SSHE Pot Equity questions (long)

[BarkingMad]

I’ve been studying SSHE for a few weeks now and I’m currently doing some homework with Pot Equity (PE). Using PE to evaluate your hand during all stages of play is an awesome concept that I’ve never read about before SSHE. The purpose of this post is to bounce my ideas off the board to make sure I’m on the right track with my thinking.

I believe that PE has implications that go beyond the coverage it’s given in the book. I’m sure Ed Miller realizes this; it’s just that you could probably fill a whole book talking solely about PE. Using PE as a tool to decide what action to take is easier said than done. The first problem is simply knowing, out of the multitude of possible hand combinations, what the approximate PE of your current hand is given the # of opponents you’re facing. For relatively weak ‘made’ hands like top or middle pair, PE varies dramatically with # of opponents. For pure draws like A [img]/images/graemlins/spade.gif[/img] 4 [img]/images/graemlins/spade.gif[/img] vs. flop: Q [img]/images/graemlins/spade.gif[/img] 9 [img]/images/graemlins/heart.gif[/img] 3 [img]/images/graemlins/spade.gif[/img], PE still increases as # of opponents decreases, but the change isn’t as dramatic because on the end you generally will have either the nut flush or nothing (ok, maybe one pair). My point is that to use PE effectively there is a lot of research and memorization to be done because there are so many different hand combinations and so many variables that affect PE. To make this learning process more efficient I’m creating tables of various hand types and their corresponding PE.

My understanding is that Ed uses showdown type simulations to figure PE. Since I obviously cannot simply use the showdown results of a given hand vs. a full table to gauge my PE vs. 5 opponents, should I use a showdown test vs. 5 opponents? Or should I compensate for the fact that my real opponents have chosen to be in the hand (thus their hands might be better than random), whereas computer showdown hands are completely random. My thought is that since we are talking about loose games vs amateur opponents, I could just use the PE for the actual number of opponents faced, rather than fudging my PE downward to compensate for the 'better than random hands' effect.

Some will view this as splitting hairs, but the fact is that PE does vary alot depending on how you test for it, & by # opponents.

For example –

You’ve got Q [img]/images/graemlins/club.gif[/img] 10 [img]/images/graemlins/club.gif[/img] in middle position, the flop comes 10 [img]/images/graemlins/heart.gif[/img] 8 [img]/images/graemlins/diamond.gif[/img] 4 [img]/images/graemlins/club.gif[/img], you’re facing 5 opponents. Quick, what’s your Pot Equity?

Using Wilson’s Turbo HE software, I did showdown simulations (i.e. tests against opponents that never fold) for this scenario. Against 9 opponents, PE = 21.8%. Against 1 opponent, PE = 80.7%. Against 5, PE = 45.5%

Another option is to use Turbo's automatic testing function to pit various computer profiles that choose to play (i.e. they bet, raise, call, & fold) against each other for this testing. For the example above, pitting the Bret Maverick profile against a table of loose low limit profiles, the PE = approx 55%. One conceivable advantage that this type of testing has is that it takes position into account, whereas showdown testing does not. One possible disadvandage is that some computer opponents may not see the flop, so the # of opponents faced may vary on each permutation of the test.

Here are some example hands and their PE results against 9 opponents.

A [img]/images/graemlins/club.gif[/img] 9 [img]/images/graemlins/club.gif[/img] flop: Q [img]/images/graemlins/club.gif[/img] 9 [img]/images/graemlins/diamond.gif[/img] 3 [img]/images/graemlins/club.gif[/img]
Showdown: 46.5%
Profile testing: 61.4%

A [img]/images/graemlins/club.gif[/img] Q [img]/images/graemlins/diamond.gif[/img] flop: 9 [img]/images/graemlins/diamond.gif[/img] 7 [img]/images/graemlins/heart.gif[/img] 3 [img]/images/graemlins/spade.gif[/img]
Showdown: 6.6%
Profile testing: 36.5%

9 [img]/images/graemlins/club.gif[/img] 9 [img]/images/graemlins/diamond.gif[/img] flop: K [img]/images/graemlins/diamond.gif[/img] 7 [img]/images/graemlins/heart.gif[/img] 5 [img]/images/graemlins/spade.gif[/img]
Showdown: 8.9%
Profile testing: 46.4%

J [img]/images/graemlins/club.gif[/img] J [img]/images/graemlins/diamond.gif[/img] flop: 9 [img]/images/graemlins/club.gif[/img] 7 [img]/images/graemlins/diamond.gif[/img] 4 [img]/images/graemlins/spade.gif[/img]
Showdown: 16.1%
Profile testing: 64.6%

Thanks for reading. To summarize, my question basically is; what method for determining Pot Equity do you think is best?

-Lance

[John Biggs]

Your hard work is admirable but I fear misguided. Although pot equity is a useful concept, it's not the only input and may not even be the most important one in some circumstances. Thus, working up tables of pot equity according to Turbo simulations (or any other method) will have you over-focusing on data that after a certain point produces diminishing returns.

[Beavis68]

Right, the way I understand it, pot equity really is just a way of deciding if you call, or raise for value.

If you are drawing to a flush, you have a 35% chance of hitting your hand reqardless of the number of opponents, if you have 3 or more opponents, your raise here would be for value, not a free card, in fact, you may even 3-bet or cap it based on the number of opponents you thought would stay in the hand.

[theghost]

[ QUOTE ]
pot equity really is just a way of deciding if you call, or raise for value.

[/ QUOTE ]
Agreed.

If you want to use a simulator to calculate it, it shouldn't be against random hands, but hands that would still be in it with you. (Was that the original question?)

[BarkingMad]

[ QUOTE ]
If you want to use a simulator to calculate it, it shouldn't be against random hands, but hands that would still be in it with you. (Was that the original question?)

[/ QUOTE ]

More or less, that was my question. I agree that Pot Equity should be fudged downward to account for the "better than random hands" effect. The problem is that it becomes a can of worms when trying to account for it when creating a table of PE's for various hand catagories.

The question Pot Equity answers is, how strong is this hand?
Anyone who has read some books knows that aces in the pocket will win (preflop / showdown) about 31% of the time against a full table, and about 85% of the time heads up. Those numbers also represent the PE of pre flop pocket aces (right?).

You can do the same thing with any hand, with any board combination, at any stage of the game. It just gets tedious because there are so many possible combinations. I think John Biggs' contention is that it's a waste of time to do all this work when you could just play the game, gain experience, and develop a good sense of what your Pot Equity / Hand Strength is. He may be right, however, I believe that because the variables are so numerous it's likely that even experienced players often misjudge the value of their hand.

Here is what I'm in the process of doing. In order to direct a profile's play, Turbo HE lumps the millions of possible hand / board combinations into 125 general catagories. 60 for no pair board. 35 for 1 pair board, and 15 for 2 pair boards and trip boards. To calculate the showdown PE against 1-9 opponents for each of the catagories is 1,125 total showdown tests. This is about two weekends of work. I could then take the XL table I've created and post it near my screen for reference when I'm multitabling.

Thanks for the replies. I'm hoping Ed, David, or Mason will find time to share thoughts as well. [img]/images/graemlins/wink.gif[/img]

-Lance

[BradleyT]

The problem with calculating the PE of hands like A[img]/images/graemlins/club.gif[/img]8[img]/images/graemlins/club.gif[/img] on a flop of 8[img]/images/graemlins/spade.gif[/img]3[img]/images/graemlins/heart.gif[/img]Q[img]/images/graemlins/diamond.gif[/img] is that there's no final board where you know you have the best hand (besides quads). With flush and straights at least you know it's obvious when you have the nuts or near nuts because of the community cards.

Think of how many times you've won with A[img]/images/graemlins/club.gif[/img]8[img]/images/graemlins/club.gif[/img] with just ace high, or maybe it took a pair of 8's to win, or maybe a pair of aces, or perhaps aces and 8's, or perhaps trip 8's, or maybe trip A's, or maybe a full house was needed to win.

It's just too hard to calculate the PE of a hand like A8s on anything except an AAA or 888 or flush/flush draw board.

[Beavis68]

I dont think this is a PE situation, here you are betting to protect your hand, in pot equity situations, you are still drawing, but the odds or completing the draw make calls from your opponents profitable.

Here, you would be hoping to knock out a hand like T9 or KJ.

[BarkingMad]

[ QUOTE ]
The problem with calculating the PE of hands like...

[/ QUOTE ]

There isn't a problem with calculating the Pot Equity (AKA - Showdown win %) of any hand. Every hand has a PE, whether it's a draw or a made hand. It's just easier to do with strong drawing hands like flushes because: 1) you can roughly assume you will always win the pot if you make your draw. And: 2) The odds of completing strong draws are well known.

For hands like the example you gave, A [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/club.gif[/img] on a flop of 8 [img]/images/graemlins/spade.gif[/img] 3 [img]/images/graemlins/heart.gif[/img] Q [img]/images/graemlins/diamond.gif[/img], its not as easy because you are not drawing to anything but trips (2 outs), 2 pair (3 outs w/ ace), and quads or full house (way < 1 out). With any of those hands (except quads or boats) you cannot assume you will always win the pot when you make them, so a showdown test must be done. The showdown result for your example hand is 35.7% vs 5 opponents with random hands. That number includes all of the following:

- The times you win with your pair of eights.
- The times you win with aces & eights.
- The times you win with eights + board pair
- The times you win with trip eights.
- The rare times you win w/ a full house or quad eights.
- The times you lose w/ all the above (except quads or top boat, which of course would be the nuts)


[ QUOTE ]
in pot equity situations, you are still drawing, but the odds or completing the draw make calls from your opponents profitable.

[/ QUOTE ]

In my understanding, and as described in SSHE, Pot Equity isn't a "situation" but rather a measurement that can be applied to any situation, draws and made hands alike.

On pg. 284 of SSHE, hand quiz #20 is 6 [img]/images/graemlins/heart.gif[/img] 6 [img]/images/graemlins/diamond.gif[/img] on a flop of T [img]/images/graemlins/spade.gif[/img] 6 [img]/images/graemlins/spade.gif[/img] 6 [img]/images/graemlins/club.gif[/img]. This certainly isn't a drawing situation, and Ed describes the Pot Equity as nearly 100%.

-Lance

[BradleyT]

[ QUOTE ]
With any of those hands (except quads or boats) you cannot assume you will always win the pot when you make them, so a showdown test must be done. The showdown result for your example hand is 35.7% vs 5 opponents with random hands.


[/ QUOTE ]
I highly doubt 35.7% is correct. Change those 5 opponents to S&M Group 1-8 hands and you're only 21% favorite. Change just 1 of those 5 opponents to S&M Group 1-3 and you're now only 15% which is a money loser. So what's the correct PE now?

Like I said, it's nearly impossible to calculate PE when you're not drawing to a defined final hand (straight, flush, full house, quads) that you know will be the nuts (or at least the most likely winning hand).

[BarkingMad]

[ QUOTE ]
I highly doubt 35.7% is correct. Change those 5 opponents to S&M Group 1-8 hands and you're only 21% favorite. Change just 1 of those 5 opponents to S&M Group 1-3 and you're now only 15% which is a money loser. So what's the correct PE now?

[/ QUOTE ]

You're right.

37.5% is the correct result for random hands, but it represents an absolute best case scenario because in actual play (perhaps even in loose small stakes games) your opponents hands would have to be given credit for being better than random. This opens a huge can of worms when trying to calculate PE / Showdown win% for putting together a table like the one I'm working on.

I think the easiest solution will be to simply create the table using showdown % vs. random hands, but then refer to the table with the understanding that the figures represent best case scenarios. For tight games w/ solid players the PE numbers would have to be adjusted downward so much they might be meaningless. For loose small stakes games they would be closer to reality but would still probably need to be fudged down considerably to compensate for the "better than random" effect.

Thanks,

-Lance