The Top Set dilemma

[jai]

[ QUOTE ]
However, aren’t you using “fresh money” considerations rather than “pot equity” to decide whose advantage it is to bet? Whatever you call it, you have provided an interesting, thought provoking example. And I follow and agree with your reasoning for the situation.

[/ QUOTE ]

Ah, I see where we may be getting hung up..."fresh money equity"is equal to "pot equity" (at least the percentage, not the absolute amount). Thus, when your equity share (your chances of winning the pot by the end) is greater than your fair share (1/# of people putting money in pot), then you are making money by putting in additional bets. You are right in that that is not the only reason to consider raising, but it is often the most important consideration.

I'll respond to your other points in bit when i have more time.

[EffenDolts]

[ QUOTE ]
[ QUOTE ]
I am trying to reconcile what Buzz wrote with the following equity calculations.

[/ QUOTE ]Hi Effen - What do you mean by "equity calculations."

[ QUOTE ]
Assume you hold KcTcKsQh. In each flop, you have no backdoor flush draw or straight draw, just top set.

[/ QUOTE ]This hand is a bit different from the hand I used, but fine, let's use this hand.

[ QUOTE ]
Simulated against 4 hands with top 20% of holdings:

[/ QUOTE ]What reasoning did you use to choose to simulate against four hands? How do you simulate against four hands with "top 20% of holdings"?

[ QUOTE ]
The other players have an average equity around 15% in each case. You are a huge favorite with every hand. You are even favored over Ah2h5cAd.

[/ QUOTE ]I'm not sure where you got these numbers. (I'm assuming you somehow got them as simulation results). I'm not sure what you mean by "equity." Do you mean they have random hands such that they each win "around 15%"? If so, how are the wins being counted? (One for a scoop, one half for winning low only, etc.)?

[/ QUOTE ]

Buzz,

I am using PokerProTools, which allows you to specify an opponents hand as "top 20% of all possible starting hands", rather than a specific 4-card hand.

If four people limp, SB folds, and I check in the BB with KKxx, I can't put any of the limpers on a specific hand. I just know that four players have better-than-average hands. The point of my post was that KKxx has very good equity against random good hands. I don't know how PokerProTools ranks starting hands, but it doesn't make much difference to my argument if I use top 20% or top 30%.

The OP did not specify PL08 or LO8, but Kurto later said he was referring to PLO8. Your analysis was more in the spirit of LO8. I think pot equity is more apropos in LO8. It also become important in all-in situations in PLO8, but we can reasonably assume that the stacks are deep on the flop.

In PLO8, position, aggresiveness and persistence of opponents, preflop actions, all affect the decision on whether to bet, raise, or smooth call a flop ok Kd3h4h.

I like your tendency to simplify. The problem posed in the OP is too ill-defined. I won't comment further on this thread, but I am reading all of the responses. The difference between pot equity and implied odds is very squishy because implied odds depend so much on the game situation, whereas equity is well-defined.

Effen

[jai]

Alright Buzz, we are on the same page with regards to fresh money equity (which as I stated before is the same as pot equity, except you multiply it by the bets going in instead of dead money in the pot to get the absolute number). Given that we know we have a "fresh money" equity edge with top set (you may not believe this yet, but hopefully you will), I will argue until my lips bleed that you can't be making a losing play by raising. Raising may not always be the best play, and you provide several important reasons for that throughout this thread. However, when you contend that it is a losing play because your hand is "drawing", you imply that it does not have "fresh money" equity, which I think is wrong.

[ QUOTE ]
You can absolutely come up with a mathemetical realtionship between the two: EV=pot equity x total amount in pot (including your calls)-amount to call.

[/ QUOTE ]I'd like your mathematical expression better if you put “total amount in pot” minus the “amount to call” in parentheses. In other words I'd like it better if you subtracted the amount to call from the total amount in the pot before multiplying by pot equity. See the difference?

[/ QUOTE ]

I see the difference. But the correct way to calculate EV using a percent equity is to include all of the bets that will go into a particular betting round, and then multiply that by your equity. The thing that you are getting hung up on is that your net "win" in a split pot case is less than when you scoop when looked at from the perspective of the middle of the hand—you can only "win" half of the dead money in the pot. However, when you include everything in the pot, including your calls, then the amount you "win" in a split pot case is exactly half of when you scoop. And it is the total size of the pot that is important in an equity calculation since you will get back, on average, your equity share of bets being put in currently as well as the dead money.

[ QUOTE ]
But although computing pot equity seems relatively simple without a split pot, arriving at pot equity in a split pot seems more complicated to me.

[/ QUOTE ]

It is more complicated when you try to use the traditional "I have x outs and my pot odds are y to 1; do i have a call?" since, as you alluded to, the amount you can win in a split pot is less than half of y. By using percent equity and including all bets put into the pot by the end of the betting round, you can avoid cumbersome calculations. To see how this is case re-read the example I provided here

Once you have convinced yourself that percent equity works and can be used to calculate EV and "fresh money" equity, try out the following calculators:

ProPoker Tools Simulator Twodimes Calculator

Try to come up with as many possible scenarios as you can to have top set on the flop texture we've been talking about. I think you'll find that top set will have better than fair share on "fresh money" equity.

But in case you still don't believe me, chew on this for a bit. You stated earlier that 2/3 of the time with top set you'll be drawn out on and won't win anything. Of the 1/3 that you win, 6/11 times you'll have to split with the low. Well let's use these numbes to figure fresh money equity. Given n players in the pot, two out of three times we will lose a bet. 6/33 times we'll win n/2-1 bets and 5/33 times we'll win n-1 bets. When n=4, we are losing 1/33 of a bet with each bet that is going in. With n=5, we are clearly winning with each bet put in. I believe your numbers are less accurate for the cases when there are fewer players (n=4 or less) because you overestimate the number of times all the draws are out against you, and you underestimate how often your opponents may have the same draws, thus eating up outs. With 3 or fewer opponents, not all low cards will fill a straight. You may even occasionally win half on a flushed board. Given these possibiliities, I think even your calculations will allow that putting extra money in with top set can be a winning play.

Hopefully that clears up the argument I've been trying to make. I hope I've at least been able to help you think about how to use equity at the tables, if not convince you that raising top set is not a losing play!

[Buzz]

Effen – Thanks. I see where the term “pot equity" comes from. It’s the term used by PokerProTools simulator. I think what is labeled as “pot equity” is basically the percentage I’d come up with if I added the percentage wins for low, high, and scoop, as provided by a Wilson simulator with a non-folding cast of players.

Very interesting how using the PokerProTools simulator you can specify a certain top percentage for the opponent’s hands simulated.

Here’s the problem as I see it: In a game with real players, as a general rule at least some of them will react to what you do and have done. And the way they react to you isn’t necessarily the same way as they’ll react to someone else. Additionally, the way they react on future betting rounds will depend on what you do here on the second betting round. It doesn’t look to me as though the PokerProTools simulator is accounting for these factors.

Honestly, if I pop it (raise) on the second betting round, at least some of my opponents are very likely to back off. And if some of my opponents pop it in the second betting round, I’ll back off myself. (I think of a pair of fours as a negative in a starting hand, but there are various hands I’d play regardless of the pair of fours. Then if I flopped a set of fours, say with A344-suited to the ace as a starting hand, I might continue playing, but certainly not if I had a clue my opponent might well have a set of kings.)

[ QUOTE ]
Kurto later said he was referring to PLO8. Your analysis was more in the spirit of LO8.

[/ QUOTE ]Yes. Had I realized Kurto was asking about how to play flopped top set in pot limit I would have stayed out of the discussion.

[ QUOTE ]
In PLO8, position, aggresiveness and persistence of opponents, preflop actions, all affect the decision on whether to bet, raise, or smooth call a flop ok Kd3h4h.

[/ QUOTE ]That’s my take on it too. These things also affect decisions in limit games too, but from what little I know, it seems to me they have more of an effect in pot limit games.

[ QUOTE ]
The difference between pot equity and implied odds is very squishy because implied odds depend so much on the game situation, whereas equity is well-defined.

[/ QUOTE ]If you’re going to add together the percentage simulation results and label the total “equity,” then it’s well defined.

I have been involved in settlements in high stakes backgammon games and also involved in settlements in tournaments. Settlements in poker hands are unknown to me personally and I doubt that I will ever be involved in such a settlement. But the only way I would use “pot equity” would be to determine my fair settlement in a poker hand.

At any rate, thanks for making what you did clear. And I hope my position is clear and reconcilable with yours. To iterate, I’m generally betting but not raising with this hand/flop on the second round in a typical, full, limit Omaha-8 game.

Buzz

[Buzz]

[ QUOTE ]
Alright Buzz, we are on the same page with regards to fresh money equity (which as I stated before is the same as pot equity, except you multiply it by the bets going in instead of dead money in the pot to get the absolute number).

[/ QUOTE ] Jai - I don’t think in terms of “equity” when making decisions about folding, calling, raising, or re-raising. Instead I think in terms of odds.

“Pot odds” is an entirely different concept than “fresh money odds.”

I don’t actually use “pot odds” at all – but I may use an estimation of “implied pot odds” or “reverse implied pot odds” as part of my decision to call.

And I may use “fresh money odds” as part of my decision to raise.

In other words, the odds I use to determine whether or not to call are different than the odds I use to determine whether or not to raise. One is based on the estimated size of the pot at showdown while the other is based on the number of players who I expect to be participating in the action. It’s possible that fresh money odds and pot odds could have the same numerical value, but generally they do not.

Someone probably associated with ProPoker (I’d guess the writer or writers of the simulation program) may have came up with the term “pot equity.” I think I see what is meant by "pot equity," in the context of the simulation, although in my humble opinion it’s a poor and misguiding term to use.

[ QUOTE ]
But the correct way to calculate EV using a percent equity is to include all of the bets that will go into a particular betting round, and then multiply that by your equity.

[/ QUOTE ]I don’t think so. I guess it depends on how you define EV. More about this below.

[ QUOTE ]
The thing that you are getting hung up on is that your net "win" in a split pot case is less than when you scoop when looked at from the perspective of the middle of the hand—you can only "win" half of the dead money in the pot. However, when you include everything in the pot, including your calls, then the amount you "win" in a split pot case is exactly half of when you scoop.

[/ QUOTE ]I’m not “hung up” on anything except maybe seeking the truth. Assuming the pots are of the same size and your cost is the same each time, the amount you net when you win two half pots and lose none is exactly the same as you net when you scoop one pot and lose another.

Get it? You have to lose one time for every time you scoop for two half wins (with no losses) to equal a scoop.

[ QUOTE ]
And it is the total size of the pot that is important in an equity calculation since you will get back, on average, your equity share of bets being put in currently as well as the dead money.

[/ QUOTE ]I include what I expect on future betting rounds in my EV computations. I think that’s a better way to proceed than just considering the current betting round. My opponents and I have the option of folding after the second betting round. When you fold after the second betting round, you don’t put any more bets into the pot.

Let’s say you see the flop 100 times with hand A and also 100 times with hand B. Let’s say the expected amount contributed to the pot by your opponents is 24 small bets, and if you stay to see the showdown, it will cost you six small bets. Let’s say you’re able to get out of both hand A and hand B easily when you miss the flop, and you do get out of the hand every time you miss the flop.

Let’s say you expect to only scoop with hand A and you expect to only win half the pot with hand B.

Let’s say you get a favorable flop 20 times and an unfavorable flop 80 times for hand A. and that you get a favorable flop 40 times and an unfavorable flop 60 times for hand B.

The PokerPro simulator would show these two starting hands as having the same “pot equity.” Similarly, the two dimes.net simulator would show these two starting hands as having the same E.V.

But look again.
You’re going to net 480-80 = 400 small bets scooping 20 times with hand A.
You’re going to net 360-60 = 300 small bets winning half 40 times with hand B.

Assuming you’re able to get out of a hand when you miss, you end up doing better with hands that scoop X times than with hands that win half the pot 2X times.

The ProPoker simulator evidently assumes you play the hand through to the showdown. However, I don’t play all hands all the way through to the showdown, and neither do most of my opponents. When one doesn’t play all hands through to the showdown, some hands that ProPoker would rate as having the same pot equity actually have different expectations.

[ QUOTE ]
Given that we know we have a "fresh money" equity edge with top set (you may not believe this yet, but hopefully you will), I will argue until my lips bleed that you can't be making a losing play by raising. Raising may not always be the best play, and you provide several important reasons for that throughout this thread. However, when you contend that it is a losing play because your hand is "drawing", you imply that it does not have "fresh money" equity, which I think is wrong.

[/ QUOTE ]It may not be a losing play for the current betting round, but you may not win as much on the next <font color="red">TWO</font> betting rounds.

[ QUOTE ]
…try out the following calculators:
ProPoker Tools Simulator Twodimes Calculator

[/ QUOTE ]Thanks for the links.

[ QUOTE ]
Try to come up with as many possible scenarios as you can to have top set on the flop texture we've been talking about. I think you'll find that top set will have better than fair share on "fresh money" equity.

[/ QUOTE ]Fresh money odds depend on the number of opponents who will call your bet or raise. I can hardly imagine folding when I flop a set of kings. But I might not bet or raise, depending.

[ QUOTE ]
You stated earlier that 2/3 of the time with top set you'll be drawn out on and won't win anything. Of the 1/3 that you win, 6/11 times you'll have to split with the low.

[/ QUOTE ]I was trying to keep things as simple as possible when I used those approximation estimates.
[ QUOTE ]
Well let's use these numbes to figure fresh money equity.

[/ QUOTE ]I don’t like the label “fresh money equity,” although I think I understand what you mean by it. Instead I prefer to use what I (and others) label as “fresh money odds.”[ QUOTE ]
Given n players in the pot, two out of three times we will lose a bet. 6/33 times we'll win n/2-1 bets and 5/33 times we'll win n-1 bets.
When n=4, we are losing 1/33 of a bet with each bet that is going in. With n=5, we are clearly winning with each bet put in.

[/ QUOTE ] Yes. Agreed. We’re winning that much on the second betting round. However, we may not win as much on the next two betting rounds as when we simply call.
[ QUOTE ]
I believe your numbers are less accurate for the cases when there are fewer players (n=4 or less) because you overestimate the number of times all the draws are out against you,

[/ QUOTE ]Good point.
[ QUOTE ]
and you underestimate how often your opponents may have the same draws, thus eating up outs.

[/ QUOTE ]That’s a two edged sword. Your opponents who have sets or two pairs eat up your own outs. But yes, opponents often have the same draws.
[ QUOTE ]
With 3 or fewer opponents, not all low cards will fill a straight. You may even occasionally win half on a flushed board.

[/ QUOTE ]Good points. Especially with three or fewer opponents, your unimproved set may win even when a flush or straight is the nuts.
[ QUOTE ]
Given these possibiliities, I think even your calculations will allow that putting extra money in with top set can be a winning play.

[/ QUOTE ]Whoa! I honestly don’t think it is, even given those possibilities. When I flop a set of kings, I’m almost invariably going to put the required money in on the second betting round, and if nobody has bet in front of me and I think nobody will bet behind me, I'll put in the first bet myself. But I’m not generally going to raise a bet after a 34K flop with nothing but top set. I’ve given my reasons already. I think I follow your reasoning for raising, and although you make some excellent points, I'm still convinced that not raising is generally better. I do believe in mixing up your play, and there could be special circumstances which would lead me to raise, but my default mode here is not to raise.
[ QUOTE ]
Hopefully that clears up the argument I've been trying to make.

[/ QUOTE ]Yes. It does. Thanks. [ QUOTE ]
I hope I've at least been able to help you think about how to use equity at the tables,

[/ QUOTE ]I see what the PokerPro simulator is doing and that you evidently believe “pot equity” is the correct way to the truth. However, if it’s all the same to you, I am going to continue to sometimes use implied pot odds or reverse implied pot odds as part of a decision to call or not, and I am going to continue to sometimes use fresh money odds as part of a decision to raise or not.[ QUOTE ]
if not convince you that raising top set is not a losing play!

[/ QUOTE ]I still don’t think you’ll net more on the second betting round by raising with only three opponents – and when you consider probable greater gains on later betting rounds when you don’t raise, more often than not, you will net less in a typical casino limit Omaha-8 game by raising on the second betting round with the hand/flop under discussion.

Although it’s true you’ll win more often with fewer opponents, you’ll want as many customers as possible when you make your draw. You can get hurt on the river with only top set when a flush or straight becomes possible, even with only three opponents. In a limit game, flopped top set with a coordinated two or three card low board just doesn’t seem all that great to me in a typical limit Omaha-8 game.

Let’s end this discussion here, or if you want the last word, I won’t respond again. We seem to be at an impasse.

Buzz

[Ergodicity]

I can't believe its taken Buzz and jai 19 posts to finally realize they are saying the exact same thing. too funny.

[luckyharr]

[ QUOTE ]
I can't believe its taken Buzz and jai 19 posts to finally realize they are saying the exact same thing. too funny.

[/ QUOTE ]

Saying the same thing but still disagreeing on the correct action. I think it comes down to Online PLO8 (jai) vs. Live LO8 (Buzz)