TD 2-7: check-raising the 3rd round

[MarkGritter]

Normally I would bet here, because I expect Villian to let it get checked through. But Villian is the type of player who hates doing that with position. He even raised me on the second round drawing one. So I feel pretty confident Villian will bet here.

How often does Villian have to bet for my check/raise to become profitable?

Let's ignore cases where Villian has a strong made hand, in which case it really doesn't matter what I do, a lot of bets will go into the pot anyway. I will also ignore any raises on the 4th round.

If Villian is pat here he will bet and probably call another bet on the river. Say there is 30% chance of this. My win here is 3BB.

If Villian is not pat then he is about 30% to make a pat hand and will call a 4th round bet (maybe raise a 7, let's ignore that for now.) In this case he bets N% of the time, we want to solve for N.

EV[check] = 0.3*3 + 0.7*(N*(2 + 0.3*1) + (1-N)*0.3*1)
= about 1.4N + 1.1

If I bet (and Villian will almost certainly call), then Villian will call a second bet on the river about 30% of the time or more.

EV[bet] = 1 + 0.30*1 = 1.3

check > bet if
1.4N + 1.1 > 1.3
1.4N > 0.2
N > 0.14

I think the odds vs. this opponent are way higher than that, especially considering the chances of him attempting to bet with a T or J should be factored in as well.

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$1/$2 Triple Draw 2-7 at UltimateBet

A is at seat 0 with $48.75.
B is at seat 1 with $168.75.
Villian is at seat 2 with $70.50.
D is at seat 3 with $87.
Hero is at seat 4 with $88.75.
The button is at seat 2.

D posts the small blind of $.50.
Hero posts the big blind of $1.

Hero: Qh Ad 7h 5h 2d

First Round:

A folds. B folds. Villian raises
to $2. D folds. Hero calls.

Hero takes 2 cards. Villian takes 2 cards.


Hero: 7h 5h 2d 4h 5c

SeCond Round:

Hero bets $1. Villian raises to $2.
Hero calls.

Hero takes 1 card. Villian takes 1 card.

Hero: 7h 2d 4h 5c 3c

Third Round:

Hero cheCks. Villian bets $2. Hero
raises to $4. Villian calls.

Hero stands pat. Villian takes 1 card.

Hero: 7h 2d 4h 5c 3c

Final Round:

Hero bets $2. Villian folds. Hero is
returned $2 (uncalled).



Hand #8369047-1987 Summary:

$.75 is raked from a pot of $16.50.
Hero wins $15.75.
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