UPF - Hypothetical situation

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Hypothetical situation, Schuster, 15. Apr 2003 15:04
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A friend and I were having a discussion about this, and I think I got the answer right, but couldn't convince him. Two players are playing heads up. One holds two black kings, the other holds 6h 7h. Both see the flop for 1 small bet. The flop is 5h 8h 2c. At this point, both players flip their hole cards face up. The player with 2 kings is first to act. What is the correct play for each player and why?
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Re: Hypothetical situation, Wren, 15. Apr 2003 15:34
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Is this limit or no limit? If it is no limit, I believe that KK should check and then fold. Because 67h has the best of it here - he/she will make a flush or straight more than 50% of the time, and has other ways of drawing out as well. If it is limit, KK should check/call and see the turn. If the turn does not improve the 67h at all, KK should bet the turn (KK now has the best of it).
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Re: Hypothetical situation, Wren, 15. Apr 2003 15:40
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Hmmm wasn't finished the evaluation, I just realized. In the limit case, if the turn improves to give 67h a pair, KK should still bet out with slightly the best of it (67h has 20 outs to the win - 9 flush, 6 non-flush straight, 5 more that give 2 pair or trips. Therefore, KK has 24 safe cards.) Obviously if the turn gives 67h a made hand, KK folds.
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Re: Hypothetical situation, Schuster, 15. Apr 2003 16:44
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That's what I figured... Assume now that the pot is zero on the flop (some rake!). Then what is the play for each?
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Re: Hypothetical situation, Schuster, 15. Apr 2003 19:26
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I guess I should clarify why I'm putting this all down. When playing heads up, over time, one person has to be winning the money and one has to be losing the money, or else break exactly even (not likely). If the same situation were played out off to infinity, one player would have more money in the end. I guess the underlying principle is that one player would be losing over time, and that one player should be able to recognize that he is losing, and not put anymore money into the pot. Or am I missing something?
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Re: Hypothetical situation, shorn, 16. Apr 2003 06:01
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on 15. Apr 2003 15:40 Wren wrote: > Hmmm wasn't finished the evaluation, I just realized. In the limit case, if the turn > improves to give 67h a pair, KK should still bet out with slightly the best of it (67h has > 20 outs to the win - 9 flush, 6 non-flush straight, 5 more that give 2 pair or trips. > Therefore, KK has 24 safe cards.) Obviously if the turn gives 67h a made hand, KK > folds. > I am not so sure that I agree that KK should check/call the flop. Checking gives the inferior hand (at this point) infinite pot odds to draw (0:pot size) which you can't do. Also, with all of the information available, you can now always make the right play so if the turn brings the 76h one of it's puts, you then check/fold. While I agree that the 76h is a favorite here, I disagree with the check/call play while you are ahead. I would guess your theory would be that the 76h would raise on the flop if bet into. But, that could happen on the turn as well (with no improvement), so why advocate betting there and not the flop? Am I missing something here? Also, two of the 76h outs (Kh and 2h) gives you redraws on the river for the boat/quads. >
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Re: Hypothetical situation, Wren, 16. Apr 2003 08:26
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KK shouldn't bet the flop because 67h has the best of it. Yes, KK is still ahead, but 67h will be the winning hand by the river more than 50% of the time.
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Re: Hypothetical situation, shorn, 16. Apr 2003 08:37
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on 16. Apr 2003 08:26 Wren wrote: > KK shouldn't bet the flop because 67h has the best of it. Yes, KK is still ahead, but 67h will be > the winning hand by the river more than 50% of the time. How close is it? I am having a lot of trouble with this one because of the infinite pot odds issue. You have the lead...you KNOW you have the lead. You will know if you should dump it when the next card hits. Why let someone else take one off for free even though you know you are not the favorite at the end? To me, I think that you are foolish to not bet even though you know the draw will call. This sounds exactly like saying you shouldn't bet into possible flush draws if they have great odds to call because they will call anyway. We all know that everyone in this forum would bet that flop head to head with KK without knowing the information.
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Re: Hypothetical situation, Wren, 16. Apr 2003 09:15
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Ok here's some math. Let's hope I didn't screw this up somewhere along the line. :) There are 4 distinct possibilities for a turn card here. (1) A card making a flush or straight for 67h that does NOT include the Kh (14/45) (2) A card making a flush with the Kh (1/45) (3) A card giving 67h a pair (6/45) (4) A card NOT improving 67h (24/45) Now let's look at the individual probability breakdowns for each case: (1) 67h (44/44), KK (0/44) (no river card can help) (2) 67h (34/44), KK (10/44) (10 river cards give KK a tight or quads) (3) 67h (20/44), KK (24/44) (20 river cards give 67 a flush, tight, trips or 2 pair) (4) 67h (15/44), KK (29/44) (15 river cards still give 67h a flush or straight) Now we can obtain the probability that 67h will win on the flop: (14/45) + (1/4534/44) + (6/4520/44) + (24/45*15/44) = 0.570707 (57%) Therefore, as stdio pointed out, KK is not GIVING a free card by checking the flop, but taking a free card, hoping for either case (3) or (4) on the turn. At this point, KK can drive the betting. However, KK must pay off a bet by 67h on the flop because there are already 2 small bets and KK has obvious pot odds to take a card off.
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Re: Hypothetical situation, shorn, 16. Apr 2003 09:39
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on 16. Apr 2003 09:15 Wren wrote: > Ok here's some math. Let's hope I didn't screw this up somewhere along the line. :) > > There are 4 distinct possibilities for a turn card here. > (1) A card making a flush or straight for 67h that does NOT include the Kh (14/45) > (2) A card making a flush with the Kh (1/45) > (3) A card giving 67h a pair (6/45) > (4) A card NOT improving 67h (24/45) > > Now let's look at the individual probability breakdowns for each case: > (1) 67h (44/44), KK (0/44) (no river card can help) > (2) 67h (34/44), KK (10/44) (10 river cards give KK a tight or quads) > (3) 67h (20/44), KK (24/44) (20 river cards give 67 a flush, tight, trips or 2 pair) > (4) 67h (15/44), KK (29/44) (15 river cards still give 67h a flush or straight) > > Now we can obtain the probability that 67h will win on the flop: > > (14/45) + (1/4534/44) + (6/4520/44) + (24/45*15/44) = 0.570707 (57%) > > Therefore, as stdio pointed out, KK is not GIVING a free card by checking the flop, but taking a free card, > hoping for either case (3) or (4) on the turn. At this point, KK can drive the betting. However, KK must pay > off a bet by 67h on the flop because there are already 2 small bets and KK has obvious pot odds to take a card > off. Wren- Love the analysis and agree with all the math. The one thing that I am struggling with is that in limit poker, KK cannot get pot committed on the flop. So, he/she can always fold the turn when it comes if there is little to no chance to win. Furthermore, on the flop, there are 24 cards that don't help the 76h and 20 that do, so ON THE NEXT CARD, KK is a favorite to still be ahead. Combine this with the fact that KK cannot get pot committed (were only talking one bet here) and (IMHO) the analysis breaks down because the turn and the river are independent trials (i.e., KK will re-evaluate and not necessarily go to the end if it is not profitable). This is not the case in pot limit or no limit where the entire decision may have to be made on the flop. While looking at the math, betting the flop might be a marginally negative EV play in limit, I don't think that you can let the 76h draw for free when you have a chance to dump on the turn if need be.
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Re: Hypothetical situation, Wren, 16. Apr 2003 10:18
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"While looking at the math, betting the flop might be a marginally negative EV play in limit, I don't think that you can let the 76h draw for free when you have a chance to dump on the turn if need be." I maintain that 76 is not drawing here - KK is. But I'm struggling with another way of shedding light on this issue since the math doesn't seem to have you convinced. Ok - let's look at the math combined with a few betting scenarios. Assume a limit $5-10 game here. Scenario 1: KK checks flop and so does 67h. ($10 in pot) Scenario 2: KK checks flop, 67h bets and KK calls. ($20 in pot) Scenario 3: KK bets, gets raised (as 67h should very well raise here) and KK calls. ($30 in pot) Now, in each scenario, KK checks/folds on the turn if 67h makes a flush or straight (For the sake of simplicity, we will assume that KK checks/folds if the Kh comes as well.) KK bets out and 67h calls if 67h makes either a pair or doesn't improve the turn (67h has odds to draw in either case in all 3 scenarios). Now, let's look at KK's EV in all 3 scenarios (again, I hope my math is ok): Scenario 1: (-$10)(15/45) + ($30)(6/45)(24/44) + (-$30)(6/45)(20/44) + ($30)(24/45)(29/44) + (-$30)(24/45)(15/44) = $2.12 Scenario 2: (-$20)(15/45) + ($40)(6/45)(24/44) + (-$40)(6/45)(20/44) + ($40)(24/45)(29/44) + (-$40)(24/45)(15/44) = $0.606 Scenario 3: (-$30)(15/45) + ($50)(6/45)(24/44) + (-$50)(6/45)(20/44) + ($50)(24/45)(29/44) + (-$50)(24/45)*(15/44) = -$0.909 So as it can be seen, KK has the highest EV when there are NO flop bets. The more bets put in on the flop, the lower KK's EV becomes. From scenario 3, we can see that KK actually has negative expectation if it bets out on the flop, because 67h will raise and make KK pay two bets. KK will, on average, lose -$.909 each time this hand plays out in this way.
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Re: Hypothetical situation, stdioh, 16. Apr 2003 10:22
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Very nice explanation and summation. Indeed, in a limit game, the drawing hand should be putting money into the pot and the made hand should not because there is a better than 50% chance that the made hand loses by the river. If the turn is a blank then the kings are extremely strong as there are only 15 cards left to call out of 44 so there is only about a 1/3 chance of the drawing hand winning now.
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Re: Hypothetical situation, shorn, 16. Apr 2003 11:14
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Again, I agree with the math assuming that the hand gets played all the way to the river. Where we disagree (amicably of course) is that the KK is drawing on the flop. Because we know the other player's hole cards, we know we are ahead at this point. We also know that the 76h MUST hit something to beat us on either the turn or the river. The only reasoning that I can think of to check the flop and then bet the turn if a blank comes (and the 76h had checked the flop also) is that the double size bet only gives the 76h 2 to 1 on the turn for a call where they actually need 2.93 to 1 to call to continue (15/44). So is the idea save a bet (or two) on the flop in case the turn hits the drawer and then if not, make them make an error by calling without pot odds? Wow, did I really just convince myself of your argument here?? :(
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Re: Hypothetical situation, stdioh, 16. Apr 2003 13:40
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Shorn. Indeed, the "drawing hand" must hit a card to win. By the same token, the kings must hit 2 cards to win. Both cards must be cards that do not complete the "drawing hand" so really, both are drawing to mutually exclusive events...well mostly. The kings can survive a pairing card to the draw, but only one and they can survive a flush card, but only if it is a king and they tighten up. Nonetheless, the chances of one of the danger cards coming within the next two hands are high and thus the chance of the drawing hand to win more money based on multiple events goes up. In a limit game he will have the odds to call down a turn bet, so he is always going to see the river here.
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Re: Hypothetical situation, stdioh, 16. Apr 2003 07:40
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This is a great question and an interesting situation. It's mostly a coin flip, but with a twist. The drawing hand has a more than 50% chance of making his hand in the next two cards, but not much more than. The made hand has the knowledge that the drawing hand cannot call a turn bet of large size if he doesn't make his hand on the river and the drawing hand knows that the made hand cannot call a bet if he does make his hand on the river. Therefore one of three outcomes will happen: There will be an all-in bet on the flop, the draw will not improve and will fold to a large bet on the turn, the draw will improve and will make a large bet on the turn, folding the kings. Now we come to some game theory. We know that we will only see a river if there is an all-in bet on the flop and the drawing hand knows that he has to hit on the turn if he doesn't bet all-in. Since he is a big dog to the kings if he only gets to see one card then he must bet and force the all-in while he is a slight favourite so as to rob the kings of the ability to bet a blank turn. If the drawing hand checks then he will make no more money than is in the pot now and if he bets he has a slightly higher than 50% chance of doubling his bet and winning what is in the pot now. The action of the kings has to do with stack size. If the pot is 0 then the kings should fold here. If the pot is X and the bet is Y where Y is gigantically larger than X then the kings should fold, but in any real life situation that will just not happen. Possiblty on the first hand of a 3 day tournament? Regardless, if the bet isn't hugely over the size of the money currently in the pot and if it is a cash game (and thus there is no intrinsic value in survival, escalating blinds, etc) then it is correct for the kings to call the all-in bet on the flop. So to make a long story short, let's say that there is $100 in the pot and each player has another $1000 back. The kings want to see the turn for free (correct strategy), but the drawing hand bets all in (correct strategy), and then the kings call (correct strategy). The kings have now been totally hamstrung because the drawing hand gets to take two cards at one.
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Re: Hypothetical situation, shorn, 16. Apr 2003 07:49
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OK, but what if it were a limit game? Do you think the KK should give a free card on the flop?
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Re: Hypothetical situation, stdioh, 16. Apr 2003 08:04
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If it is a limit game, then it is to be played out the same way. KK isn't giving a free card because KK is not a favourite. KK is drawing for a card that doesn't help his opponent. Thus he should take the free card if possible and then play accordingly on the turn. He should bet if he has the best of it on the turn. Now if his opponent improves to one pair on the turn then he has 20 outs which is still slightly less than half the number of cards in the deck (44) and thus the kings should bet the turn as long as they are winning, but the drawing hand should call this bet if it turned 2 pair. What gets more interesting is if the board pairs and makes the draw for the drawing hand. Now the kings have outs to a tight. There is then a 1-11 shot that the kings redraw on the river and win anyway. Thus if we somehow manufacture some money in the pot (for the sake of argument) to give the kings pot odds then a call can be made. So if we are playing pot limit, this gets to be a very interesting excercise. The drawing hand is correct in betting the pot on the flop and the kings are correct in calling. Now if the draw is made and the board pairs then the drawing hand is correct in betting the pot and the kings must fold, but if the drawing hand doesn't have enough money to lay worse than 11-1 pot odds on the kings then the kings must call the drawing hand's all-in bet. Conversely, if the turn comes to give the drawing hand a pair, the kings' prerogative is to make a pot sized raise, but the drawing hand has pot odds to call. Thus in a pot limit game the following would be correct play. Flop: drawing hand bets pot - made hand calls. Turn (pairs the drawing hand): made hand bets pot - drawing hand calls. River: winner takes money in the pot which is now nine times the value that it was on the flop.
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Re: Hypothetical situation, 4 POKER, 16. Apr 2003 07:51
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on 16. Apr 2003 07:40 stdioh wrote: > This is a great question and an interesting situation. It's mostly a coin flip, but > with a twist. The drawing hand has a more than 50% chance of making his hand in the > next two cards, but not much more than. The made hand has the knowledge that the > drawing hand cannot call a turn bet of large size if he doesn't make his hand on the > river and the drawing hand knows that the made hand cannot call a bet if he does make > his hand on the river. > > Therefore one of three outcomes will happen: > There will be an all-in bet on the flop, the draw will not improve and will fold to > a large bet on the turn, the draw will improve and will make a large bet on the turn, > folding the kings. > > Now we come to some game theory. We know that we will only see a river if there is > an all-in bet on the flop and the drawing hand knows that he has to hit on the turn > if he doesn't bet all-in. Since he is a big dog to the kings if he only gets to see > one card then he must bet and force the all-in while he is a slight favourite so as > to rob the kings of the ability to bet a blank turn. If the drawing hand checks then > he will make no more money than is in the pot now and if he bets he has a slightly > higher than 50% chance of doubling his bet and winning what is in the pot now. > > The action of the kings has to do with stack size. If the pot is 0 then the kings > should fold here. If the pot is X and the bet is Y where Y is gigantically larger > than X then the kings should fold, but in any real life situation that will just not > happen. Possiblty on the first hand of a 3 day tournament? Regardless, if the bet > isn't hugely over the size of the money currently in the pot and if it is a cash game > (and thus there is no intrinsic value in survival, escalating blinds, etc) then it is > correct for the kings to call the all-in bet on the flop. > > So to make a long story short, let's say that there is $100 in the pot and each > player has another $1000 back. The kings want to see the turn for free (correct > strategy), but the drawing hand bets all in (correct strategy), and then the kings > call (correct strategy). The kings have now been totally hamstrung because the > drawing hand gets to take two cards at one. Very interesting and well thought out response. 4 POKER
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Re: Hypothetical situation, stdioh, 16. Apr 2003 08:06
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Thanks. Puzzles like this really amuze me. Hmmm...perhaps if I have some spare time on my hands this weekend I'll make up some poker logic puzzles. Assume all players play correctly, these are their cards and stacks and here is what happens, how much money is in the pot at the end, etc.
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Re: Hypothetical situation, Wren, 16. Apr 2003 08:29
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That's a good idea. Let's do it. BTW your spelling sometimes amuses me :P
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Massive Importance of Stack Size., stdioh, 16. Apr 2003 09:57
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I know...I am a bad bad speller - but my vocabulary is spliferiffic, so that makes up for supmin' :) Now I've been thinking about this hand in pot limit and it is even more complex. What if it is pot limit and the stacks of both players are unlimited? Although the drawing hand is a favourite, he knows that he will not see a river unless he hits a pair on the turn. Thus he has 15 outs that win the pot on the turn and 6 outs that see a river against a pot sized bet. Of those 6 outs he is close to a coin flip to win the hand, so we can discount them from our calculations. There are 45 unseen cards, 15 good and 6 neutral, so then there are 24 cards that will make him fold on the turn to a pot sized bet from the kings. Kings will always bet to take the pot if the drawing hand does not improve. Thus there is a 24/45 chance that he loses the pot on the turn and a 15/45 chance that he wins the pot on the turn, with a 6/45 chance that he is in a neutral position with respect to the pot on the turn. Thus, the drawing hand should obviously not put money into the pot unless he can get all in or put his opponent all in (or close enough to all in for practical purposes) with a pot sized bet. Thus, in this case it is incorrect for the drawing hand to put money in and correct for the made hand to put money in. Thus the kings should be making a pot sized bet here. With a full pot sized bet here and a 1/3 chance of winning on the turn either move of calling or folding is a +0 EV move, so we must examine the neutral case more closely. As we discussed previously, if the drawing hand has paired on the turn then he has 20 outs from a remaining 44 cards and thus has a little less than a 50% chance of winning. Thus the neutral case above should be called a slightly negative case and he should fold to the pot sized bet. So how is this for being counterintuitive: If the game is pot limit and the hands are face up, the mathimatically most correct play is for the kings to make a pot sized bet, even though not the favourite to win on the river and for the drawing hand to do one of the following actions: raise all-in if it is possible to put either player all-in on the flop (or close enough to all-in that any turn card will result in a mathematically correct all-in on the turn for either player), otherwise, if the stack sizes are big enough then fold. The worst thing the drawing hand can do here is call. How is that for counter-intuition. Now we can take this to another level. The kings know the size of the stacks as well, so if the drawing hand can raise to make it all-in then he cannot make the pot sized bet. He cannot make a smaller bet either or he is giving the drawing hand odds to call. So if the stack sizes are large enough that a pot sized bet followed by a pot sized raise will result in an all-in then the correct move for kings is to check AND THEN the correct move for the drawing hand is to ALSO check. If that won't spin you around in your chair I don't know what will. So in a pot limit game here, depending on the stack sizes it could get checked to the turn, pot-bet by the kings and folded by the draw, or all-in by the draw and called by the kings. And this I say to anybody who thinks that stack sizes aren't that improtant: :P
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Re: Massive Importance of Stack Size., shorn, 16. Apr 2003 10:07
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Note to self...do not sit down at a PL game with stdioh unless you have A LOT OF TIME on your hands. Seriously though, a great look into it for PL.
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Re: Massive Importance of Stack Size., stdioh, 16. Apr 2003 10:15
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Indeed. I would say that limit hold'em is learning how to drive a car. No limit hold'em is taking that skill and learning how to drive a racecar. Pot limit is then akin to taking an F-18 on a strike into hostile territory against a superior enemy with a lot of anti-aircraft guns. A lot of players seem that think that pot-limit is necessarilly "easier" than no-limit because there is less money that can be bet at any given moment, but indeed it just means that there are less cut-and-dry situations and many situations involve really high levels of complexity in reasoning.
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Re: Massive Importance of Stack Size., Schuster, 16. Apr 2003 10:55
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Am I correct in saying that if the game were no limit and the each players stack size were somehow infinite, the Kings could always play this hand profitably?
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Re: Massive Importance of Stack Size., Wren, 16. Apr 2003 10:59
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No. If each player was playing perfectly, KK would check and fold to a very large flop bet made by 67h.
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Re: Massive Importance of Stack Size., stdioh, 16. Apr 2003 11:05
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Indeed, as wreny states, if the stacks are infinitely large, then the hand with an advantage on the flop can make a bet big enough that the kings do not have pot odds to call. The kings are drawing to a card that does not help the draw - which is currently a favourite.
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Re: Massive Importance of Stack Size., stdioh, 16. Apr 2003 11:07
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As an add-on, in pot limit, the kings want to put as much money as possible in on the flop, so long as that amount is small enough in relation to stack size that the drawing hand can be folded off of an unmade draw on the turn. The drawing hand is profitable if it gets all (or the vast majority of) its money in on the flop - otherwise it is vulnerable because it will not have proper odds on a bad turn and will be forced to either forfeit the pot or put in a bet against odds.
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Re: Massive Importance of Stack Size., Wren, 16. Apr 2003 10:53
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"As we discussed previously, if the drawing hand has paired on the turn then he has 20 outs from a remaining 44 cards and thus has a little less than a 50% chance of winning. Thus the neutral case above should be called a slightly negative case and he should fold to the pot sized bet." Huh?! The neutral case is getting 2:1 on his call, and so should obviously call here. Infact, the "negative" case is still getting pot odds to call a pot-sized bet on the turn (15/44 = slightly better than 1:2).
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Re: Massive Importance of Stack Size., stdioh, 16. Apr 2003 11:03
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Nope. Here's the crux of the matter. You're looking at your chances of winning the pot that currently is. You have 15/45 (not 44) to do that on the flop which is exactly your 1:2. If you don't do that, but do pair the board then you have to look at this as a negligeable win, since in order to win you have to draw again on the river in your less than 50% scenario, but in order to see that river card you will need to call another pot sized bet. This triples the pot and thus divides your EV by much more than 3 as you are tripling the stakes when you are a <50% to win. Essentially, you're being dragged along and sucked in here. Since you know that there will be full action on the turn, nomatter the card, then you know that you shouldn't be getting that far if you can avoid it. Essentially this problem bases down as such. Kings want to put as much money in the pot as possible without violating the condition that draw has something left to lose in his stack.
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Re: Massive Importance of Stack Size., shorn, 16. Apr 2003 11:21
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So, let' s change it a little bit...we can't see each other's cards. Now what does KK do?? Please tell me that if you hold KK you have to bet or I quit!!!!!
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Re: Massive Importance of Stack Size., stdioh, 16. Apr 2003 13:41
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on 16. Apr 2003 11:21 shorn wrote: > So, let' s change it a little bit...we can't see each other's cards. Now what does KK do?? Please tell me that if you > hold KK you have to bet or I quit!!!!! Of course. By the same token, you could hold AA, but if I don't know it then I'll still bet Billy-B-Damned out of my KK. That's poker.
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Re: Massive Importance of Stack Size., Wren, 16. Apr 2003 11:28
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Riight....gotcha! Here's some math: KK's EV with no flop bet (PL): $2.12 KK's EV with a pot-sized flop bet (PL): $6.36 KK's EV with a pot-sized flop bet and then raise (PL): $19.09 That's really interesting that 67h should fold to a pot-sized bet on the flop. However, if 67h (stupidly) decides to call the bet on the flop and see the turn, he/she is actually making a mistake NOT to call a potsized bet here, even if he/she doesn't improve! Funny how that works...
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Re: Massive Importance of Stack Size., stdioh, 16. Apr 2003 13:43
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The drawing hand has to improve to call a pot sized bet on the turn...it is correct to call if it improves to a pair with draw and correct to fold if there is no improvement at all.
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Re: Hypothetical situation - spin off, chasepoker, 17. Apr 2003 04:23
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Just as an extra to this me and a friend played a game of hold em once where we both had to show one card on the flop ( you could choose which ) made the game interesting ! You should try it we argued for hours over decisions made, useful for thinking about the game more than as a game itself !
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Re: Hypothetical situation - spin off, stdioh, 17. Apr 2003 11:26
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Interesting, though when you have the choice of the card to show, it muddles reasoning quite a bit because of the question of whether you want to show strength or weakness, etc. I always thought that an interesting hold'em variant would be crazy pineapple where everybody's discards come face up into the muck in turn fter flop betting. Thus you might be about to chuck your K out of AAK on a board of K72, but after two aces get chucked you now throw away one of your aces instead.
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Re: Hypothetical situation - spin off, Andrew Wells, 18. Apr 2003 01:38
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I might still keep the aces in case someone has top two, but I understand what you mean. Actually had a home game 20 years ago where this Open Pineapple was infrequently called. When someone threw away top pair it usually meant set or draw. Curiously it didn't necessarily mean strength. I have thrown away top pair with a ten or less if I was going to fold to a flop bet anyway. I remember chucking a top pair jack and keeping pocket nines instead one time because I had a gut shot straight-flush draw. They all read it for strength and checked to me on the flop. It looked psychic when I made runner-runner quads instead!
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