33 flops second pair, so I raise...

[bottomset]

^ i don't think thats the right approach Tom

if he has 99-AA he's a 95% favorite, and will win 2bets from you if you just call,call .. 3bets if you 3bet, call there are 33combos of those hands

if he has AK,AQ(32combos) you win 87% of the time prob 2bets, but lose 2bets 13% of the time

both scenarios are about equally likely, honestly the only possible way to make this play is if you are sure he'd still do the turn c/r with AJ, KQ so you would be 2/1fav overcards vs pair

I didn't work all the math out, but im pretty sure its -EV both calling the c/r and 3betting

also if you plan on folding to any A,K,Q on the river the play is for sure -EV

[KingOtter]

[ QUOTE ]
Pocket overpair 99-AA: 6/221 = 2.7%


[/ QUOTE ]

Where'd you get this number 6/221?

The reason I ask is because it looks like you're using a 'combinations number' (220 possible combinations to make pairs), but only counting 1 combination of each pair.

Which, at the end of the hand there are 6 ways to make AA, KK, and JJ, and 4 ways to make 99 and QQ... so 26 ways, 26/220, more than 10%.

Edit: Hmm... reading further elsewhere I think I'm way off... but I wanted to make sure you're counting all combinations and not just each pair. But I like bottomset's approach better.

KO

[TomBrooks]

[ QUOTE ]
Where'd you get this number 6/221?

[/ QUOTE ]
The chances of being dealt any given pair such as AA or TT are 1 in 221. The chances of being dealt any of the 13 possible pairs are 13/221 or 5.9% or 1 in 17 or 16:1. The chances of making any of 6 chosen pairs are 6/221 = 2.7%

[ QUOTE ]
Edit: Hmm... reading further elsewhere I think I'm way off. But I like bottomset's approach better.

[/ QUOTE ]
Otter,
If you count the combinations you have 6 ways of making each pair. So for 6 pairs there are 36 ways to make them. But then you do not divide by 221, you divide by the number of all possible starting combinations. I think that is 1269 combinations but I am going from memory, may be off, and I couldn't find it written anywhere. But if it is 1269, divide 36/1269 = 2.8%.

bottomset's approach uses the betting pattern to try to decide if villian already has a pair or only has overcards. My simplified approach assumed one would ignore the betting pattern and just go by the percentages. I believe this will correctly predicts how often you will win. But you might win small pots 71% of the time and loss big pots 29% of the time with this method.

I haven't thought carefully about that part yet, but it would depend largely on how willing your opponent would be to bet/call/raise with just overcards. I think most opponents wouldn't raise with them but would raise with a pocket pair, so if your getting raised or checkraised I think you're usually in trouble.

[KingOtter]

Okay... I don't deal with those kind of calculations much... I've verified that part.

But... aren't you making the scope too big? You say 'Assuming he will raise with 99-AA or any two overcards' but then take the percentage chance of him holding 99-AA from all hands, not just raising hands.

So if he raise with AK, AQ, AJ, or KQ... each one of those is 16 ways. Assuming 6 ways per pair, 36 ways to make a 99-AA pair. 16x4 = 64 + 36 = 100 hands he would raise with.

36% chance that once he raised he had a 99-AA (he raised, he must have a raising hand).
13% to make a pair on turn with AK, AQ, AJ, or KQ.
13% to make a pair on river with AK, AQ, AJ, or KQ.
---
62% chance villain prevails.

No?

KO

[chesspain]

[ QUOTE ]
You say 'Assuming he will raise with 99-AA..."

[/ QUOTE ]

Actually, if he is a solid player, he likely is also openraising with 88 after two folders.


[ QUOTE ]
So if he raises with AK, AQ, AJ, or KQ... each one of those is 16 ways.

[/ QUOTE ]

I'ld also include the four combinations of KJs.

Consequently, assuming 6 ways per pair, 42 ways to make a 88-AA pair. [16x4 = 64] + 4 + 42 = 110 hands with which he would raise.

At the very least, then, we need to realize that there is approx. a 38% chance of our opponent having an overpair, which I would not consider to be "slim" odds. Secondly, when we are behind, we are drawing to two outs (or runner-runner for the str8), and when we are ahead, our opponent is drawing very live to six outs, without our knowing which two overcards we need to dodge.

But I guess that none of this matters when one is hell-bent on reading an opponent for having only the cards that don't dominate us. [img]/images/graemlins/smirk.gif[/img]

[TomBrooks]

Hi chesspain,

I just realized a giant flaw in my simplified calculation. I took the six top pairs to represent 2.7% of what he might be holding because there is a 2.7% chance of being dealt those cards. But since he doesn't raise with any two cards, the fact he raised makes that statistic useless. [img]/images/graemlins/crazy.gif[/img]

Continuing with your calculations.

Chance of Overpair: 38%
Chance Overcards spike a pair on turn: 13%
Chance Overcards spike a pair on river: 13%

minus

Hero spikes trips on turn: 4.3%
Hero spikes trips on river: 4.3%
Hero makes backdoor straight: 3% (approx. I think)

Villian wins: 38 + 13 + 13 - 4.3 - 4.3 -3% = 52%
Hero wins: 48%

But when you factor in the betting, Villian's stands to win more when he's ahead and loss less when he's behind because he can check/call while he drawing, check/fold the river when he misses and bet/raise/checkraise any street when he hits. Hero can guess that 62% of the time he is ahead on the flop, but the 89% of the time he doesn't make trips or a straight, he is not sure which times fall into that 62%. Hero's equity can go up on the river with a low card that doesn't make a straight to about 68% 62+13-4-3. Overall though, I think hero stands to lose more when he's behind and make less when he's ahead.

Revised assessment: <font color="red">Fold Pre-flop. Fold Flop.</font>

[Aaron W.]

[ QUOTE ]

Chance of Overpair: 38%
Chance Overcards spike a pair on turn: 13%
Chance Overcards spike a pair on river: 13%

minus

Hero spikes trips on turn: 4.3%
Hero spikes trips on river: 4.3%
Hero makes backdoor straight: 3% (approx. I think)

Villian wins: 38 + 13 + 13 - 4.3 - 4.3 -3% = 52%
Hero wins: 48%

[/ QUOTE ]

You shouldn't be adding those percents. The probably of a six outer improving by the river is not 26%.

The probability is given by

1 - (Probability of missing twice)
= 1 - (1 - (6/45))*(1 - (6/44))
= 1 - (39/45)(38/44)
= 25.1%

The reason why it only seems like a tiny error is that you didn't use all of your information above. It looks like you got the 13% number by taking 6/47 = 12.7% and 6/46 = 13.0%, ignoring the fact that you know which two cards he's holding. The correct numbers should be 6/45 = 13.3% and 6/44 = 13.6%

Conceptually, your mistake comes down to a "miscounting" of the possibilities.

You have a 13.3% chance of hitting the card on the turn. On these times, it doesn't matter what the river is. Of the 86.7% of the time you miss on the turn (*this factor is what is missing*), you have a 13.6% chance of catching the card on the river.

To do it your way, you want to have .133 + (.867*.136) = .133 + .118 = .251

[TomBrooks]

Hi Aarron, I was just rounding it out roughly, but it's good to see how to do it correctly. Thanks.