Calculating real equity and expected value over mult streets

[Bren_Osoro]

How do you calculate your real equity as opposed to your hot/cold equity. Obviously hot/cold equity doesn't take into account how often your opponent(s) will fold at some point during the hand while your real equity does. Calculating the EV of a strategy using real equity is much more accurate than using hot/cold equity and I'm not sure how to go about doing that.

I understand how to calculate the EV of a single decision in a hand, but I'm not sure how to factor in different streets. For instance, say your out of position with a flush draw in a limit holdem game, and your opponent was the pre-flop aggressor. You check raise the flop with your draw, and plan on betting the turn if he calls. Your opponent probably doesn't fold on the flop often enough to make that single decision profitable, but it has implied fold equity for your turn bet. That's an obvious example but almost any action on one street will affect your expection on future streets. Any help woud be appreciated.

[nsidestrate]

I have to do it by hand, because I haven't found a tool that I like for it. I'll give you a quick real-world example that matches your scenario. Let's say that there was a MP raiser. I three bet with JJ from the SB and the MP player caps. From experience, I know that his range is exactly AK/QQ+. The flop comes down T92r and I am considering the equity of a check-raise/turn bet. This particular player will call my check-raise with his entire range and fold AK unimproved to my turn bet and raise the turn with AA-QQ, so long as it is still an overpair or better. I'm really not sure what he will do with QQ and KK if the turn is an Ace, but I assume he will call down.

His range is:

AA x 6
KK x 6
QQ x 6
AK x 16

The turn card with be an Ace or King 17% of the time.

That gives us the following percentage outcomes:

He has a pair 53% of the time.
He has AK and catches an Ace or King 8% of the time.
He has AK and misses 39% of the time.

You will lose 2 BBs in the first two cases and win 5 BBs in the final case (this assumes I will always fold to his turn raise). In that scenario, I'm well ahead with my check-raise because 61% of the time I lose 2 BBs and 39% of the time I win 5. (.61 * (-2)) + (.39 * 5) = 0.73, so I gain 3/4th of a big bet with this play.

Of course, this gets harder and harder to calculate when you don't know the other players range and when he might take actions you can not predict. It also is more complex when the scenario involves calldowns instead of folds, because you have to determine the equity at showdown too. Even in my example, I have oversimplified, because if the turn was a Jack, I will win a lot more than I have claimed. If the turn was a Queen, I will continue because I have the odds to chase my draw.

[Bugsbunny]

Just to add what Nside said. What you're asking for is really a function if educated guesses (and sometimes not so educated guesses). You need to estimate the various probabilities involved and then use those to get the final answer. If your estimates are accurate then it'll give you an accurate anser, if not they won't.

In the example you gave when you're planning on betting the turn there are a number of possibilities. We'll assume that you're drawing to the nut flush, and that the A is you're only overcard.

1) the flush card came, you bet. This will happen 19.5% of the time (rounding off to make it easier to figure). Assume he folds here 50% of the time (pulling this number out of thin air - it's just an example), calls 50%, raises 0%.

So 9.75% of the time he calls (giving you a 100% win, we'll ignore straight flushes and boats for simplification purposes) and 9.75% he folds, also giving you a 100% win

2) an A comes (6.5%): He folds 40% calls 60% (2.6%, 3.9%)

3) No flush card comes, no A (74%), you bet. Now he still folds 40% of the time, calls 40%, raises 20% (29.6%, 29.6%, 14.8%)

so that gives us the following amounts:
He folds: 9.75 + 2.6 + 29.6 = 41.95% of the time

He calls: 9.75 + 3.9 + 29.6 = 43.25%

He raises: 14.8%

14.8+43.25+41.95=100%

Of the 43.25% he called the split could be 13.65 you're ahead and win (grossly simplified, since I'm assuming a pair of A's wins) and 29.6% he's ahead - but you'll win 26.6% * 29.6% = 7.9% on the river when you hit a flush or A.

and the 14.8% of the time he raised you'll win 14.8% * 26.6% = 3.9%

Now you said you know how to figure the basic stuff so I left out pot sizes, how much you win in each situation, etc. And the percentages are just out of the air numbers to show you how it's done.

Normally you would also recalculate some of the actions with a check on the turn rather than a bet - since you may get more with a check (when you hit your hand). And you can manipulate percentages to see how often he has to do action A to make it profitable for you to do action B.

Then you go through the process again on the river, to get a final answer.

As I mentioned the above is grossly simplified since it ignores sets, 2 pairs, boats etc. It assumed you always win with a flush or pair of A's (which is obviously not always going to be the case) - but I wanted to add a slightly higher degree of difficulty to show you how it's done.

You're simply combining percentages and then using those to get the final result. And obviously you don't do this at the table But run it often enough off table against various scenarios and you'll begin to get a feel for what's what.

[Fumseck]

StoxEV Software will do those calculations for you.

http://www.stoxpoker.com/forums/showthread.php?t=9767

[Bren_Osoro]

I've been watching a lot of Bryce Paradis's videos, and I've read his articles and his philosophy towards poker inspired me to learn the mathematics.

[scylla]

Hi guys,

You can do these sorts of calculations and much more with StoxEV, which is a free application that can do very complex EV calculations for you.

You can get the latest version at www .stoxev . com.

To learn how to use it, try watching the video manual. You can start it by going to help->video manual in the program.

For questions or comments you can go to the thread at twoplustwo.

Cheers,

Scylla

[Nutjob]

This is way over my head.

[Suited_Jock]

[Nutjob]

Can't argue with that logic.

[Suited_Jock]

[Fumseck]