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Big Draw On The Turn


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#21 simo_8ball

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Posted 23 August 2008 - 03:37 PM

I really should proofread things like this and go through the trivial cases to confirm. I always make a stupid little mistake somewhere and it destroys everything all the way down.Here I just assumed that because the 68% of the time we check and then c/f disappears (we lose 0), that I didn't need to bother with that step. Unfortunately it meant I missed out a relevant 32% factor.EDIT: P(Payoff) isn't just the % he calls. It's the % we hit and then he calls. Wait, I might need to revise things further. In fact I might just delete that post entirely.

#22 simo_8ball

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Posted 23 August 2008 - 03:49 PM

Shove+fold = +27Shove+call = 71 x .32 = 22.72. We are shoving 22 to get that though, so it's basically breakeven when we get called.Check through and miss river = 0Check through+paid off = +49Check through+not paid off = +27(assume he always pays off river after he bets turn)C/c bet of $Z and miss = -$ZC/c $Z and hit = +$49C/c $Z overall = .32x49 - .68xZFor a $10 bet, that is 15.68 - 6.8 = +$8.9P(Fold)P(Check)P(Pay Off) [note: we have to hit for him to pay us off]Shoving:P(Fold) x $27 = EquityChecking (ignoring the chance of say a $10 bet):club:(check) x [ P(Payoff)x$49 + (1 - P(Payoff))x$27 ]P(check) x [ P(Payoff)x$49 + 27 - P(Payoff)x$27 ]P(check) x [ P(Payoff)x($49-$27) + 27 ]P(check) x [ P(Payoff)x$22 + $27 ] = equityIf he pays us off 100%, then P(Payoff) = 0.32 x 1 = 0.32.If he checks we get a minimum of .32 x $27 = ~$9.So, if he always calls the river, then our equity from him checking is (0.32x22) + 27 = $34.Okay so far I think.Checking (including $10 bet probability):ts(check)x(value from check) + P($10 bet)x(value from $10 bet)P(check) x [ P(Payoff)x$22 + $27 ] + P($10 bet) x $8.9.Okay so far still. Using David's numbers:Shoving gives $6.75.Checking gives:.25 x [ (.85 x .32 x 22) + 27 ] x .32 + .25 x $8.9= .25 x 33 + $2.225 = $10.475FOR THE LOVE OF GOD PLEASE SAY THAT'S RIGHT.

#23 simo_8ball

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Posted 23 August 2008 - 03:56 PM

Ok, going for pretty much a worst case option for checking, and quite good for shoving:Suppose it's 30% fold equity from a shove,That's 0.3x27 = +$8.1 from shoving.When checked to, villain will check behind 10%, bet $10 10% of the time, and shove 80%. He will pay off a river shove 50% of the time when he checks behind and 100% of the time when he bets $10.P(check) x [ P(Payoff)x$22 + $27 ] + P($10 bet) x $8.9 = Equity.1 x [ (.32x.5)x22 +27 ] + .1 x $8.9= $3.1 +0.9 = $4.Worst case scenario for checking is about $4 worse than shoving.With David's numbers we are about $3.75 better by checking.I think it will work out to be a pretty close run thing.I have also destroyed this thread.

#24 AimHigher

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Posted 24 August 2008 - 01:42 AM

View Postsimo_8ball, on Sunday, August 24th, 2008, 12:56 AM, said:

Ok, going for pretty much a worst case option for checking, and quite good for shoving:Suppose it's 30% fold equity from a shove,That's 0.3x27 = +$8.1 from shoving.When checked to, villain will check behind 10%, bet $10 10% of the time, and shove 80%. He will pay off a river shove 50% of the time when he checks behind and 100% of the time when he bets $10.P(check) x [ P(Payoff)x$22 + $27 ] + P($10 bet) x $8.9 = Equity.1 x [ (.32x.5)x22 +27 ] + .1 x $8.9= $3.1 +0.9 = $4.Worst case scenario for checking is about $4 worse than shoving.With David's numbers we are about $3.75 better by checking.I think it will work out to be a pretty close run thing.I have also destroyed this thread.
If his range is AT+, 99+ and 33 then JJ - KK only makes up 22% of his range. (66 possible card combinations, 15 of which he'll presumably fold).Also, check-calling against this range is slightly -EV since we sacrifice our fold equity. I don't think the fact that 1 in 5 times our EV is increased because he lets us draw cheaply compensates for the fact that 4 in 5 times we're going to be facing an inferior wager.

#25 simo_8ball

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Posted 24 August 2008 - 02:26 AM

View PostAimHigher, on Sunday, August 24th, 2008, 10:42 AM, said:

If his range is AT+, 99+ and 33 then JJ - KK only makes up 22% of his range. (66 possible card combinations, 15 of which he'll presumably fold).Also, check-calling against this range is slightly -EV since we sacrifice our fold equity. I don't think the fact that 1 in 5 times our EV is increased because he lets us draw cheaply compensates for the fact that 4 in 5 times we're going to be facing an inferior wager.
I think you might be missing something because no line is -EV. Open shoving is at worst 0EV, and check/calling is at worst 0EV.Also, shoving and getting called is the exact same equity as checking and calling a shove. The equations all work, so put in the numbers that you think are true. You think we have 22% fold equity (JJ-KK), so that's 22% of $27, or about $6 from shoving. FWIW, I'd say KK usually gets it in preflop, and JJ/QQ are a lot more likely to fold the flop than AT-AK."I don't think the fact that 1 in 5 times our EV is increased because he lets us draw cheaply compensates for the fact that 4 in 5 times we're going to be facing an inferior wager"I have absolutely no idea what you mean by this. Surely facing an inferior wager IS drawing cheaply?

#26 AimHigher

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Posted 24 August 2008 - 05:49 AM

View Postsimo_8ball, on Sunday, August 24th, 2008, 11:26 AM, said:

I think you might be missing something because no line is -EV. Open shoving is at worst 0EV, and check/calling is at worst 0EV.Also, shoving and getting called is the exact same equity as checking and calling a shove. The equations all work, so put in the numbers that you think are true. You think we have 22% fold equity (JJ-KK), so that's 22% of $27, or about $6 from shoving. FWIW, I'd say KK usually gets it in preflop, and JJ/QQ are a lot more likely to fold the flop than AT-AK."I don't think the fact that 1 in 5 times our EV is increased because he lets us draw cheaply compensates for the fact that 4 in 5 times we're going to be facing an inferior wager"I have absolutely no idea what you mean by this. Surely facing an inferior wager IS drawing cheaply?
Ah ok, I made a mistake. I thought against AT+, 33, 99+ check/calling a shove was very slightly -EV, but it's actually very slightly +EV (~$0.10). It only becomes -EV if you include A9 in his range.What I meant is: "I don't think the fact that 1 in 5 times our EV is increased compensates for the fact that 4 out of 5 times we're going to be check-calling a shove with an EV of only 10 cents. "
Board: 3s Ts 9h AdDead:  	equity 	win 	tie 		  pots won 	pots tied	Hand 0: 	31.192%	  31.19% 	00.00% 			   947 			0.00   { Js8s }Hand 1: 	68.808%	  68.81% 	00.00% 			  2089 			0.00   { 99+, 33, ATs+, ATo+ }
EV for check-calling a shove: $0.10 = ($49.15 * 0.312) + (-22.15 * 0.688)EV for check-calling $10 (I'm going to assume he always calls on the river when we hit since he'll be getting odds): $8.45 = ($49.15 * 0.312) + (-$10 * 0.688)EV for check-check (I'm just going to guess he'll call 70% of the time if we put him in on the river and we'll be good. It may be optimistic/incorrect). $19.16 = ($49.15 * 0.312 * 0.70) + ($27 * 0.312)EV for checking: $2.84 = ($0.10 * 0.8) + ($8.45 * 0.10) + ($19.16 * 0.10)EV for a shove: $6.04 = ($27 * 0.22) + ($49.15 * 0.312) + (-$22.15 * 0.688)I know your math is a lot better than mine so please let me know if I've made any mistakes (I probably have).

#27 simo_8ball

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Posted 24 August 2008 - 06:25 AM

View PostAimHigher, on Sunday, August 24th, 2008, 2:49 PM, said:

Ah ok, I made a mistake. I thought against AT+, 33, 99+ check/calling a shove was very slightly -EV, but it's actually very slightly +EV (~$0.10). It only becomes -EV if you include A9 in his range.What I meant is: "I don't think the fact that 1 in 5 times our EV is increased compensates for the fact that 4 out of 5 times we're going to be check-calling a shove with an EV of only 10 cents. "
Board: 3s Ts 9h AdDead:  	equity 	win 	tie 		  pots won 	pots tied	Hand 0: 	31.192%	  31.19% 	00.00% 			   947 			0.00   { Js8s }Hand 1: 	68.808%	  68.81% 	00.00% 			  2089 			0.00   { 99+, 33, ATs+, ATo+ }
EV for check-calling a shove: $0.10 = ($49.15 * 0.312) + (-22.15 * 0.688)EV for check-calling $10 (I'm going to assume he always calls on the river when we hit since he'll be getting odds): $8.45 = ($49.15 * 0.312) + (-$10 * 0.688)EV for check-check (I'm just going to guess he'll call 70% of the time if we put him in on the river and we'll be good. It may be optimistic/incorrect). $19.16 = ($49.15 * 0.312 * 0.70) + ($27 * 0.312)EV for checking: $2.84 = ($0.10 * 0.8) + ($8.45 * 0.10) + ($19.16 * 0.10)EV for a shove: $6.04 = ($27 * 0.22) + ($49.15 * 0.312) + (-$22.15 * 0.688)I know your math is a lot better than mine so please let me know if I've made any mistakes (I probably have).
Because getting it in on the turn is pretty much 0EV, it makes it easier to ignore those in the calculations. It's pointless and equates out. 10c won/lost either way is going to be destroyed for accuracy when you take into account the rake anyway. BTW, I used a lot of rounding in my equations so they aren't as precise.With those figures you used (22% fold equity, 10% check back, 80% shove, 10% small bet, 70% pay-off when checked), shoving is $3.2 better than checking. That does assume that he is shoving 80% of his range on the turn given the chance, and it assumes he folds 22% of the time. I think both of those are quite high tbh.I think the numbers you have given are for one of the worst case scenarios.One thing that you didn't take into account is that KK shoves preflop usually, and that TT-KK aren't as likely to call the flop bet as an ace. I think you need to weight the range a little more to hands like AT-AK.

#28 AcesUp46

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Posted 24 August 2008 - 06:36 AM

So basically, the outcome of all the math calculations is that it's can't be too wrong to just open shove turn, right?

#29 simo_8ball

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Posted 24 August 2008 - 06:38 AM

View PostAcesUp46, on Sunday, August 24th, 2008, 3:36 PM, said:

So basically, the outcome of all the math calculations is that it's can't be too wrong to just open shove turn, right?
I think you've missed the point of this discussion.Shoving is good. There's no question about that. The question is, how good is check/calling? Is it a clear shove, or is there a strong case for check/calling?

#30 Giggidy

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Posted 24 August 2008 - 06:48 AM

View Postsimo_8ball, on Sunday, August 24th, 2008, 12:56 AM, said:

Ok, going for pretty much a worst case option for checking, and quite good for shoving:Suppose it's 30% fold equity from a shove,That's 0.3x27 = +$8.1 from shoving.When checked to, villain will check behind 10%, bet $10 10% of the time, and shove 80%. He will pay off a river shove 50% of the time when he checks behind and 100% of the time when he bets $10.P(check) x [ P(Payoff)x$22 + $27 ] + P($10 bet) x $8.9 = Equity.1 x [ (.32x.5)x22 +27 ] + .1 x $8.9= $3.1 +0.9 = $4.Worst case scenario for checking is about $4 worse than shoving.With David's numbers we are about $3.75 better by checking.I think it will work out to be a pretty close run thing.
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#31 trussdude

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Posted 24 August 2008 - 11:38 AM

What if both stacks are 400 bbs deep?I was in the same situation in a hand yesterday.

#32 Snamuh

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Posted 24 August 2008 - 05:21 PM

Explain how calling is not -EV?We need to be at least 31.7% to win (I accounted slightly for rake) according to pot odds. Our equity according to the shoving range you gave him is 31.2% We aren't getting the odds to call? That makes it -EV?????
Snamuh raises to $76.75, and is all in
BigKamp: yyou lose
BigKamp has 15 seconds left to act
BigKamp calls $24.50, and is all in
Seat 1: BigKamp (small blind) mucked [Ad Ac] - a full house, Aces full of Kings
Seat 2: Snamuh (big blind) showed [Kd Kh] and won ($102.50) with four of a kind, Kings
Snamuh: you lose

#33 simo_8ball

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Posted 25 August 2008 - 12:56 AM

View PostSnamuh, on Monday, August 25th, 2008, 2:21 AM, said:

Explain how calling is not -EV?We need to be at least 31.7% to win (I accounted slightly for rake) according to pot odds. Our equity according to the shoving range you gave him is 31.2% We aren't getting the odds to call? That makes it -EV?????
Check/calling a shove is pretty much neutral. Just like if we shove and he calls.Oh, and if check/calling a shove is -EV, then we check/fold to a shove. It's pretty simple.

#34 simo_8ball

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Posted 25 August 2008 - 01:31 AM

Snamuh, you've argued strongly that "turn shove >>>>>>>>>>>>>>>>>>>>>>>>> check/call" but you haven't given any numbers.If you can give some rough figures (or ranges such as 'folds 15%-35% of the time to a turn shove') that you think are realistic, they can just be put into the equations and it tells us which line it better and by how much. If you give ranges I can get upper and lower limits of each line.1) What % does he fold to a turn shove?2) What % does he check behind on the turn if checked to?3) What % does he bet something like $10 on the turn if checked to?4) What % does he shove the turn if checked to?5) What % does he call the river given that he checks behind on the turn?David Nicoson's numbers show that check/calling is better. Other numbers show that shoving is better.

#35 Deftones150

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Posted 25 August 2008 - 06:49 AM

Where can I look to find all these equations and explanations
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#121656 (33) - 02/24/2009 at 6:01am by secret123 - misc - I agree, your life is f***ed (5965) - you deserved

#36 simo_8ball

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Posted 25 August 2008 - 06:50 AM

View PostDeftones150, on Monday, August 25th, 2008, 3:49 PM, said:

Where can I look to find all these equations and explanations
In the posts above.edit: I'm not sure what you mean. I've done the equations in my above posts. Admittedly they may not be too easy to follow, but the equations are all written out.

#37 Deftones150

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Posted 25 August 2008 - 10:12 AM

Sorry I wasn't specific. I meant the general equations (a+b=c) and how they were derived and the person that formulated them. I'm better at using equations when I can look at all that. I can follow your but when I try to use them myself I will probably get lost (just like every statistics test I didn't study for).
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#121656 (33) - 02/24/2009 at 6:01am by secret123 - misc - I agree, your life is f***ed (5965) - you deserved

#38 David_Nicoson

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Posted 25 August 2008 - 03:06 PM

I hope everybody realizes I pulled those percentages out of my ass.
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#39 simo_8ball

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Posted 25 August 2008 - 03:16 PM

View PostDavid_Nicoson, on Tuesday, August 26th, 2008, 12:06 AM, said:

I hope everybody realizes I pulled those percentages out of my ass.
It's pretty difficult to work out those figures accurately, so rough educated guesses are as good as we can get without very specific reads.All I wanted to show is that it is actually a close decision, and hopefully I've pretty much done that.

#40 Snamuh

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Posted 25 August 2008 - 04:09 PM

View Postsimo_8ball, on Monday, August 25th, 2008, 4:56 AM, said:

Check/calling a shove is pretty much neutral. Just like if we shove and he calls.Oh, and if check/calling a shove is -EV, then we check/fold to a shove. It's pretty simple.
To be honest Simo, I don't spend time doing these complex calculations. I go with my intuition. And in a spot like this, if the decisions are close, I'd rather go with the more aggressive choice because even if it's slightly lower EV in the moment (which I don't believe it is), it's higher EV for overall gameplay because shoving the turn with hands like this will get you paid off with your other hands a lot easier.That's something you can't measure. If you get him to fold here, he's pretty much not going to fold a close decision next time (when you ideally have a stronger hand). It's how I get paid off in 3bet pots. Not every move needs to be +EV in the moment, but I guarantee it's more +EV for your session to shove turn here than to check/call.
Snamuh raises to $76.75, and is all in
BigKamp: yyou lose
BigKamp has 15 seconds left to act
BigKamp calls $24.50, and is all in
Seat 1: BigKamp (small blind) mucked [Ad Ac] - a full house, Aces full of Kings
Seat 2: Snamuh (big blind) showed [Kd Kh] and won ($102.50) with four of a kind, Kings
Snamuh: you lose




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