How often do you pull something like this?

[Aaron W.]

[ QUOTE ]
No reads on UTG - he just sat down and posted. BB has been around for a short while and is a bit fishy.

Party Poker 0.50/1 Hold'em (4 handed) FTR converter on zerodivide.cx

Preflop: Hero is SB with 4[img]/images/graemlins/diamond.gif[/img], 4[img]/images/graemlins/spade.gif[/img]. UTG posts a blind of $0.50.
UTG (poster) checks, Button calls, Hero completes, BB checks.

Flop: (4 SB) A[img]/images/graemlins/heart.gif[/img], 6[img]/images/graemlins/club.gif[/img], 3[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(4 players)</font>
Hero checks, BB checks, <font color="#CC3333">UTG bets</font>, Button folds, <font color="#CC3333">Hero raises</font>...

[/ QUOTE ]

Villains folded, Hero takes down the pot. I had planned to fold to a 3-bet, bet-fold the turn, and check-fold the river if I was only called on the turn.

This was the first time (as far as I can remember) that I've pulled this play without a read and without a solid reason. It made me wonder if there was ever a good time to check-raise the flop with nothing in short-handed games.

If villains fold outright, then I've invested 1 BB to win 2.5 BB and this needs to work about 29% of the time.

If only UTG calls and if he calls all the time -- then when I lead the turn, I've invested 2 BB to win 3 BB, so I must take it down by the turn bet 40% of the time to show a profit.

It looks bad when framed that way, but is it possible for a combination of the two to lead to profit?

Suppose the probability villain folds immediately is X and the probability that he calls the check raise and folds on the turn is Y. What is the relationship between X and Y to make money? (Ignoring flop 3-bets for now)

EV = X*(+2.5) + (1-X)*Y*(+3) + (1-X)*(1-Y)*(-2)
= 2.5*X + 3*Y - 3*X*Y - 2 + 2*X + 2*Y - 2*X*Y
= -X*Y + .5*X + Y + 2

So we want EV &gt; 0. A little bit of algebra and this inequality becomes

Y &gt; .9 - .5/(1-X)

Rather than try to figure out a way of graphing it and pasting the image onto this post, I'll just make a table. If X is some value, what is the smallest Y can be for this to still be profitable?

<font class="small">Code:</font><hr /><pre>X = .. | Y &gt; ..
.00 | .40
.10 | .34
.20 | .275
.30 | .19
.40 | .07
.44 | .00</pre><hr />

Anyone care to speculate how often villain folds to a check-raise here? In other words, how often is villain betting at the pot with basically nothing? I don't know the answer and I don't have anything *CLOSE* to a guess.

But it's been my experience that villain folds 100% of the time to this check-raise... [img]/images/graemlins/grin.gif[/img]