# Tying the pot and EV of a poker hand

Just recently heard of the concept of Expected Value of a hand. This guy explained it well: https://www.youtube.com/watch?v=jiPmaif9szQ But there is still one case he hasn't looked at. It is a split pot. So, it just so happens that in the case he imagined, he could've won 13\$ (opponent's bet), could've lost 11\$ (which he would've placed to try to win the pot), or they could've split the pot, resulting in neither winning nor losing, in this case. But it could be a case, where drawing would result in a much higher EV, than 0. Calling 10\$ and drawing would mean, for example, tying a pot of 40\$, so it's way better than not calling. Is there a way to include the draw part in this equation?

EV is calculated as a sum of outcome * probability.

As an example, lets assume you are in a hand where you have a 50% chance of winning, 5% chance of chopping, and 45% chance of losing. Both you and your opponent went all in for \$100 preflop and the pot is \$200.

The EV calculation would be: (\$100 * .5) + (-100 * .45) + (0 * .05) = \$5

where the dollar amounts are the outcomes and the decimals are the probability of the outcome.

As you can see, the chop does not change the EV calculation because the outcome is a gain of \$0. If there were other players blinds in play there would be a little bit more than 0, but it would be so small that it would barely change the EV. It is important to factor in the probability of chopping (in this example if it was 50/50 the ev would be \$0), but most of the time the probability of a split pot is so small that it isn't something that really needs to be taken into account.

• This example I get, yet still there are other situations. Assume, you've been playing till the river. Preflop - guys go \$1 each: pot is 6 bucks. Flop - three of the players go 2\$, three of the guys fold. It makes 12\$. River - a guy bets 5\$, you call, the third guy folds. 22\$. And here comes the river - and here comes a full house on the table, which makes your chances of splitting the pot EXTREMELY HIGH, yet no chance of winning, 'cause it's Aces full of Jacks on the table, and you sit on a pocket pair of Tens. And now your opponent goes all-in with the \$40 stack. What do you do? Apr 27 '20 at 20:09
• If it is Aces full of Jacks on the table, there are only 4 hands you don't chop with (Ax, QQ, KK, JJ). If you are very sure your opponent has one of those hands then you should fold, otherwise call. Apr 27 '20 at 22:31
• @winwin There is only one A in the deck and 7 combinations of other hands, if you call and lose it is a pretty bad beat but very hard to put anyone on those exact hands. Apr 27 '20 at 22:35