Pot Equity vs. Pot Odds

[agoldenbear]

Alright, so I'm trying to clear up a discrepancy I see in one explanation of pot equity.

In Angel Largay's book, in the "Pot Equity" section beginning on p.64, he gives an example where it's fourth street, you have the nut straight and you are convinced your opponent has a set. As a result, your opponent has 10 outs to hit on the river to fill up, and since you know his hole cards so precisely, is 34:10 or 3.4 to 1 against drawing out on you. After what seems like some gratuitous calculations, he concludes this represents a pot equity percentage of 22.73%. Since 1/4.4 also equals 22.73, it is clear pot odds and pot equity, up to this point in the example, are are one in the same.

Largay then goes on to advise you force your opponent to call a larger percentage of the pot than is correct given his equity. In the example, he says a bet of $100 into a $200 pot will require your opponent to call an amount equal to 33% of the pot ($100 to see a pot of $300), a mistake in light of his 22.73% equity.

While I understand all of this, my question mainly concerns the conflicting information one would seem to have from considerations of your opponent's equity vs. considerations of the pot odds your are offering your opponent. You are offering your opponent pot odds of 3:1 in the example, so if he were 25% to win, as opposed to 22.73%, wouldn't his call be break even? If instead he somehow had 12 outs, his draw would be 28.6% to come in, so he would still be making a mistake calling amount equal to 33% of the pot in terms of equity. However, getting 3:1 pot odds, wouldn't his call be +EV?

Thanks in advance for clarification.

[SplawnDarts]

The confusion comes in as follows: when you have equity in a pot, the "cost" of your call is discounted because you will also own a piece of it once it's in the pot.

So say there's a $40 pot, I own 23% of it, and there's a $10 bet to me. If I call, I own 23% of a $50 pot, or $11.50, so my equity will be more than the cost of the call.

It's MUCH easier to think in terms of odds rather than equity though.

[agoldenbear]

Alright, that makes much more sense. Thanks.

You say it's a lot easier to think in terms of odds rather than equity, and I'd defintely agree in the example I cited from Largay's book. If you deny your opponent profitable odds when drawing, he'll naturally be contributing more money than his his equity should profitably allow.

Largay's next example involves how to factor equity when giving your opponent a free card that might give him a second best hand he'll be willing to push with. Are there other common situations where one should think of equity rather than odds? Put another way, when I hear players like Gus Hansen referred to as being "very good with equity calculations", what exactly does that mean? Under what circumstances does his knowledge of equity calculations give him an edge?

[SplawnDarts]

[ QUOTE ]
Alright, that makes much more sense. Thanks.

You say it's a lot easier to think in terms of odds rather than equity, and I'd defintely agree in the example I cited from Largay's book. If you deny your opponent profitable odds when drawing, he'll naturally be contributing more money than his his equity should profitably allow.

Largay's next example involves how to factor equity when giving your opponent a free card that might give him a second best hand he'll be willing to push with. Are there other common situations where one should think of equity rather than odds? Put another way, when I hear players like Gus Hansen referred to as being "very good with equity calculations", what exactly does that mean? Under what circumstances does his knowledge of equity calculations give him an edge?

[/ QUOTE ]

I always think in odds, not equity, except when posting here. How other people do it, I don't know. But it's the exact same math, just structured in ratios instead of fractions. Being good at one gives you the same "what play should I make?" results as being good at the other, and I have no idea which way Gus Hansen thinks about it.

Generally speaking, old school players think odds, and the newer school thinks equity when solving the exact same problems. I think it's because equity simulators and calculators use that notation, but I'm not sure.