Factoring implied odds into FE and PE.

[Isles]

I am trying to aply the implied odds to my draw equity.

Can someone tell me if I have this concept correct?

If I have the nut flush draw on the flop my pot equity is at least 39% for the draw.

If the pot is $100, and I bet $100, the total pot is $300.

If I can expect my opponent will call a half pot bet at least 50% of the time, then I can factor in another $150/2 or $75.

So for my $100 bet I am getting a total of $275, which is 36%, making my bet +EV.

Is this correct?

[IFoldPktOnes]

I would say you have the concept correct, but that if you are betting out instead of calling there are alot more factors involved.

You should include the chance your opponent will fold to your flop bet in working out the EV of the bet, thats one of the main reasons for betting out on a draw. This depends on the number of players in the pot, for example say everyone folds to your bet 50% of the time, thats 100/2 = 50 more chips.

You have also assumed that your opponent will allow you a free card on the turn, this is fairly reasonable if you are acting behind them considering your large flop bet. This free card is another reason you bet the draw.

The last key reason you bet a draw is to deceive your opponent so that they dont put you on a flush draw. Because of this I think you could expect to get more than 75 chips out of your opponent on average when you hit your draw. For example, if a flush card comes on the turn you can check off, your opponent may sense weakness and bet out on the river. Your opponent could have even called you on a smaller flush draw (hoping for implied odds when they saw your large flop bet).

So I would say you have underestimated the EV of betting out on a strong draw (especially if you are in position). If you are just interested in applying the concepts of implied odds a more simple example where you are just calling would be a lot easier to analyse.

[AaronBrown]

No, your math is a bit off. IFoldPktOnes explained some of the other things to take into account, I will just address the basic math.

First of all, I don't know how you get the 39%. The chance of making your flush by the river is 35%. But you don't win all those times, people do get full houses and quads, and straight flushes. You may win sometimes without filling your flush, especially since the nut flush means an Ace or other high card in your hand, but in some of those cases you won't know it and will fold.

Using your 39%, with $100 in the pot, you have $39 of pot equity. If you bet $100 and get called, you have increased your pot equity by $78 at the cost of $100, for a $22 loss. You can't consider the pot equity on the entire $300, because you have $39 of that without betting.

You also assume that the other player will call a half-pot bet half the time if you hit. You call that $75 of EV because she calls half of $300 half the time. But you should only consider $200, the extra implied odds from your bet, for the same reason as above. And this only happens the 39% of the time you hit. So it's $200*0.5*0.5*0.39 or $19.50 instead of $75. $19.50 doesn't make up for -$22; although it makes this a close call.

There are good reasons to make the $100 bet on the flop as IFoldPktOnes discussed, but the simple pot odds/implied odds calculation you've done shows a break-even decision, not a +EV one.

[IFoldPktOnes]

Hi AaronBrown nice analysis.

I haven't done many calculations using pot equity but I understand the logic behind your calculations. I was wondering that if the situation were reversed, and your opponent bets 100 into the 100 pot would the call be +EV, even though betting out wasn't? (this is assuming the turn card is still free, so its not realistic just hypothetical)

I ask this because if your opponent bets out you can no longer consider that 25 of the 75 chips expected through implied odds were already yours, so you would include the full 75 chips in the implied odds calculations. Is this correct?

[AaronBrown]

Remember that pot equity and implied odds are just definitions, to evaluate a decision you have to consider all possible scenarios, as you did in your first post. A decision may increase pot equity more than the amount bet, and thus look +EV, without being a good decision.

Your understanding of the concepts is correct. The $100 bet means a $100 call gives you 39% x $300 = $117 pot equity more than the zero pot equity of folding. The implied odds, as you say, add another $150 x 0.5 x 0.39 = $29.25 of expected value, which you obviously don't get if you fold. So this looks like a +EV call (of course, the EV of raising might be even greater, you'd have to compute this as well). It might fail, if for example we assume that if you don't hit the turn the other player goes all-in, or that not all the 39% of the time you win do you know you've won.