Bottom trips...worth capping? 1/2 LO8

[GrahamW]

I'm still a relative O8 beginner, but I would cap it on the flop for sure. You have trips and a backdoor draw to the nut low with counterfeit protection. The turn I'm not so sure about.

[Phat Mack]

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3/2/44 you scoop. +4.5 for you.

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3/2/44 is the same as saying 1.5/44, correct? (for the .5 times the A hits and he scoops...)

[Buzz]

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3/2/44 is the same as saying 1.5/44, correct? (for the .5 times the A hits and he scoops...)

[/ QUOTE ]Hi Mack - Yes. Exactly.

There are three aces in the stub. Villain's betting represents a flopped full house. But of course it's possible Villain doesn't actually have a full house, and that turns out to be the case here.

An expert player might semi-bluff with only trip sevens. A novice might simply overplay trip sevens (as here).

Assuming Villain has flopped a full house it's either 99977 or 77799, and with three nines and one seven unseen, very roughly equally likely to be either.

9997 1 way
999X 1*41 = 41 ways
997X 3*1*41 = 123 ways
99XY 3*41*40/2 = 2460 ways
97XY 3*1*41*40/2 = 2460 ways.

Because of some overlap, Villain is slightly more likely to have been dealt a hand that would make nines full than a hand that would make sevens full. But Villain's probably not playing any of the first three possibilities listed above. Thus there are about 2460 ways Villain could have either full house. That's out of 148995 possible hands Villain could have been dealt. So it's almost 30 to 1 against Villain having a full house. However, Villain is betting as though having a full house, and accordingly, I think Hero should exercise a modicum of restraint on the turn and not raise.

But at any rate, since Hero wins high if the river is an ace only if Villain has 77799, Hero figures to win high (continuing to assume Villain has a full house) half the time when the river card is an ace and lose the other half of the time when the river card is an ace (and when Villain has 99977).

So I divided 3 (for the three aces) by 2 and typed it as 3/2. As I think about it, I might have made my meaning clearer by putting the 3/2 inside parentheses.

Buzz