|
Here some math I've already done. The scenerio: It's folded to you in the SB with A5o. You accidently flip your hand over, and your opponent now sees your hand. You still wonder if you should shove, even knowing your opponent will only call if he is a favorite against your hand. Should you fold or should you shove?
Okay. So according to Sklansky - Chubukov Rankings, A5o has a number of 56.54. This is regarding a 1/2 game so effectively 28bb (56/2). This means if you have 28bb or less you can profitable shove even if he knows your hand. If you have 29+bb then you should fold (or at least don't push). Let's look at the math and see.
Okay assuming you have 28bb this is the math. If you shove, opponent is getting 1.05:1 pot odds (29.5/28), or 48.7%. Therefore, he needs at least 48.7% equity against your hand to be breakeven.
The only hand that has that much equity is [22+, A5s+, A5o+]. And this range is 16.7% of hands. Also, this ranges equity against our hand is 66.29%. With some math we get.
*we shove, they fold (profit of 1.5bb): [1 - .167] * 1.5 =1.2495
*we shove, they call, we win (profit of 29.5bb): [.167] * [1 - .6629] * [29.5] = 1.66
*we shove, they call, we lose (loss of -28bb): [.167] * [.6629] * [-20] =-2.21
*So: 1.2495 + 1.66 + -2.21 = 0.6995bb/hand
______________________________________________
Let's see what this is like with say 29bb, instead of the 28bb.
With 29bb, the BB is being offered 1.0517:1 pot odds, so he needs 48.74% equity. The range will still be the same [22+, A5o+, A5s+]. So we still have this as 16.7% of hands with an equity of 66.29% against A5o.
*we shove, they fold (profit of 1.5bb): [1 - .167] * 1.5 = 1.2495
*we shove, they call, we win (profit of 30.5bb): [.167] * [1 - .6629] * [30.5] = 1.7170
*we shove, they call, we lose(loss of 29bb): [.167] * [.6629] * [-29] = -3.2104
So: 1.2495 + 1.7170 - 3.2104 = -0.2439bb/hand
Assuming my math is correct there (which I hope it is) with even just 1bb over the number you will be making a -ev move. This is to say that if the blinds were say 50/100 and you have 2800 chips you could shove A5o into the bb, even if you showed him your hand. However, if you have 29bb if you do so you will be losing money over the long run.
|