The Top Set dilemma

[portisfreak]

Mr. Zee (sounds like that new series of car commercials), have you ever considered adding a loose game section to your original Eight or Better book or even writing an entirely new book to loose, small stakes O8 games?

[Ray Zee]

no, working on a high stakes limit holdem book now with dave fromme

[Buzz]

[ QUOTE ]
Same situation but now there's also 2 suits

[/ QUOTE ]Kurto - Let's start with this one. Suppose you hold
K[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/spade.gif[/img], T[img]/images/graemlins/club.gif[/img], T[img]/images/graemlins/spade.gif[/img].

In a full game, 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], you figure to win mainly when the board pairs and you make kings full or quad kings. A significant problem when you play this hand/flop is you’re going to end up with (unimproved) three kings on the river approximately two times out of three. And by the time you’ve gotten that far, there’ll be enough in the pot so that you may want to see the showdown, just in case the person betting only has a low and/or nobody has a high better than trip kings. Thus you may be stuck for a bet on the fourth betting round, even when your set of kings doesn’t improve.

After a flop with two wheel cards plus a king there’s no guarantee one of your still active opponents will make a straight, but in a typical full, loose ring game, there’s a very strong chance somebody will. Two cards in the same suit increase the chances for an opponent to out-draw you by adding the flush draw. Note that with this flop
(3[img]/images/graemlins/heart.gif[/img], 4[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/diamond.gif[/img]), there are only 27/990 two card combinations (for the turn and river) that do not enable a better hand than trip kings. Although trip kings is the best hand possible immediately after the flop, it’s about 97% certain trip kings won’t be the best possible hand at the showdown. Although trip kings might often win even when not still the best possible hand at the showdown, after this flop in a typical full, loose game that usually will not be the case.

Considering your cards and the flop cards, when the board does pair, low will be possible roughly 6/11 and not be possible 5/11. Thus you’ll win for high and split with low approximately 6/11 when the board pairs, while you’ll win for high and scoop approximately 5/11 when the board pairs. With this flop and your hand there’s also a slight chance that if you make kings full, you will be beaten by aces full, quads, or a straight flush. (But let’s ignore that possibility for now).

From your vantage point you can see seven cards. Considering your cards and the flop, there are 990 possible turn/river combinations. Of these, 336 pair the board, 6 make trip threes or trip fours on the board, while 648 do not pair the board. Thus the probability of the board having one or two pairs on the river is 0.339 (very close to one in three).

Whether or not you continue with your set of kings if you don’t improve, let’s think in terms of winning about one out of three and losing the other two out of three. I think that’s pretty close to what actually will happen in a typical full game. The times your set of kings will prevail is somewhat (although not quite) counter-balanced by the extra cost when you don't improve and by the times you’ll make kings full, only to lose to aces full, quads, or a straight flush.

But let’s keep things as simple as possible. In 33 tries, if you figure to lose 22 times, and win 11 times. Roughly:
<ul type="square">5 times you scoop,
6 times you win the high half
22 times you lose.[/list]That’s a reasonably good approximation, I think.

Let’s assume the betting after the turn and river has no dependence on the action before or immediately after the flop. That’s not quite true, but it’s hard to know how the second round action will affect future betting. If anything, alerting your opponents that you have a strong hand will make it more difficult to extract bets from your opponents on future betting rounds when you do get a favorable card on the turn or river. But let’s ignore this effect in the interest of simplicity.

Isolate the betting on the second betting round.
To do that, think only in terms of what happens to every bet made on the second betting round. With three opponents matching your investment on the second betting round, when you get to the showdown, just in terms of what happens to the second round bets:
<ul type="square">5 times you’ll scoop and win three bets (subtotal +15 bets),
6 times you’ll win the high half and win one bet (subtotal +6 bets), and
22 times you’ll lose one bet (subtotal -22 bets).[/list]It’s close, but the positives don’t quite make up for the negatives.

That’s with three opponents matching your investment. With less than three opponents who will call, you do even worse. In order to get favorable odds to initiate money into this pot, you need more than three opponents who will call your bet or raise.

In general, you want as many paying customers as possible when the board pairs. The more the merrier! However, at least some of your opponents probably react to heavy action on the second betting round by folding non-nut draws.

This can work to your advantage. You’d obviously like to knock out anybody who would otherwise end up beating you while keeping everybody who would lose to you in the pot as a paying customer on the river.

For example, if you knew the turn card or the river card would be a three, you’d like to knock out an opponent holding a pair of threes (and who would thus make quad threes). Similarly, if you knew that the river and the turn would both be threes, you’d like to knock out anybody holding a single three (and who would thus make quad threes). However, you don’t know what the turn or river will be.

I’m not proposing you should necessarily fold unless the board pairs, but for the sake of simplicity in this discussion, let’s assume you will fold unless the board pairs. And let’s ignore the possibility an opponent will make aces full, quads, or a straight flush.

<ul type="square">When the board pairs, anybody with a set has either made quads or a full house. Let’s assume another opponent has a hand with a pair of threes and has thus flopped a set of threes. Knowing that if the turn or river is a three this opponent will have quad threes, do we want this opponent in the pot or not?

For the purpose of this discussion, let’s give an opponent a flopped set of threes, but nothing else. In this case, if the turn or river is a three, then you’ll have kings full but this opponent will have quad threes. Let’s make this opponent’s hand:
3[img]/images/graemlins/spade.gif[/img], 3[img]/images/graemlins/spade.gif[/img], 2[img]/images/graemlins/club.gif[/img], 2[img]/images/graemlins/club.gif[/img]. Do we want this opponent staying in this pot or not?

Since we know this opponents hand (3322), we have more information. What happens in terms of times per hundred given above are different. (In this case, the board would only pair 246/903). If we’re only going to stay in the hand when the board pairs anyhow, then we beat the opponent holding 3322 about fives times more often than this opponent beats us.
It's 206/246 for Hero and 40/246 for Villain.[/list]Thus when the board pairs after the flop, unless your average share of the pot is going to be more than five times your total investment after the flop (and considering how often you’ll have to split, a five to one ratio is almost impossible and certainly unrealistic), you should want the player with 3322 staying in the hand. One time out of six you’re going to get burned by quad threes when the board pairs (with threes and no king or with running deuces), but the other five times out of six your opponent holding 3322 will be a paying customer, likely paying off with an inferior full house. Better yet, you like Villain with an inferior full house betting into you. To achieve this, you certainly don’t want to alert Villain to the possibility you have flopped top set (by raising on the second betting round).

Similarly, you want everyone who flops an inferior set or two pairs to stay in the hand as a potential customer.

Therefore.....
<ul type="square">Rule one: You want as many customers as possible in the hand with you when you make a winning hand.
Rule two: Since you’re drawing (to make a full house or quads) with only a poor chance to win when you miss, you want to draw as cheaply as possible.[/list]Thus jamming with a flopped set is not generally the thing to do on the second betting round. But in order to get a better idea of where I stand, and also because of the way I play certain other hands/flops, (and also to get rid of freeloaders who, having terrible odds on various back-door draws, would fold to a bet, but who might out-draw me if given a free ride), I like to make sure one bet goes into the pot on the second betting round. And you probably should too. That doesn’t mean you should necessarily bet yourself on the second betting round. And you certainly shouldn’t raise if by doing so you risk losing potential customers, and/or when you have fewer than four opponents who will call your raise.

Unless maybe you’re a super math genius (and maybe even if you are), I don’t think you can figure that all out during the play of a hand. You just have to remember what to do with top flopped set when the flop also has two wheel cards.

Summary: How do you play top flopped set (but nothing else) 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]? Call if someone else has bet in front of you. When you are reasonably certain there will be a bet behind you if you check, then check. When you think everyone will check if you check, then bet. When you don't know, then bet. But don't raise!

[ QUOTE ]
Same situation but its not 2 wheel cards?
(3) Ex Flop of K82 (rainbow)? Because the straight is less likely, do I know play it more aggressively?

[/ QUOTE ]Yes, you play it more aggressively.

In this case, nobody can have a direct flush draw or straight draw. Anyone betting or continuing probably has a low draw, and/or possibly a non-nut set or two pairs. If you can limit the field by aggressive betting, then even when a flush or straight comes in via the back door, your (non-nut) set of kings will probably prevail. Thus you want to bet very aggressively in an attempt to limit the field and reduce the chance of an opponent backing into a flush or straight. Also by betting very aggressively, you increase your chances of scooping by possibly knocking out someone with a non-nut low draw plus a back-door high chance. You should probably be staying in for the showdown regardless of whether you improve or not. Instead of wanting as many customers on the river as possible, in case you make your draw, you want the very opposite, in case you don’t make your draw.

[ QUOTE ]
(1) ex Flop K34 (rainbow). There is a bet and a call in front of you. Do I want to be very aggressive here?

[/ QUOTE ]No. This is in-between the other flops discussed above, but the three and four (two wheel cards) make it more similar to the first flop discussed than the 28K flop in terms of how you cope. You're unlikely to push someone off a straight draw plus a low draw. And though you may call on the river even when you don't improve, you'll probably have to improve in order to win.

The above discussion has not covered all the possibilities of flopped sets. The issue is very complex with lots of different cases.

I have hesitated in posting this since Ray Zee has already posted a response, and since I agree with his response. I don't want to be presumptive, but maybe my response supplements his.

Buzz

[Ray Zee]

always great to have you in a discussion buzz as you do all the hard leg work. in the end we get the point most pass by, is that when the board gets coordinated one way hands become close to junk hands unless the circumstances really go well..

[EffenDolts]

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

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

Simulated against 4 hands with top 20% of holdings:

1) board: 3h4sKd Pot equity 39.1%
2) board: 3h4hKd Pot equity 35.4%
2a) board: 3h7hKd Pot equity 40.9%
3) board: 3h7sKd Pot equity 45.2%

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. Obviously, you don't want it checked around. According to OP: "There is a bet and a call in front of you." If I am last to act, I can't see much downside to raising in late position on any of these flops. The turn might pair the board or brick the other draws. How well are you going to get paid off in that case?

I think the hands that you fold out with a raise weren't going to pay you off anyway, and they might even hit runner-runner and scoop you.

If there is no bet in front of you, you have to bet unless there was a PF raiser yet to act who is almost certain to C-bet.

If there is a bet, I am second to act, and there are 3 to act behind me, then I call rather than make them call 2 bets cold.

The one danger is that all of the good cards are in one hand. If you end up headsup against Ah2h5cAd on a 3h4hKd board, you are in deep doo doo. If the good cards and draws are spread around, you need to make them pay to draw.

Effen

[Mendacious]

Situation 1: I bet less than the pot, probably half the pot. I want to build the pot, and this is the same type of move I make with a decent wheel draw, so my holding should be somewhat disguised. If someone else bets, I may raise and get frisky.

Situation 2: I check this at least 50% of the time. The remaining times I bet no more than half the pot. If someone pots it to me I call.

Situation 3: 1/2 pot to full pot bet most of the time, (rarely check to mix things up, and if I think there is a good chance everyone will fold if I bet, but that 2 players would pay me off if the low card came)

[mrroyboy]

Kurto
In the 25 buyin party poker game Hand 2 should be played cautiously. Get in cheap. Possible dump on the turn.
Hand 3 should be played aggressively and hand 1 is somewhere in between.
KK and other high pairs are much more profitable at 25 level so that you can play them in any position IF you can get in cheap.
Remember many players will pay you off with lesser fullhouses which is the key.

[Buzz]

[ 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.)?

A general problem with high/low simulations is if a hand plays 10,000 times and wins half 4,000 times (losing the other 6,000 times), assuming the pots are of equal average sizes, the hand ends up with exactly as much as if the hand plays 10,000 times and wins the whole pot 2,000 times (losing the other 8,000 times). This might lead one to falsely believe winning half a pot 4,000 times is the same as scooping 2,000 times.

But it's not - unless you play and lose with the hand that scoops more often than you play and lose with the hand that wins half the pot.

If you play and lose with each hand the same number of times, then the hand that scoops is better.

2 half pot wins = 1 scoop + 1 loss,

Keeping in mind that the 1 loss is a negative, when you take that negative away from the one side of the equation, the scoop is clearly worth more than 2 half pot wins.

I think probably what your simulator is doing (or you're doing in interpreting the results) is counting two half pot wins as equivalent to one scoop.

Instead, two half pots wins are equivalent to one scoop and one loss.

[ QUOTE ]
Obviously, you don't want it checked around.

[/ QUOTE ]I agree with you on this point.

[ QUOTE ]
According to OP: "There is a bet and a call in front of you." If I am last to act, I can't see much downside to raising in late position on any of these flops.

[/ QUOTE ]I'm not sure why you've chosen four opponents, but fine, let's say you have four opponents. If the first three opponents check and the player immediately in front of you bets, you confront the player in first position with a double bet with the possibility of a re-raise. And if he folds, then the player in second position......etc. The first downside is you may lose customers.

If the player in first position has bet and the intervening players have called, then when you raise, the player in first position may re-raise, confronting the intervening players with a double bet with the possibility of a re-raise. Again, the downside is you may lose customers.

There's another downside for you. In reading your posts, you seem like a solid player to me. When you raise the flop, rigthly or wrongly at least some of your opponents are going to suspect you possibly have top set. And that will make it more difficult for you to collect from these players later if the board pairs and you have the winning hand. I can think of ways you can (at least try to) get around your probable solid table image dilemma, but if you have that image, I think it's better for you to simply not raise the flop with top set and nothing else.

The third downside is that unless you have at least four opponents calling your raise on this round, you actually net more by not raising.

By not raising here, unless you have four opponents who match your raise, you net more for this betting round and you net more in terms of the final pot. Your sub-total gain (when you win) with less than four opponents is less than your sub-total loss (when you lose).

At any rate, you wrote, "I can't see much downside to raising in late position on any of these flops." Those are three downsides.

[ QUOTE ]
The turn might pair the board or brick the other draws. How well are you going to get paid off in that case?

[/ QUOTE ]You're obviously going to bet and raise on the fourth betting round if the turn pairs the board. If by doing so, you drive out the low draws and scoop without the river card being shown, then that's wonderful. If the low draws stay in the pot and miss, that's also wonderful. You don't have to raise the flop to be absolutely delighted when the turn pairs the board.

Hard to see how the turn bricks the other draws. Well... a high card is probably a brick for most draws after this flop (but it opens other possibilities) - and I suppose it's possible that the turn counterfeits some (maybe all) draws. After the 34K flop, anything that counterfeits the other draws is a pretty scary card for Hero. But, yes, it's possible that Hero would do better by raising after this flop. It's often possible in Omaha-8 (or any form of poker) that you can do the wrong thing, play against the odds, and it will turn out well for you. That's true if you play the slots too.

[ QUOTE ]
I think the hands that you fold out with a raise weren't going to pay you off anyway, and they might even hit runner-runner and scoop you.

[/ QUOTE ]Yes. That's true for some of them. But when they do, you have missed your own draw.

Two questions are, "Will the flopped top set hold up or not?" and "Will low be enabled or not?" When the flop is 34K, usually a flopped set of kings will not hold up and usually low will be enabled. Hero can win anyhow, and Hero is probably stuck in the hand anyhow. But Hero doesn't have to make his situation worse by raising after the flop.

[ QUOTE ]
If there is no bet in front of you, you have to bet unless there was a PF raiser yet to act who is almost certain to C-bet.

[/ QUOTE ]I agree you should generally bet if there is no bet in front of you. What does "C-bet" mean?

[ QUOTE ]
If there is a bet, I am second to act, and there are 3 to act behind me, then I call rather than make them call 2 bets cold.

[/ QUOTE ]Exactly.

[ QUOTE ]
The one danger is that all of the good cards are in one hand.

[/ QUOTE ]That's a danger, but I don't think it's the only danger.

[ QUOTE ]
If the good cards and draws are spread around, you need to make them pay to draw.

[/ 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!

Buzz

[jai]

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.

In the situation effen described, if the KK has 40% equity on the flop and the pot size is $100 on the flop and the bets are $20, then the KK can expect to return $40 from the pot on average+$8 from each bet (including its own) that goes in on the flop. Since it's equity is greater than the amount of money it is putting in with each bet, the KK is making money with each additional bet.

[jai]

[ 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 ]

Buzz,

This is flat out wrong. Well, technically you are correct since you are making it more expensive when you lose. 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. Your statement is only correct when your pot equity on bets going in is less than amount you are putting in. This will only be true in rare instances for top set in the situations described.