Pot equity in a split pot?

[TheScareCard]

How do I factor in the possibility of a split pot when calculating my pot equity and weighing that against the pot odds?

Let's say I estimate that the pot will be a two-way chop on the river x% of the time. That doesn't mean I have 50% pot equity x% of the time, or does it?
50% pot equity would mean I estimate to WIN the whole pot x% of the time on the river.
But in case of a chop, I only get HALF the pot x% of the time.

Example (taken from the MTT board):

My opponent puts me all-in on the flop. The odds to call are 2-to-1.
I have KJ.

The board is: K J 2 rainbow

I estimate that my opponent has:

a) 22 in the hole 50% of the time.
b) KJ in the hole 50% of the time.

IF I call:
With two cards to come, against 22 I win about 8% of the time by filling up (4 outs x 4 x 50%).
The other 50% of the time I'll split the pot.
So how do I factor in the split pot scenario to estimate my total equity?

[nsidestrate]

Let's assume you have to call 10,000 and the pot contains 15,000 in chips:

(.42 * -10,000) + (.08 * 15,000) + (.5 * 7,500) = + 750 EV

If you had to call 50,000 and the pot contained 60,000:

(.42 * -50,000) + (.08 * 60,000) + (.5 * 30,000) = -1,200 EV

[TheScareCard]

OK, so in case of a 2-to-1 pot odds scenario, say I have to call 5k to win 10k, for a total pot of 15k, the math is:

(.08 x 15k) + (.5 x 7.5k) - (.42 x 5k) = +2850 EV

If I estimated villain's range correctly I have an easy call, right?


If I change the numbers above to 80% for 22 and 20% for KJ I get:

(.13 x 15k) + (.2 x 7.5k) - (.67 x 5k) = +100 EV

Which makes the call a pretty close one. If I fold I won't be giving up much.

I got it.
But isn't there a way to convert the split pot scenario to pot equity instead of calculating my EV?

[nsidestrate]

I was thinking about this at lunch and I think I screwed up. I think in the first example you really only have:

(.42 * -10,000) + (.08 * 15,000) + (.5 * 2,500) = -1,750 EV

The problem is that unlike the usual scenario, you really don't get your initial bet back when you win. So even though you get 7,500 from the pot, you lose 5,000 of your bet.

[TheScareCard]

Funny thing is, I'm flipping thru my 2+2 books and I can't find anything on split pots.

[Bugsbunny]

yes, ot does mean you have 50% pot equity x% of the time And it changes your odds drastically (depending on split pot percentage).

pot already contains 500, he bets 500, which is what you have left. So you're getting (on the face of it) 2 to 1. Total pot =1500

Using your numbers:

50% of the time it's a split
46% of the time you lose
4% of the time you win. (it's 8% against 22, but he only has 22 50% of the time)

So, using 100 hands, your equity is:
(50 * 750 + 4 * 1500)/100 = $435

It's costing you 500 so your odds are .87 to 1

Basically if the chances are that you split or lose you should usually fold. If it's split or win then you should play. Obviously the exact pot size and the amount of the bet come into play - but that should be your first instinct..

Off the top of my head I think that Small Stakes Hold'em has material on split pots and equity. It's a limit book, but the principles still hold true. I haven't checked though, so I may be mistaken (about the book).

[Bugsbunny]

I looked at the numbers a bit closer and posted in the MTT thread.

[TheScareCard]

Thanks Bugs, it finally makes sense.

So in your example, my "fair share" of the pot is 435$, the call is 500$, so calling is -EV.

With odds of 3-to-1, your equity goes up to 580$, so here calling would be correct given you have a small pot equity edge.

Of course, everything hinges on the % of the time you expect to chop the pot.

Got it.

[doubleup]

What is a good book that will hold your hand through the equity process? How often is this used and in what types of games are they used? I have never heard any say anything about equity until I got on here. Is this used to determine whether the correct play was done after the fact or ???? Reason I ask is cause I don't see professional poker players at tables with calculators. Do they basically just "know" these types of things or what? Trying to figure out what the value of determining equity has and how common it is to actually know the equity of any given hand without utilizing a calculator.

[Bugsbunny]

[doubleup]

So in order to know the equity you have to know exactly what your opponent(s) holding?

[TheScareCard]