Fold Equity - A Couple of Questions

[Alex Scott]

Hi guys,

I'm not a regular here, but I've come here because I respect the advice (don't let me down now!). I'm writing an article, which I'm hoping will be published in Inside Edge, about Fold Equity. There are a couple of things I'm not so sure about, but would like to get right.

1. Who came up with the term 'Fold Equity'? I've always assumed it was someone here at the 2+2 forums, and it must be fairly new because when I first started playing, nobody ever talked about it (and even the 'game theory expert' Chris Ferguson doesn't know what it is).

2. I'm a little stuck on the intricacies of the maths when it comes to a particular part of the article (I try not to get too bogged down in the maths, so I want to keep it simple).

My example centres around working out exactly how often we need our opponent to fold for a play to break even. The scenario is:

It's the last round of betting, and the pot is £100. Our opponent bets £50. We can raise all-in for £250 more, and for simplicity if our opponent calls, he'll always have us beat.

How much FE do we need to break even? How often does he need to fold for us to gain that equity?

I've worked it out myself, but basically I'd like to double check them before I submit the article.

Lastly, I'm making it a trend to include real life hands as examples illustrating the concept I'm discussing. So far I'm thinking about including some hands from this year's TOC, but if anybody knows any good examples of FE in action, preferably involving famous players, please share them.

Thanks for any help!

[SplawnDarts]

Ok, so the pot is 100 (not sure how to make a pound sign) and the flop action is opponent leads for 50. We're comparing two possible actions, namely a raise to 250 which our opponent covers, or a fold. The fold, as always, has an EV of 0. The raise costs you an additional 250 if he calls, and wins you 150 if he folds. So the EV of the raise is (P(fold) * 150) - ((1 - P(fold) * 250). The play is break even if it has the same EV as the fold, or 0. So we solve:

(P(fold) * 150) - ((1 - P(fold)) * 250) = 0
(P(fold) * 150) - 250 + (P(fold) * 250) = 0
P(fold) * 400 = 250
P(fold) = .625 = 62.5%


Alternatly, you can do the math via "odds" or ratio notation: we're risking 250 to win 150 (5:3), so we need himn to fold 250 times for every 150 he calls, or odds of a fold of at least 5:3. As a percent rather than a ratio, that 5/(5+3) or 5/8 or .625 or 62.5%. Luckily we got the same result [img]/images/graemlins/wink.gif[/img] I find the "odds" style computation to be much easier at the table.

[Alex Scott]

Well, I got 55%, but I have figured out where I'm going wrong, I think. I'm stupidly including the full size of the pot, including our 250 raise in the calculation, and I made a typo to boot. I'm glad I asked here.

Anyone get a different figure to 62.5%?

[Nicefeather]

Can you point me in the right direction of a resource or book where I can learn this math. I am not very good at math top begin with so this is like greek to me but I want to learn so I can improve my game .

[godofPOPOV]

[ QUOTE ]
Can you point me in the right direction of a resource or book where I can learn this math. I am not very good at math top begin with so this is like greek to me but I want to learn so I can improve my game .

[/ QUOTE ]

ditto

[RacersEdge]

It's 250/400.

Just think about it this way , when he makes this move, he will gain 150 x% of the time, and he will lose 250 (1-x)% of the time. So set those two equal to each other to see where the 0 EV point is.

[tarheeljks]

[ QUOTE ]
[ QUOTE ]
Can you point me in the right direction of a resource or book where I can learn this math. I am not very good at math top begin with so this is like greek to me but I want to learn so I can improve my game .

[/ QUOTE ]

ditto

[/ QUOTE ]

hit up the master sticky in the small stakes no limit forum. there is a poobah post about fe in there somewhere.

[sh58]

fold equity is not important on the river, what you are talking about is how sucessful must my bluff be.

fold equity is the most relevant when there are cards to come, because you usually don't have the best hand, but by making a sizable raise you can make the play profitable, by winning the pot right there sometimes (fold equity) whilst also winning it sometimes by sucking out on later streets. obviously, this is semi bluffing.

the typical example of this is a flush draw on the flop. here you are a 2 - 1 dog, but by check raising allin you can represent enough strength to make an opponent fold (x)% of the time.

you can then add the numbers. say you can force them to fold 1/2 the time, the pot is 100, opponent bets 100, you raise all in for 400.
so you will win 200 50% of the time (100 in pot + opponents bet)

you will lose 400 33% of the time (your raise)

and you will win 500 16.5% of the time (the pot + plus opponent calling your raise)

so + 100 - 132 + 82.5 = 50.5

that check raise becomes profitable, you earn 50.5 on average every time you make the 400 raise, but it is only profitable because of fold equity

[JocK]

http://www.google.com/base/a/1121639...16285364122504

[Kurn, son of Mogh]

Here's a way to simplify it. In your example, lets say you are on the turn and have a flush draw. If you shove for the additional 250 and are called, you will only win when you make your flush.

If you shove and your opponent folds 100% of the time, youe EV is 400 (the 250 in your hand + the 150 in the pot)

If you shove and your opponent calls 100% of the time, your EV is 130 (the 150 in the pot + the 250 you bet + the 250 he calls [650] * .2 [the probability you hit your draw])

The EV of folding to the $50 bet is 250.

Thus for your fold equity to have sufficient value to make it correct to shove, your opponent must fold often enough to make your EV > 250.

Now let's start by assuming your opponent folds half the time. Now the EV of the shove is 400*0.5 + 130*0.5 = 265.

Close enough. In your example, under the parameters I suggested, your opponent must fold at least half the time for your fold equity to overcome your lack of showdown equity.

Make sense?