30/60 vets: Postflop estimate

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I haven’t done this kind of math in ten years so if the math guys could correct any mistakes in results (or notation if they feel like it).
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What I find difficult is there seems to be an inverse relationship between the size of the pot and the chance my middle pair is good. Unless the player is a complete newbie h/she has experienced that when pots get big, players don’t fold as much. Therefore bluffs work less often in big pots. So that’s always in the back of a player’s head during a hand. Players may ignore that from time to time but on average they don’t ignore the fact that players call down in big pots.

And in small pots I’m really not calling down/raising much in the scenario given because I don’t have odds. Recap:
The game is 30/60 online. Assume you have raised an UTG+1 limper with JJ in LP. BB calls, UTG+1 calls.

Flop is A96 (barely coordinated and contains an Ace, rainbow)
You bet BB folds and UTG+1 check-raises.

UTG is not a maniac. What percent is JJ good here if UTG+1 is:
A) LA
B) LP
C) TA
D) Player is new to you

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As stoxtrader pointed out you can’t look for a rule to apply to all situations. However, I’m often folding in that spot and I’m wondering if this might be a mistake.

I’m getting 9.5:1 after my opponent check-raises. Let’s use Windsor Kid’s 25% number vs. an unknown.
I’m winning
JJ is currently leading = CL(x)
Opponent sucks out = OS(x )
I win when leading = WWL(CL(x) * [1-OS(x)])
I’m losing
I suckout = IS(x)
I win = W(WWL(x) + IS(x))
I lose = L(1-W(x))

When I am ahead: So we estimate 25% of the time JJ is good. Of those times opponent will suckout between 20-25% given the hand range I input into twodimes. If opponent has specifically 78 then their suckout % is between 34 and 37 % depending on the suits. So for simplicity sake lets use 25%. Note: I excluded no-draw, no pair hands because I’ve excluded the Opponent classification of maniac from my original post. Though something like KQ isn’t out of the realm of possibility for simplicity’s sake I’ve excluded it. Ok……so when JJ is good it will only stay good 75% of the time meaning I will win 18.75% of the time when leading..
CL(.25) * [1- OS(.25)] = WWL(.1875)

When I am behind: I am ruling out AA altogether based on the action. Every other hand I will suckout out on about 9% of the time, except for AJ which cripples my outs so I’ll shade 9% down to 8.25%. So my total chance of winning the hand when I am behind or leading is 27%.
WWL(.1875) + IS(.0825) = W(.27)
L(.73) = I lose

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Let’s assume in the hand that I always call down. And again for simplicity’s sake let’s assume opponent bets turn and river and I call. The pot would be 9.25 BB’s.

I win (.27 x 9.25 BB’s = 2.565 BB’s)
Since the question is: “Should I continue when I am check-raised on the flop?” the money already in the pot is not part of the equation. It’s gonzo. When I lose, I calculate only the money I put in the pot after I’m check-raised which equals 2.5 BB’s.
So I lose (.73 x 2.5 BB’s = 1.825 BB’s)

Total: +2.565-1.825= +.74 BB’s

I didn’t think an estimate that 25% of the time I’m good with JJ would be so clearly profitable to continue. So that’s a little eye opening for me.

Using the above calculations the breakeven point is ~ 17.25%.


If applied to a different scenario, a larger pot I think it becomes much more interesting because as I mentioned the opponents bluffing percentage goes down. Let’s say I there is another limper and the SB also called preflop.

I have JJ on the button. UTG limps , UTG+1 limps, I raise in MP. Blinds and limpers call. Pot = 10 SB’s. I bet the flop blinds fold UTG raises and UTG+1 folds. Now I’m getting 13:1 but it is more likely UTG has an Ace. Let’s say JJ is good here 15% of the time:
CL(.15) * [1- OS(.25)] = WWL(.1125)
WWL(.1125) + IS(.0825) = W(.1925)
L(.805) = I lose
I win (.1925 x 11 BB’s = 2.145 BB’s)
I lose (.8075 x 2.5 BB’s = 2.01875 BB’s)
Interestingly that’s close to breakeven.

When you factor in:
A) those times your opponent checks the turn or river
B) those times you can value bet
C) positive image reinforcement
D) information gained from seeing your opponents hand
I guess this really isn’t all that close.

Anyway this may be basic stuff for most but thought I’d share since it was a helpful exercise for me (assuming the calculations are correct).

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Very very interesting. This goes to show how it is not always about direct pot odds and the chance of you making your hand when behind. Never would have thought it is such a profitable situation, with your hand being good only 25% of the time. This call down strategy has something going for it; no wonder the fish can do so well [img]/images/graemlins/tongue.gif[/img]

[Vic Ferrari]

I wouldn't have thought that either. My gut says 17% is too low for a breakeven point. But your calculations seem fine. However, I'm not a NASA engineer.

[disjunction]

Hi, I only skimmed quick, but where you get IS = 8.25%, don't you have to multiply by .75? I didn't see that anywhere. That would affect your numbers and breakeven point a little bit.

Apologies if I missed something. Nice analysis.

[Robb]

[ QUOTE ]
Poster: disjunction
Subject: Re: Thoughts (long)

Hi, I only skimmed quick, but where you get IS = 8.25%, don't you have to multiply by .75?



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from here:
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When I am behind: I am ruling out AA altogether based on the action. Every other hand I will suckout out on about 9% of the time, except for AJ which cripples my outs so I’ll shade 9% down to 8.25%.

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My chances of hitting a Jack on the turn or river is 8.8% I think, except when my opponent has one of my Jacks like when he has J9. Then my chances are about 4.3%. So I just ballparked it down from 9% (or precisely 8.8%) to 8.25%.

[tallstack]

I think you may have an error in one of your calcs.

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Let’s assume in the hand that I always call down. And again for simplicity’s sake let’s assume opponent bets turn and river and I call. The pot would be 9.25 BB’s.

I win (.27 x 9.25 BB’s = 2.565 BB’s)
Since the question is: “Should I continue when I am check-raised on the flop?” the money already in the pot is not part of the equation. It’s gonzo. When I lose, I calculate only the money I put in the pot after I’m check-raised which equals 2.5 BB’s.
So I lose (.73 x 2.5 BB’s = 1.825 BB’s)

Total: +2.565-1.825= +.74 BB’s

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If the current pot is 9.5 SB's (4.75 BB's) then isn't the amount you can win in a showdown with your opponent betting to the end (excluding what you have to put in yourself) 6.75 BB's? The rest of your pot is your own money that you haven't put in yet before this decision. For the amount that you win, I would think it should be:
I win (.27 x 6.75 BB's = 1.8225).

With the net result:

Total: +1.8225 - 1.825 = -.0025 BB's

I think you can alternatively include the money you put in for your win case if you consider that you pay the 2.5 BB's win or lose (not just the .73 of cases).

I win (.27 x 9.25 BB's) - 1.00 x 2.5 BB's = -.0025 BB's

If I have pooched these calcs myself then please let me know.

Dave

[willie24]

a)25
b)5
c)28
d)22

fyi i have no statistical basis for this. i thought the question was fun though.

also i took the question to mean- what is the chance that JJ is good at showdown...

obviously neither my answer, nor anyone else's is that important, as TAs and LAs and TPs don't necessarily group neatly with others of their like for this issue.

also the question is extremely dependant on your opponent's perception of you

[theBruiser500]

For stoxtrader, 14:5 are the odds I get calling down the whole way. It's a lot worse than I would have thought.

[Robb]

Duh. Thanks Dave. The right side of the pot odds ratio is the amount I have to put in and I don't include that in the left hand side of the ratio.

[ QUOTE ]
If the current pot is 9.5 SB's (4.75 BB's) then isn't the amount you can win in a showdown with your opponent betting to the end (excluding what you have to put in yourself) 6.75 BB's? The rest of your pot is your own money that you haven't put in yet before this decision. For the amount that you win, I would think it should be:
I win (.27 x 6.75 BB's = 1.8225).

With the net result:

Total: +1.8225 - 1.825 = -.0025 BB's

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So that's close enough to zero that our original estimate of 25% that JJ is good also happens to be the breakeven point. So against certain types clearly not correct to call and against others clearly so.

[stoxtrader]

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For stoxtrader, 14:5 are the odds I get calling down the whole way. It's a lot worse than I would have thought.

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This is the number that I use (I got 13.5 : 5), and I've never been really sure about this math, but it helps me to sit there and think

1. is this the type of player who could make this play on a complete bluff?
2. is there a draw out there where he may be more likely to do this?

also remember to factor in the fact that you may improve.

[DeeJ]

Your percentages don't add up to 100 [img]/images/graemlins/blush.gif[/img]

Seriously though, I'd put the odds at
Loose Aggressive : 35%
Loose Passive : 5%
Tight Aggressive : 25%
Unknown : 25%

See, my numbers don't add up to 100 either [img]/images/graemlins/grin.gif[/img]