raising with a hand that is behind hot and cold may gain value for you if you will win more than your share of the pots.

[helter skelter]

This is funny. Once, in a limit freeroll I played in, there was a guy who played exactly like this. It wasn't HU, though.

I'm no game theory expert, but I think rufus has the right idea.

You have a number of possible river boards with b number of possible pot sizes, c number of possible turn boards with d number of possible pot sizes, e number of possible flop boards with f number of possible pot sizes, g number of possible pot sizes for preflop with each of h number of possible starting hands.

Anyone want to do the math?