EV Calcs - Channeling my inner nerd
This entry is taken from a post I made on CardRunners.com. In that thread, Lou asked if he should call a big overbet on a draw with one card to come. Based on a lot of the responses, it was clear people were missing some things about pot odds and EV, so I made the following post.Ok, let's talk a little bit about EV calcs and pot odds here. Earlier there was horrendously false statement by someone to the effect of "you should never get your money in as an underdog". Hopefully by the end of this post, you'll see how absolutely silly that is.
Let's first start with my original "of course" example in my earlier post. Why is it my example an "of course I call!" example? In that scenario we're 45% to win. There's $999 in the pot and $1 to call. So what's our EV of call or fold? (you can't raise me, because I'm all in for my last $1).
EV(fold) by definition is 0. You lose/gain nothing more.
In English:
EV(call) = (the amount you get when you have the best hand) minus (the amount you invested when you dont end up with the best hand). We've stated that we're 45% to win.
In math terms:
EV(call) = (45% * $1000) - (55% * $1) .... again just so we're clear this can be read as, 45% of the time you make $999(pot) + $1(my bet) and 55% of the time you lose $1(your call)
EV(call) = $450 - .55 = $449.45, which means your expected value on the $1 call is $449.45.
Duh Wilt, I told you of course I call!
So to answer the second question I posed above, if I'm pushing in with my $1 and my 55% equity, I'm PRAYING you fold, because then I'd win $999. If you call, then I win on average $1000 - $449.45 = $550.55. Again, even though I'm a favorite at 55%, I'm hoping you fold. This should be sooooo obvious, but you'd be shocked how many people screw this up!
So now on to your real example:
Just so we're all on the same page, here's the hand and numbers that I've pieced together from Lou's posts:
We're oop on the turn with 5c6c and the board reads Jx 4c 7c 5x. There's $220 in the pot, and we check. Villain shoves and it's $550 for Lou to call.
We've stated that we have 46% equity in this hand. There's $220 in the middle and it's $550 more for us to call. So that means we need to call $550 to win $770 (note, we don't add our own call into the amount we "win", think of it as we invest X to win Y).
So, same as above:
EV(call) = 46%($770) - 54%($550)
EV(call) = $354.20 - $297
EV(call) = $57.20
We expect to make $57.20 on average when we make this call.
So you might say, gee Wilt, how the hell am I supposed to do this at the table?
Well, the answer is two fold.
1) You should be practicing some of these EV calcs on your own in different scenarios to get a better feel for it
2) You can do a bit of fudging the numbers to make it a bit easier.
46% is close to 50% right? What pot odds would you need for 50% equity? The answer is 1:1 would be break even. You put up 1 to win 1. You break even if you win 1/2 of the time. So, when he bets $550 and we're about 50/50 to win, we know we can call because there's dead money which makes the pot odds on the call 1:1.40 (or, while we're sweating at the table wondering what to do, we know we're better than 1:1 on our call)
So now the question is, how much would he have to bet for this call to be - EV? To figure this out takes a little more work, but it makes sense when you think about it in English terms. For the math all we have to do is substitute X in for what we call, then solve for X where the total is zero. If it's zero, then we know any more than X would be - EV and any less would be +EV. Make sense?
English: 46% of the time and we win his bet(X) + the pot(220) and 54% of the time we'll lose what he bets (X)
In math terms:
0 = .46(220 + X) - .54(X)
.54X = 101.20 + .46X
.08X = 101.20
X = $1265
So this means that he would have to bet $1265 into a $220 pot for our call to be break even.
Let's check our work. If he bets $1265 into a $220 that means we have to call $1265 to win $1485. So let's set up our EV calc again for practice.
EV(call) = .46(1485) - .54(1265)
EV(call) = 683.10 - 683.10
EV(call) = 0
Looks like we were correct! Anything more than his $1265 bet, and we couldn't call profitably. Anything less is a profitable call. Surprise you? This means that our decision here of calling $550 isn't particularly close, as he could bet more than double that and we'd still be correct to call.
It's also worth noting that the image considerations will net you some EV too. Many people (as evidence by this very thread) won't realize this is an easy call. They say/think "WHAT? YOU CALLED ON A DRAW! YOU PUT $ IN THE POT AS AN UNDERDOG? LOL FISH!" I'd bet they'll think twice the next time they want to try to run a big bluff on you "LOL THAT DONKEY CALLED $550 WITH A PAIR OF 5's LAST TIME!"
Something to think about.
Aaron
posted by WiltOnTilt at 10:38 AM
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