Thoughts (long)
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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