The Top Set dilemma

[Buzz]

[ QUOTE ]
What you are saying about two half-pot wins not being as good as one scoop is true due to losing half of current and future bets, but is irrelevant in pot equity calculations because you count the sum total of all bets, including your own, and then compare it to your equity to figure out if you are in a +EV situation.

[/ QUOTE ]Jai - I appreciate your trying to explain this to me. I really do. But it's not irrelevant in my pot equity calculations.

If you and I were playing a hand of Texas hold 'em and we decided to settle, rather than finish the hand, I'd want my fair settlement to be the amount in the pot multiplied by the probability I'd win the pot.

Thus it seems to me as though the total amount in the pot multiplied by the probability you'll win the pot is your "pot equity."

It sounds like you're thinking of "pot equity" as meaning something else or in a more contorted way than I am.

I figure "expected value" (also known as "E.V.") to be the net you expect to win (if positive) or lose (if negative). In Texas hold 'em, that's based on the probability you'll win the hand, how much will be in the pot when you win, and what it will cost you to see the showdown.

In Omaha-8 (or any split pot game) the issue is complicated by the split pot nature of the game. The plain truth, and you seem to clearly recognize it, is that <font color="red">when you scoop a pot, you actually win more than twice as much as when you win half a pot</font>. And because of this you CAN NOT simply multiply your half pot wins by two and add them to your scoop wins and use the combined total to correctly get your E.V.

One scoop win is only equivalent to two half pot wins in a simulation, where actually you are counting
one scoop win + one total loss as equal to two half pot wins (and no loss).

In Omaha-8 (or other split pot games) how much you win when you win part of the pot varies with and depends on how many players are involved in the split. (Everyone you split with can be thought of as getting part of your contribution, with you getting part of theirs).

Think of it this way, when you're playing heads-up and you split evenly for high and low, you win nothing. Two times nothing is nothing.

Buzz

[gergery]

[ QUOTE ]
Buzz,

I believe the correct way to use the equity calculators is as follows: let's say you have 25% equity in a pot. Your opponent bets $25 into a $50 pot. So after this betting round the pot will be $100, and your equity is 25% of that, or $25. Thus, the play is EV neutral.

What you are saying about two half-pot wins not being as good as one scoop is true due to losing half of current and future bets, but is irrelevant in pot equity calculations because you count the sum total of all bets, including your own, and then compare it to your equity to figure out if you are in a +EV situation.


[/ QUOTE ]

All that is true, and well and good, as long as you recognize the limitations of twodimes-style equity calculations.

Specifically, they assume the hand is "frozen" and no more bets are going in. Another way to think about it I suppose is that the equity calcs give you tell you how much value your hand has, but don't tell you how much you are going to have to pay (in future bets) for that value.

The further you are from showdown, the less helpful EV calcs are because the inherent assumptions aren't real.

-g

[Buzz]

[ QUOTE ]
This is flat out wrong. Well, technically you are correct since you are making it more expensive when you lose.

[/ QUOTE ]Jai - In a full loose game, you are going to lose here about two times out of every three. Honest. And when you win, six times out of eleven you'll only win the high half of the pot. Honest.

[ QUOTE ]
But that is like arguing that one should not bet the nut flush on turn because the river will pair the board and thus you will lose more by betting/raising the nuts in that spot.

[/ QUOTE ]Not at all the same! In one case you'll lose more often than you win and in the other case you'll win more often than you lose.
Big difference!

[ QUOTE ]
Your statement is only correct when your pot equity on bets going in is less than amount you are putting in.

[/ QUOTE ]I'm still not sure what you mean by "pot equity" (and I think I have a good enough command of the English language to understand what "pot equity" should mean). No matter. Do you mean the following statement is incorrect most of the time? [ QUOTE ]
"Unless you think your set of kings is going to hold up, you're drawing yourself! By raising, you're making if more expensive for yourself when you lose!"

[/ QUOTE ]How can that statement possibly be wrong?

And I'm not trying to be tricky about it. You obviously make it more expensive for yourself when you raise (duh) - and I truly believe you lose more often than you win (at a typical, full, limit-Omaha-8-ring table as commonly encountered in a casino) when you flop top set with nothing else on a 34K flop. There's no doubt whatsoever in my own mind about it.

I suppose you might possibly encounter a situation where things would somehow be different, but it wouldn't be in a typical Omaha-8 ring game.

[ QUOTE ]
This will only be true in rare instances for top set in the situations described.

[/ QUOTE ]I'm not sure what you mean by "rare instances."

When you play a hand with a pair of kings, you're only going to see a king on approximately one flop out of eight. But when you do make a set of kings, it's not unusual at all to see two wheel cards on the flop.

With no wheel cards in the hand with the kings,
P=(20*16/2)*(1/1128) = about fourteen per cent. Approximately one time in every seven when you flop a set of kings with no wheel cards in your own hand there will be two different ranks of wheel cards on the flop. When it happens, it will be an action flop and you should know what to do.

Drawing for half the pot in Omaha-8 is, in general, the pits. You have to do it sometimes, as here, but in this case, at least, (flopped top set with nothing else and with two wheel cards on the flop at a typical full table) you don't have to make matters worse by raising after the flop with your draw.

Buzz

[KneeCo]

buzz,

Great work as always. Keep it up.

[gergery]

[ QUOTE ]
Jai - In a full loose game, you are going to lose here about two times out of every three. Honest. And when you win, six times out of eleven you'll only win the high half of the pot. Honest.

[/ QUOTE ]

I'm not sure I agree. It seems like you calculated the POSSIBILITY that those things would occur. But in reality your opponents will not always have hands that fit. ie. you could be against A2JJ,A2JJ, and AQQT suited and have turn/river come 2,9 meaning low is enabled but it doesn't make anyone a low. Obviously that is somewhat rare, but it does mean your #s slightly underestimate your true win %. same idea with flushes/straights.

[ QUOTE ]
[ QUOTE ]
"Unless you think your set of kings is going to hold up, you're drawing yourself! By raising, you're making if more expensive for yourself when you lose!"

[/ QUOTE ]How can that statement possibly be wrong?

[/ QUOTE ]

If you lose 2 out of 3 times here, but for every bet you put in you get 8 callers then obviously you'd be losing more than you win but still be correct to put more bets in. Similar principle here.

You don't need to be a favorite for it to be correct to put bets in. You just need to win more than your fair share of new money going in.

-g

[jai]

[ QUOTE ]
Thus it seems to me as though the total amount in the pot multiplied by the probability you'll win the pot is your "pot equity."

[/ QUOTE ]

Yes. But this includes all bets put in the pot, including the ones from the current betting round (this means your bet as well), which is where the confusion is arising. In a traditional EV calc, you don't include your bet in what you can "win", and this creates a lot of headaches for figuring equity in split pot games by the normal means. Which is why percent equity is much easier to work with.

[ QUOTE ]
I figure "expected value" (also known as "E.V.") to be the net you expect to win (if positive) or lose (if negative). In Texas hold 'em, that's based on the probability you'll win the hand, how much will be in the pot when you win, and what it will cost you to see the showdown.

[/ QUOTE ]

Just to make sure we're on the same page, let's see if we agree on the following analysis for HE (or any non-split pot game). On the turn, I have 20% equity (roughly equivalent to having 9 outs). You bet $25 into a $100 pot. Should I call or fold? Assume implied odds don't matter. Well, if I call there will be $150 in the pot (which is what I stand to win). My cost for playing is $25. 20% of $150 is $30, so I profit $5 by making the call. Note that we could have come up with the same answer by a tradtional EV calc (assume 45 unseen cards to make the math nice): EV= (9/45)$125-36/45($25)=$5.

[ QUOTE ]
In Omaha-8 (or any split pot game) the issue is complicated by the split pot nature of the game. The plain truth, and you seem to clearly recognize it, is that <font color="red">when you scoop a pot, you actually win more than twice as much as when you win half a pot</font>. And because of this you CAN NOT simply multiply your half pot wins by two and add them to your scoop wins and use the combined total to correctly get your E.V.

[/ QUOTE ]

EV and pot equity are different things in this context. When we say you have pot equity of x%, we do not mean this number alone will give you EV. This depends on other things, like size of the pot, humber of players in, and the amount you have call.

Let's see if this example can show you what I mean. Your are playing PLO8. On the turn, you have nut flush and nut low draw. You know your opponent has top set with no other redraws and no blockers. He bets pot all-in for $50. Can you call profitably? Well, you have 7 non-pairing flush cards to give you a scoop. 16 low cards give you nut low, but 4 of them are already counted as flush outs. So that is 12 outs for half the pot. Let's assume 40 unseen cards. So 7/40 times you win 100 (+$17.50). 12/42 times you win 1/2. Now this is the tricky part. You will win only 1/2 of $50, the times you win low, not 1/2 of $100. So your net win in that case is 12/42*25=$7.50. 21/40 times you lose your whole $50 bet and get nothing back, for a net loss of $26.25. So that means we lose about $1.25 on average in this case. So how can we use pot equity to get the same answer? Well, we 7 outs to the whole pot, 12 outs to half, so we'll count that as 6. Thus out pot equity is 7/40+6/40=13/40, which is a little bet less than 1/3. Since at exactly 1/3 we would be getting exactly right odds to call a pot sized bet (1/3 equity*$150=$50, which is the cost of playing), the simple pot equity analysis shows us that we are making a slightly losing play by calling, just like the more thorough EV calc did above.


[ QUOTE ]
Think of it this way, when you're playing heads-up and you split evenly for high and low, you win nothing. Two times nothing is nothing.

[/ QUOTE ]

Not exactly correct. You "win" 2x half the dead money in the pot (your net is zero in the heads up case, but that is not what is important for EV calcs). You win nothing on future and current bets.

Also, Buzz, I think you are generally a good poster, so I hope you don't feel offended by me challenging you on this point.

[jai]

[ QUOTE ]
In a full loose game, you are going to lose here about two times out of every three. Honest. And when you win, six times out of eleven you'll only win the high half of the pot. Honest.

[/ QUOTE ]

This depends way too heavily on number of opponents and hand ranges to make this broad of a statement with any precision. How about we put in some reasonable hand ranges for whatever number of opponents we think is appropriate, and then see what happens in specific scenarios? And as gergery already pointed out, we may not win a hand very often, but still make money by winning a lot the times we do win.

[ QUOTE ]
[ QUOTE ]
But that is like arguing that one should not bet the nut flush on turn because the river will pair the board and thus you will lose more by betting/raising the nuts in that spot.

[/ QUOTE ]Not at all the same! In one case you'll lose more often than you win and in the other case you'll win more often than you lose.
Big difference!

[/ QUOTE ]

I think we disagree on how often the set will hold up here. I think the equity calulators agree with me given reasonable ranges for your opponents. (this may change if there are something like 8 people in the pot with implicit collusion and whatnot, I'm not sure...my feeble little mind can't analyze situations that complex.)

[ QUOTE ]
And I'm not trying to be tricky about it. You obviously make it more expensive for yourself when you raise (duh) - and I truly believe you lose more often than you win (at a typical, full, limit-Omaha-8-ring table as commonly encountered in a casino) when you flop top set with nothing else on a 34K flop. There's no doubt whatsoever in my own mind about it.

[/ QUOTE ]

Yes you will probably lose more pots than you win multiway. No one is disputing that. But that is not the same as whether you are making money by playing a certain hand. You might lose money if you never folded your sets on unfavorable turns or rivers, but I'm fairly sure you can't be doing anything wrong by jamming the flop.

[jai]

[ QUOTE ]
The further you are from showdown, the less helpful EV calcs are because the inherent assumptions aren't real.

[/ QUOTE ]

Sure. But given that you have an equity edge on any round of betting, you cannot say that you are losing money on that round of betting by putting in as money bets as possible. It may be bad for other reasons, like bloating the pot to the point where you now have to put in a lot of bets at a later street with a serious equity disadvantage. i'm just not sure top set in O/8 necessarily fits this criterion for not putting in more bets when you have a current equity edge.

[Buzz]

[ QUOTE ]
It seems like you calculated the POSSIBILITY that those things would occur.

[/ QUOTE ]Hi Greg. Not exactly. But I can see why you might think so.

[ QUOTE ]
But in reality your opponents will not always have hands that fit. ie. you could be against A2JJ,A2JJ, and AQQT suited and have turn/river come 2,9 meaning low is enabled but it doesn't make anyone a low.

[/ QUOTE ]I agree that’s a good possibility. You also can lose when you make kings full (to aces full, quads, or a straight flush). But these two opposite effects don’t actually compensate equally for each other. I was rounding off, trying to keep the math as simple as possible for ease in understanding. But yes, you have a very good point. I actually did the calculations and reasoning in more detail, but then tried to simplify leaving out some low probabilities and rounding off others in order to explain more clearly. And you have now nailed me for it. Mea culpa.

[ QUOTE ]
Obviously that is somewhat rare, but it does mean your #s slightly underestimate your true win %. same idea with flushes/straights.

[/ QUOTE ]Yes. It’s rare in my games. And like I said, I was trying to make it simple.

[ QUOTE ]
If you lose 2 out of 3 times here, but for every bet you put in you get 8 callers then obviously you'd be losing more than you win but still be correct to put more bets in.

[/ QUOTE ]Yes. I thought I covered this concept somewhere, but maybe I didn’t make it clear. Whether to raise or not depends directly on the number of opponents who will call your raise. (And also on the effect the raise will have on their betting on subsequent betting rounds).

But yes, if you have eight callers and if one of them is going to jam all the way to the showdown and the rest will chase when you end up with a winner, then by all means raise it up.

[ QUOTE ]
You don't need to be a favorite for it to be correct to put bets in. You just need to win more than your fair share of new money going in.

[/ QUOTE ]Yes. This is further complicated by the effect a raise might have on your opponents on the final two betting rounds. In my humble opinion, a raise by Hero here can really cool things off when the board pairs. But maybe your experience is different than mine.

Buzz

[Buzz]

[ QUOTE ]
Just to make sure we're on the same page,…

[/ QUOTE ]Sorry, Jai. We’re not.

(1) If there’s $1000 dollars already in the pot and (2) if you have a one in three chance of scooping the pot and (3) if you only have one opponent, and (4) if all you have in front of you is a $100, (5) and if your opponent bets $100,… then I think you should call the bet. After you call the bet, your pot equity will be $400, one third of the pot, not that your pot equity matters much (IMHO) unless you’re looking for a settlement.

But if you agree to settle after the money is in the pot and the river card is still unknown, then your fair share is $400, one third of the pot, and that is your “pot equity” to my way of thinking. Before there’s that last $100 bet, your “pot equity” is $333.33, one third of the amount in the pot, since you figure to win the pot one time out of three.

Because of the size of the pot ($1000), you have favorable odds to call a $100 bet. However, you don’t have favorable odds to initiate fresh money into the pot yourself since you’re only getting one to one for fresh money while your chance to win the pot is one in three.

Seems crystal clear to me, but maybe I’m not explaining it well enough.

At any rate, I don’t think whether or not you should bet (or raise) depends on your “pot equity.”

However, it would be possible to relate whether or not you should call to your pot equity. I don’t think of it in that way, but I guess one could come up with a mathematical relationship between the two.

[ QUOTE ]
I hope you don't feel offended by me challenging you on this point.

[/ QUOTE ]Not at all. Rightly or wrongly, I feel I have a very solid understanding of the principles involved in calculating poker probabilities and odds for this type of situation. I’m just sorry that I was evidently unable to communicate my understanding to you this time.

Buzz