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.

<font class="small">Code:</font><hr /><pre>
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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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[randomstumbl]

The bigger question than the math is what Villian is going to think you have. It took me awhile, but I realized that almost no one checkraises here without a wheel.

So, against a smart player, you're killing the action. He can't 3 bet, he shouldn't call and draw. No one checkraises without a wheel in this situation.

Against a LAG, who'll bet 3/4 of the time or more, you might as well just checkraise and bet out.

The game theory optimal solution is not worth thinking about because there aren't close decisions. You're giving out a ton of information by checkraising. You just can't use it unless you're against an aggressive opponent who you'd checkraise in this situation with more than just a wheel.

[MarkGritter]

[ QUOTE ]
The bigger question than the math is what Villian is going to think you have. It took me awhile, but I realized that almost no one checkraises here without a wheel.

So, against a smart player, you're killing the action. He can't 3 bet, he shouldn't call and draw. No one checkraises without a wheel in this situation.

Against a LAG, who'll bet 3/4 of the time or more, you might as well just checkraise and bet out.

The game theory optimal solution is not worth thinking about because there aren't close decisions. You're giving out a ton of information by checkraising. You just can't use it unless you're against an aggressive opponent who you'd checkraise in this situation with more than just a wheel.

[/ QUOTE ]

I would be happy checkraising with a #2 as well and probably anything up to #5 here. Yes, without a wheel it is possible that Villian is drawing to beat me, but I think it's worth getting the extra bet in if possible. Villian is also unlikely to raise the river with anything but a wheel, so in the cases where he beats me I am usually putting in the same number of bets anyway.

[randomstumbl]

Rereading my post, I really oversold my point.I'm not sure of what the indifference points are and they'd probably be interesting. Still, I think it's more important to be able to use this sparingly when you're fairly sure your opponent enjoys betting light in position.

The bigger issue is how checkraising in this spot will affect your opponent in this hand and later hands.

On this hand, you're getting either 2 or zero BB now and vastly decreasing the chance that you'll get paid off on the river. So, checkraising is only worth it if you're fairly certain your opponent will bet and call a majority of the time.

In later hands, your opponent is probably going to remember that you like to checkraise your best hands. So, it's important to use a mixed strategy against thinking opponents. You can probably get a big benefit from playing your roughest pat hands using the same betting pattern if you're going to attempt to checkraise with your best hands.