The Top Set dilemma

[jai]

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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.

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Agree 100%.

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

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Now let's see how can we use it to help us decide whether or not to bet. Let's use a real life example from Texas Hold'Em. Let's say there are 4 hands: Th Jh, 9c 9s, As Ac, 6d 7d.

Let's say the flop is: 9h 8h 5c

Well, who would be profiting by betting and raising on this round of betting? Here is the calculation:

http://twodimes.net/h/?z=2052349
pokenum -h jh th - ac as - 9c 9s - 6d 7d -- 9h 8h 5c
Holdem Hi: 820 enumerated boards containing 5c 9h 8h
cards win %win lose %lose tie %tie EV
Jh Th 346 42.20 474 57.80 0 0.00 0.422
As Ac 13 1.59 807 98.41 0 0.00 0.016
9s 9c 270 32.93 550 67.07 0 0.00 0.329
7d 6d 191 23.29 629 76.71 0 0.00 0.233,

Let's the say size of the bet is $25. How much would everyone profit by putting in bets on the flop? Well, for each bet put in, the Jh Th returns on average 42%. So if everyone puts in one bet, the total would be $100, and the Jh Th would expect $42 of that on average. Thus, it is making $17 (42-25) of each bet that is put in. On the other hand, 6d7d has equity of only 23%. Thus, with each additional bet put into the pot, it is actually losing $2. So who should be betting and raising in this scenario? The big draw and the set both have greater than 25% equity, and will profit from all additional money that goes into the pot. The AA and the straight lose by putting additional money in the pot.

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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.

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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.

What I was trying to tell you before was that the top set example is exactly analagous to the hold 'em hand I just talked about above. In a four handed pot, it will be rare for top set, even on that board, to have less than 25% equity against three hands, thus it is making money by putting in bets on that round if everyone calls.

Is it just me, or isn't this all very basic?

[chaos]

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i'd never play KKxx that didn't have a quality low possibility, with the exception of the big blind.

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I think this is too tight. Hands with suited Kings and coordinated cards will show a profit (e.g. KKQJ ss or ds). So will two big pair (KKQQ, KKJJ) especially if at least one of the Kings is suited up.

[toots]

Man, I just love it when Buzz and Gergery get into math geek mode. I live for this sort of thing.

But, to respond to chaos, I'd play KKxx where x and x are both high. I'd play KKxx where x and x are both wheel cards, especially when one or more is suited with a king. What I doubt I'd play is KKxx where x or x is a 7/8/9, even if it's suited. The high only hands work great when no low is possible, and the high/low hands work fine when there's both possible, but having a KK and no realistic shot at low and without two backup high cards... I don't know how I'd want to play that hand.

[luckyharr]

jai:

I'm pretty sure he's understanding the equity calcs. I think he's saying the reverse implied odds of top set negate the equity advantage present on the flop. Here's a disgusting example...

http://twodimes.net/h/?z=2052964
pokenum -o8 kc kd qh jd - ah 2h 6s 8s - ad 5d 6c 7s - 4c 4s 2s 3c -- ks 3h 4h
Omaha Hi/Low 8-or-better: 528 enumerated boards containing Ks 4h 3h
cards scoop HIwin HIlos HItie LOwin LOlos LOtie EV
Kc Kd Jd Qh 102 198 330 0 0 0 0 0.284
8s 6s Ah 2h 166 185 343 0 302 57 16 0.501
7s 6c Ad 5d 36 114 414 0 57 312 6 0.165
4s 2s 4c 3c 17 31 497 0 0 57 10 0.050

Top set has .034 more than fair share. If 8 BB go in on the flop (capped four ways,) your booking .272 BB in profit. If you are always paying off bets on later streets, then it is a losing proposition.

[davebreal]

limp with AA UTG 24% of the time?

lol

[jai]

luckyharr,

That is one disgusting example. Note that even with that murderer's row set of hands, the top set still has an equity advantage. There will often be scenarios where that top set does much better on the flop.

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If you are always paying off bets on later streets, then it is a losing proposition.

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True. I think I mentioned something to that effect earlier. But we are allowed to fold when the situation becomes dire.

Buzz may or may not understand what we mean by equity. But based on these statements:

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...not that your pot equity matters much (IMHO) unless you’re looking for a settlement.

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and

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

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clearly indicate that he doesn't think pot equity plays much, if any, role in betting decisions. I strongly disagree with that assertion.

[luckyharr]

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

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clearly indicate that he doesn't think pot equity plays much, if any, role in betting decisions. I strongly disagree with that assertion.

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As long as we have an equity advantage, we should be willing to put in as many bets as we can, right? Ray Zee pointed out earlier that more customers will likely provide us a larger equity advantage, and a less aggressive approach to induce multiway action is likely the best line. That makes sense as a reason to not face the field with two cold, but if we're presented the opportunity to face the whole field with another bet, I don't see why we would pass up that opportunity.

[luckyharr]

Also Jai, I laughed at this part of the thread.

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I figure "expected value" (also known as "E.V.") to be the net you expect to win (if positive) or lose (if negative).

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[Buzz]

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Let's use a real life example from Texas Hold'Em. Let's say there are 4 hands: Th Jh, 9c 9s, As Ac, 6d 7d.
Let's say the flop is: 9h 8h 5c

[/ QUOTE ]Jai - Very interesting simulation results. 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.

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The big draw and the set both have greater than 25% equity, and will profit from all additional money that goes into the pot.

[/ QUOTE ]I see what you’re saying, and I agree – but your reasoning is in terms of the fresh (additional) money going into the pot rather than also involving whatever was in the pot before the second betting round. I’d say you’re using “fresh money equity” rather than “pot equity.”

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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?

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. And even in Texas hold ‘em your pot equity, except for a settlement, seems largely irrelevant to me. Maybe there’s some indirect way you can use pot equity, to determine if it’s correct for you to call or not, or even to determine if it’s correct to bet or raise or not – but I don’t see any direct relationship.

You seem so sure of yourself that I can’t help but wonder if some of the words we’re using have different meanings for you than for me. Indeed, in your Texas hold ‘em example, you’re not using what I would call “pot equity” to determine the advisability of betting.

What hero should do depends on how many opponents Hero has and how they play. But in a typical casino limit ring game in the $3/$6 to $6/$12 range, holding only top set and nothing else worthwhile after a flop of 3[img]/images/graemlins/heart.gif[/img], 4[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/diamond.gif[/img], I think Hero does better by not jamming on the second betting round. You want Hero to jam here and I don’t. I guess we'll never agree on that point. With some hands/flops, I would think jamming with top set is in order – just not this particular time.

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What I was trying to tell you before was that the top set example is exactly analagous to the hold 'em hand I just talked about above.

[/ QUOTE ]I don't think so. I don’t think they're very analogous situations. There’s a big difference between the value of top set in Texas hold ‘em and Omaha-8. And there’s a substantial difference between outs for the whole pot and outs for part of the pot.

Have you considered the possibility that even if you are somehow using "pot equity," there might be more than one way to figure when it is right to bet? Have you considered the possibility it may not be necessary to compute “pot equity”?

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Is it just me, or isn't this all very basic?

[/ QUOTE ] I don’t know. What is “very basic” to one person may not be basic to another. Maybe once you think you understand something very well it seems “basic.”

I wasn’t sure what Effen meant by "equity calculations." And then when you responded to my response to Effen, I wasn’t sure what you meant. No offense intended. Perhaps “equity” means something different to me than to you.


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Buzz may or may not understand what we mean by equity. But …(snip)… he doesn't think pot equity plays much, if any, role in betting decisions.

[/ QUOTE ]Yes. That is correct. I’m not sure I understand what you mean by equity. No offense intended. And I don’t think pot equity plays much, if any, role in betting decisions.

When I’m drawing, I compare the odds against making my draw to the “implied pot odds” in deciding whether I have favorable odds to call or not.

There are various considerations besides just having favorable odds involved in betting or raising. But sometimes as part of my decision, I compare the odds against making my draw to “fresh money odds.”

I think of my “pot equity” as being my fair share of the pot if a settlement was to be made. (That is very different than my share of fresh money going into the pot). I’m not ever consciously using what I think of as “pot equity” in betting decisions and I don’t even see a direct relationship.

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I strongly disagree with that assertion.

[/ QUOTE ]Then in my humble opinion you either don’t know what you’re doing or the term “pot equity” has a different meaning to you than to me.

<ul type="square">As used here:
“hand odds” = the odds against making my draw.

Read David Sklansky’s The Theory of Poker to see what implied pot odds are.

fresh money odds = the portion of the money my opponents are putting in the pot on the current betting round that I stand to win if I make my draw compared to the money I will put into the pot on the current betting round.

By “compared to,” I mean divide one by the other.[/list]
I hope this (finally) makes it clear.

Buzz

[Buzz]

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Buzz may or may not understand what we mean by equity.

[/ QUOTE ]Luckyharr - The word “equity.” does have a certain meaning to me. It’s a word I use from time to time. The concept of “equity in a poker pot” (which I’d call “pot equity” for short) has a more specific meaning to me. However, I’m not sure if it means the same thing to you as to me. No offense intended.

If “pot equity” did have the same meaning to you as to me, then assuming you know what you’re doing, I don’t think you would involve it in the decision whether to raise or not.

There are lots of reasons to raise in poker. Having a certain pot equity, if we’re thinking of the same thing, is not involved in any of them.

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Also Jai, I laughed at this part of the thread.
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I figure "expected value" (also known as "E.V.") to be the net you expect to win (if positive) or lose (if negative).

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I imagine you are aware that people sometimes have different meanings for the words or terms they use. I suppose it can be funny when they do.

However, in this case it was a matter of failing to communicate with a reader and wondering if the words and terms I was using meant the same thing to the reader as they meant to me. I don’t know why you would find such an attempt to communicate laughable, but if it has amused you, fine.

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As long as we have an equity advantage, we should be willing to put in as many bets as we can, right?

[/ QUOTE ]I don’t know what you mean by “equity advantage.” I’m not trying to be tricky. I can interpret “an equity advantage” in more than one way.

As long as it’s to your advantage to raise, then you should (obviously) put in as many bets as you can. Whether or not it’s to your advantage to raise often depends on how many customers you will have on this and future betting rounds if you raise now as opposed to just calling at this point. (It's not exactly the same as slow playing flopped quads, but similar).

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Ray Zee pointed out earlier that more customers will likely provide us a larger equity advantage, and a less aggressive approach to induce multiway action is likely the best line.

[/ QUOTE ]I wouldn’t say “equity” advantage. But yes, more customers are better when you make a winning hand. And yes, a less aggressive approach is the best line in this particular case (and in similar cases). Jai evidently disagrees about a less aggressive approach being better. (And from what you write below, I would guess you disagree too).

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That makes sense as a reason to not face the field with two cold, but if we're presented the opportunity to face the whole field with another bet, I don't see why we would pass up that opportunity.

[/ QUOTE ]I’ll give you three direct reasons and I can also think of some indirect, more subtle reasons that I won’t mention: (1) When you raise to get more money in the pot, the fellow right behind you may re-raise so as to “face the field with two cold,” thus making it more difficult for opponents to continue, even though they’ve already put in one bet on the current betting round. Remember, when the action gets back to you, you can re-raise, and everybody who is not an idiot knows they might be facing more bets. (2) When you raise on the second betting round, it often will be more difficult to get in multiple bets on a later betting round. (3) It costs you twice as much when you raise.

That’s why. There’s a bit more to it than just that, but that should be enough for you to at least realize that sometimes it’s better to “pass up that opportunity.”

Buzz