Mathematic question about semi-bluffing in poker!

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Mathematic question about semi-bluffing in poker!

Hello everyone,

This is an assertion as much as it is a question.
I have a calculation but I'm not sure if I'm thinking right. Therefore, it would be helpful if other eyes can look at this and say if it is right or wrong. If that's wrong, I'd love to learn how to think about it instead.

We have 65 of harts and villain have AA without harts.
Flopp is KQ9 with two harts.
Therefore, we have a flushdraw on the flop without overcards and we have 37,5% chans of winning.

The pot is $1000 and the action is,
Villian bets $500 and hero shove all in for $2000.

We all know that if villian folds hero win $1000(pot)+$500(villians bet)=$1500
If he calls we loose $2000 but we can draw out on him therefore we only loose:

-- This is my calculation --
$2000(hero bet)+$2000(villian bet)+$1000(pot)=$5000
..37,5% is hero chans of winning when called..
$5000*0,375=$1875
$2000(hero bet)-$1875(getting back when called)=$125
-- End of calculation --

Now we can say:
If he folds we win $1500
If he calls we loose $125

So then,
1500/(1500+125) = .9

So if he calls 90% we’re breaking even. Any less and we’re in the positive.

I think im right but I really need to get lectured if im wrong.

Thanks to all that did take time to read this!

2 Comments

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Samu Patronen 6 years, 10 months ago

Looks right to me, BUT it's not all that useful in and off itself. Just because a play is +EV, it doesn't mean that we should do it. We would have to compare the EV of shoving to EV of calling in order to determine whether or not we should be shoving.

Kevin Rabichow 6 years, 10 months ago

The calculation is correct.

The way I would confirm that you're supposed to see such a high figure is to think about how much equity you would've needed to call a shove on flop (which is equivalent to the situation where villain never folds to your shove). That figure is easily calculated as 40% (call $2k to win $5k). You have 37.5% equity so clearly you will need very few folds to make this play break even.

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