No-Limit Holdem quiz

[M.B.E.]

Suppose you’re one of seven players left in a winner-take-all NLHE satellite. Your stack is T1000, below average, with blinds 15/30. You are in the cutoff and open-raise to T100. The button (who has you covered) reraises to T300, and the blinds fold. The question is whether to fold, call, or reraise in each of the two scenarios set out below. In both scenarios you have some information about your opponent’s holding (based on a very reliable tell). You also know that (a) if you reraise all-in preflop your opponent will call, and (b) if you just smoothcall preflop your opponent is unlikely to make a FTOP-mistake on the flop—in other words, if your opponent flops the best hand he will likely get his chips in the middle, but if you flop the best hand he will likely not pay you off.

Scenario A: You have KQs and you put your opponent on a pocket pair from 55 to JJ inclusive.

Scenario B: You have 99 and you put your opponent on suited broadway cards.

In each scenario, what is your play after your opponent reraises to T300, and why?

[Guy McSucker]

Excellent question.

I think I fold the 99 and call with the KQs. Here's why.

In either case, if I push all-in, it's essentially 50-50 as to who wins. The amount of dead money in the pot is not enough to make this an edge worth playing for, so I don't want to do that.

However, I know that if I am ahead after the flop, I get to win what's in the pot with a bet. Therefore the question is whether I have pot odds right now to take the flop and get ahead, and know that I am ahead, so I can take it down with a bet.

With 99: I am getting 2-1 pot odds, and will be the favourite any time my opponent does not pair his cards or flop a flush draw. Trouble is, I don't know the values or suit of his cards. If I know he has KQ of spades, for example, then I think I will get a flop to my liking (no K, no Q, no more than one spade) just over half the time, so I could call, getting 2-1 on a 50-50 shot. But with the information I have, the only flop I can like is a rainboow one with no overcards, which are few and far between. I do not like my chances of catching a flop I like, so I fold.

With KQs: same game, but here I am looking to hit a K or Q, or flop a draw. Any of these will make me a favourite, as long as my opponent does not hit his set. I will hit such a flop almost half the time (rough calculation in my head, could be way off), and my opponent will only hit his set twice in 17 attempts, so my odds of getting a good flop are better than 2-1.

In this case, when I catch a pair or flush draw, I have to take my chances that the opponent has a set. The set is sufficiently unlikely that I am prepared to do that; this is what sets this case apart from the other, where the opponent's hitting a pair happens 1/3 of the time, and I have to fear all overcards, which will flop a very large amount of the time.

Guy.

[TheGrifter]

Scenario A: Cold call. Push in on any flop that contains a Queen/King/Ace. If he won't pay off my top pair he will fold if an Ace flops as well.

Scenario B: Fold. I don't mind getting my cards in on a coin flip if there is also some possiblity that my opponent will fold, but with only 10% of my stack involved here, I fold.

[Bozeman]

KQs: allin

99: call, bet ~200 on the flop, unless there are lots of overcards

Craig

[Al_Capone_Junior]

in scenario 1, where I have KQ and I know he has a pair JJ or lower, I flat call his raise preflop. If an ace, king, or queen comes, I go all-in.

in scenario 2, where I have 99 and I put him on two broadway cards, I push it all-in. It's a gamble, yes, but it's winner take all, and you need to get some chips. So there's little reason to play it safe at this point. There are too many flops that will miss him, but still force me to fold anyway. Therefore I'd rather take the indecision out of the hand and push it in now.

al

[Che]

A: Fold.

If you push and he calls, the T45 from the blinds makes it virtually 0 EV. No reason to risk your whole stack for that.

If you call, you win the pot when you flop a pair (and he misses his set). If this was the only way you could win, you would fold since you don't hit a pair on the flop (without him hitting a set) often enough to justify the basically 2:1 call.

However, if you flop a flush-draw/overcards combo, all the money goes in since you and your opponent are getting 2:1 for it and you're only a slight favorite. This offsets the negative expectation of the flopped-pair alone, but not by enough to justify the variance IMHO. At least that's what my guess is since I'm not actually sure how often you flop an overcards/flush-draw in this case. I just assume it's not very often (<8%?).

B: Push in. You're the favorite and you're getting better than even money thanks to the blinds contribution.

[dsw1977]

Assuming stacks started at T1000 (or T1500), it seems that you're not a short enough stack (even in a winner-take-all tourney) to want to (a) push your chips in when you know it is 50-50 and there will still be 6 players left or (b) throw another 20+% of your stack when it is unlikely you'll get paid off anything additional if you hit the flop. Unless I'm entirely outclassed at this table, I dump both hands and wait for a better opportunity with T900. But I'm a newbie.

[M.B.E.]

[ QUOTE ]
A: Fold.

If you push and he calls, the T45 from the blinds makes it virtually 0 EV. No reason to risk your whole stack for that.

[/ QUOTE ]
You're overlooking something here. It costs you 900 more to move in, and your opponent will call so you'd be getting pot odds of 1145:900, or 56:44.

That's pretty good considering that your hand is almost even money running hot and cold. At worst your opponent is a 53.5:46.5 favourite, but if his pair is 88/77/66/55, he's only a 51:49 favourite. The odds the pot is laying you are too good to pass up (despite the risk of losing your 900 stack). Folding would be an error.

Look at it another way: consider your overall Chip-EV for the hand, taking account of the 100 you've already put in the pot. If you fold, your CEV for the hand is -100. If you move in, you'll have a 48% chance of winning 1045 and a 52% chance of losing 1000, for a CEV of -18.4. Even though moving in gives you overall negative CEV for the hand, it's still better than folding by a wide margin (81.6 chips to be exact). It is a winner-take-all tourney, so "survival" per se is not an important consideration.

So folding is wrong; the question then is whether to move in or call. (Incidentally, you can show that folding is wrong in Scenario B too by the same reasoning.)

When I originally crafted this quiz, I intended that the correct answer would be to reraise in scenario A and smoothcall in scenario B. I still think that's correct but it's closer than I thought and I have to think some more about the solutions to scenario A posed by The Grifter and Al Capone Junior. One thing to keep in mind is that with KdQd if we flop a flush draw or openended straight draw we are a favourite over a pocket pair less than queens (unless it flopped a set of course). We have either 14 or 15 outs, with two chances to hit. Using that information we can improve somewhat on their suggested strategy of smoothcalling preflop, then betting any flop with an ace, king, or queen. We'd be looking for a strategy that gives us an overall CEV for the hand greater than -18.4, the CEV of moving in preflop.

[TheGrifter]

Maybe this is just me, but I have no problem putting my money in knowing I'm a coin flip to win IF my opponent is capable of folding. If I KNOW my opponent will call (In a tourney, not a cash game) I want to be pretty certain I'm a favorite....anyone else see this differently?

[PrayingMantis]

As I understand it, winner-takes-all NL tournies should be played essentially like NL ring games, i.e. CEV=$EV. It is even more so if it's early, like it seems to be in this quiz, and there are no specified ability differences between the opponents.

If so, in what way should the fact that it's a NL satellite, and not a NL ring game, change my decision here?

[AleoMagus]

It's winner take all and I am assuming that I am equally skilled with all my opposition.

Scenario A is a tough one. My first instinct was to say call and wait for the flop, but I am not sure now. The problem is, despite these hands being a near coin flip, that is really only true after seven cards. If he is ahead on the flop (which he will be quite a bit more than 50% of the time) he's gonna push me out before I see the turn and river. I think now I'd rather push. 900 more to win 1145 with about 46-48% win rate. I suppose I'd need to know the exact odds that a medium pair will still be ahead on the flop to be sure.

Secenario B is easy. Move in. I am the favorite and Winner take all plays like a ring game. I will take any edge I can get, especially when my stack is below average.

Obviously, if I felt I was far more skilled, or could again exploit this tell, I might be less inclined to gamble with any edge, as I could probably outplay my opposition in better spots.

Regards,
Brad S

[AleoMagus]

[ QUOTE ]
If I KNOW my opponent will call (In a tourney, not a cash game) I want to be pretty certain I'm a favorite

[/ QUOTE ]

That's just the thing. Tourneys only play differently because of percentage payback for more than just the winner. Winner take all plays exactly like a cash game (take any edge).

So yeah, I agree with you, but it doesn't apply here

Regards,
Brad S

[M.B.E.]

[ QUOTE ]
As I understand it, winner-takes-all NL tournies should be played essentially like NL ring games, i.e. CEV=$EV. It is even more so if it's early, like it seems to be in this quiz, and there are no specified ability differences between the opponents.

If so, in what way should the fact that it's a NL satellite, and not a NL ring game, change my decision here?

[/ QUOTE ]
It shouldn't. You are right, in my view. I specified that it was a satellite because I posted in the one-table tournament forum.

[TheGrifter]

I see your point but I think even a winner takes all 10 person tourney is significantly different than a cash game in that you do not have the ability to buy back in if your coin flip goes sour.

That being said, the only time I play winner takes all tournies is when I'm trying to pick up a seat in a bigger event (which is rare) so maybe my reasoning is off here.

[M.B.E.]

[ QUOTE ]
I see your point but I think even a winner takes all 10 person tourney is significantly different than a cash game in that you do not have the ability to buy back in if your coin flip goes sour.

That being said, the only time I play winner takes all tournies is when I'm trying to pick up a seat in a bigger event (which is rare) so maybe my reasoning is off here.

[/ QUOTE ]
Theoretically there is a difference if you are more skilled than your current competition. If the other six players remaining at your table are poor players (especially those with the largest stacks), then there is a lot of $EV in the opportunity to continue to play against them, even with a shorter stack. However, in this case the CEV cost of folding is 81.6 chips (compared to moving in), which is so much that even if you're the best player at the table you would still do the play giving you highest CEV.

That's especially true since it is now seven-handed; the players who have already busted out were probably among the worst.

[Vince Lepore]

Scenario A: Call. If you have as good a read on your opponent as you say and he plays post flop as you state then even if you do not make a hand on the flop you will almost always be able to out play him. Do not move in and take awya your chance to out play him. folding is better than raising all-in but not acceptable in my opinion.

Scenario B. Same as A.

[Guy McSucker]

[ QUOTE ]

It shouldn't. You are right, in my view. I specified that it was a satellite because I posted in the one-table tournament forum.


[/ QUOTE ]

There is a strategic difference between this tournament and a cash game: if you bust, you're done. Sklansky puts it like this: you should sometimes pass up on a good bet today, if losing that bet will deny you the chance of a better bet tomorrow.

So, in the scenario proposed, the question of all-in versus fold, which MBE showed makes a difference of 81.6 chips, comes down to this: will you be faced with a better opportunity later?

Our stack is currently 900, so we're looking at a +EV of 9% of our stack if we move in. Is this too good to pass up? I don't know. FossilMan has strong opinions on how much edge is too much to pass up. It would be good if we were to hear from him.

The pedant in me cannot help but point out that the move Al and Grifter suggest, of moving in when an ace falls, does not really fit the original question, which said that the opponent would not make a FTOP mistake post flop. Okay, it said it was unlikely, but I read it as "not going to happen". In real life it might happen; but in real life we wouldn't have such an accurate read on our foe, would we?

Guy.

[Al_Capone_Junior]

After reading the diverse responses, I have changed my position on this. I also emailed a pro friend of mine and asked his opinion, tho for his privacy I cannot post his email. However, he said the same thing that I have concluded since then, which is different from my original reply here.

The correct play in both cases (IMO) is to just call the raise. There's no reason to gamble when you're going to have a good shot at outplaying him after the flop. Also, if you miss, you still have chips left.

al

[M.B.E.]

[ QUOTE ]
The pedant in me cannot help but point out that the move Al and Grifter suggest, of moving in when an ace falls, does not really fit the original question, which said that the opponent would not make a FTOP mistake post flop.

[/ QUOTE ]
Guy, good point: what I probably should have said in framing the problem is that when the flop comes we (but not our opponent) are required to turn our cards face-up. We can still bet, but our opponent wouldn't call unless either he was ahead or was getting correct pot odds. Thus our opponent might still try to bluff, but we can't bluff him. I think that with the condition expressed this way the answer comes out to what I intended: reraise in Scenario A but smoothcall in Scenario B.

This isn't realistic obviously, but I was trying to make a theoretical point.

Despite that it can get interesting to analyse Al and Grifter's solution on the assumption that the opponent doesn't know exactly what we have, though he knows we have one of AK, AQ, and KQ.

Now, we've got KdQd and our opponent has some pocket pair 55-JJ. How often will there be an A, K, or Q on the flop? With 48 cards remaining there are 17,296 possible flops. Of those, 8860 have at least one A/K/Q (51.2%) and 8436 have no A/K/Q (48.8%).

Of course, sometimes the flop will have an A/K/Q and we'll bet it, but our opponent will have flopped a set or quads. By my count there are 820 such flops (4.7%). Of course we will still win a few of those, by hitting a backdoor draw.

So let's calculate the overall EV for the hand, recalling that moving in preflop gives us EV of -18.4.

48.8% of the time we lose 300, 46.5% of the time we win 345, and the remaining 4.7% of the time we lose on average 900 (usually losing 1000 but occasionally winning 1045). That works out to EV of -28.3. So moving in preflop is still preferable.

But we should adjust this system to take account that occasionally we will flop a made straight or flush, and other times we will flop a straight or flush draw which will make us a favourite on the flop (save if the opponent flopped a set). Those times we should probably move all in. Anyway that's more math to calculate which I'm a bit too lazy for right now, but I think it would improve the EV to more than -18.4.

However, there's one more thing to think about. Our flop bet is going to be 700, so the opponent will get pot odds of 1345:700, or almost 2:1. If the opponent knows we have top pair, he can't call with those odds just to try to hit a set (the odds against hitting a set with two cards to come are 10:1). But let's say the opponent knows we might be bluffing. Suppose he knows we will bet any flop with an A/K/Q even though only two of those three cards will hit our hand. That means that when exactly one of those cards hits and we bet out, the opponent knows the probability we're bluffing is 40%. That means he has correct odds to call when the flop has exactly one A/K/Q, but will fold if there is more than one. I think that should nullify any advantage we'd get from bluffing.

[M.B.E.]

[ QUOTE ]
Scenario A: Call. If you have as good a read on your opponent as you say and he plays post flop as you state then even if you do not make a hand on the flop you will almost always be able to out play him.

[/ QUOTE ]
Vince -- happy to see you posting here again.

What I was trying to get at in framing this quiz was that you have a good read on your opponent preflop, but on the flop it's reversed and your opponent has a good read on you. I didn't quite get that idea across in my original post in this thread.

The point I was trying to get at with this quiz is this: when there's a headsup matchup between a pocket pair and two overcards, in general the overcards benefits from getting all the chips in the pot preflop, while the pocket pair benefits from saving some chips to bet on the flop. Here is the reason: if the pocket pair is behind on the flop, it has very little chance to improve, whereas if the overcards is behind on the flop it's usually only a 60:40 dog, so it benefits a lot from being able to see the turn and river.

[Guy McSucker]

I have just realised that I don't fully understand your position.

Why smooth call with the nines? What is your plan after the flop? My original response said that I don't like very many flops here, and I had already discounted moving in (too much risk for too little edge, I thought, although I am prepared be swayed on this), so I voted for a fold. If we think moving in is okay, then I think moving in is better than calling, so that's my new preference.

Why is calling superior?

Guy.

[Prickly Pete]

Maybe I'm missing something here, but if we know that our opponent will only make perfect decisions post-flop (and we may not), doesn't that make this an All-In or fold situation? And considering that you have pot odds in each, I'd say reraise allin in both.

[Bozeman]

"usually only a 60:40 dog"

Huh? If it only has overcard outs, it is a 75:25 dog, and even with possible flushes, str8's and two pair above your pp, it is still probably usually 70:30 or worse.

Craig

[SossMan]

[ QUOTE ]
As I understand it, winner-takes-all NL tournies should be played essentially like NL ring games, i.e. CEV=$EV. It is even more so if it's early, like it seems to be in this quiz, and there are no specified ability differences between the opponents.

If so, in what way should the fact that it's a NL satellite, and not a NL ring game, change my decision here?

[/ QUOTE ]

Well, the fact that when you go broke, you can't pull out more cash and buy more chips that would enable you to make additional and, possibly, bigger EV bets. When you are in a cash game, all decisions are made in regards to the potential EV of this hand. But when the result of this hand can impair the ability to make +EV decisions in the future, it can sometimes turn a slightly +EV call to a fold.
I'm not saying that this is the case here, but there still are differences between even winner take all tourneys and cash games. David talks about this in TPFAP.

[Bozeman]

Case B

allin: 1145*.524-900*.476=171.58

call, bet 300 into any flop: -500*.34+445*.66=123.7

I calculate chance of:
23.5 no overcards 72%
45.3 1 50%
26.5 2 27%
4.7 3 9%

So call, bet one or less overcards yields:
-200*.312+445*.235+2/3*.453*445-1/3*.453*500=101

Thus it looks like you should put it allin preflop (and that I was wrong in my first answer), since you are otherwise putting in 500 to win 445, and you can't tell when you are ahead if any overcards flop.

Or did I do the math wrong?

Looks like you didn't quite succeed in making the example you wanted, MBE,
Craig

[PrayingMantis]

[ QUOTE ]
when you go broke, you can't pull out more cash and buy more chips.

[/ QUOTE ]

That *by itself*, is not a reason for treating it differently from a ring game. On-line, for example, you might be able to start immidiately a similar new satellite, or sit at a ring game.

I would rather think about other reasons why it could be different from a ring game: for example, you know that all (or many) of your opponents here are weaker than you (or stronger), or that this is a once in a life time opportunity (world championship?).

But here, I cannot see (and M.B.E agreed) what makes this situation any different from a parallel situation at a NL ring game, with the same blinds and stacks.

[Bozeman]

This difference only comes up when it is much easier than a typical game, such that the +EV situations you'd get in this game are much better than the available alternatives. These differences will not in most cases be big enough to warrant a significant change in strategy. Conversely, you could be in an unusually tough tourney (say a 2+2 SnG /images/graemlins/smile.gif )such that you would have better EV in another game so you should consider taking a slightly -EV bet.

Craig

[SossMan]

[ QUOTE ]
That *by itself*, is not a reason for treating it differently from a ring game. On-line, for example, you might be able to start immidiately a similar new satellite, or sit at a ring game.

I would rather think about other reasons why it could be different from a ring game: for example, you know that all (or many) of your opponents here are weaker than you (or stronger), or that this is a once in a life time opportunity (world championship?).

But here, I cannot see (and M.B.E agreed) what makes this situation any different from a parallel situation at a NL ring game, with the same blinds and stacks.



[/ QUOTE ]
Point taken.

[M.B.E.]

[ QUOTE ]
"usually only a 60:40 dog"

Huh? If it only has overcard outs, it is a 75:25 dog, and even with possible flushes, str8's and two pair above your pp, it is still probably usually 70:30 or worse.

[/ QUOTE ]
Ha, you're right. Sorry. (In order for the pocket pair to be only a 60:40 favourite over your KQs, you would have to flop a gutshot like AT2.)

[Canada Kelly]

A. Fold - you are going to have to hit to win

B. Re-raise - all-in, make him make the decision of whether or not he wants to have to catch to win.

[Canada Kelly]

sure you put him on JJ or 55, but who says he isn't re-raising you with ATs or AJs.

I still think that you fold A.

I think that going all-in with 99 is a gamble, but you are getting the odds, you are already ahead of the guy, you have a positive EV.

If you call B, then any overcards that flop are putting you at risk, and you are out of position to boot.

That is why I say go all-in with B

[M.B.E.]

[ QUOTE ]
Thus it looks like you should put it allin preflop (and that I was wrong in my first answer), since you are otherwise putting in 500 to win 445, and you can't tell when you are ahead if any overcards flop.

Or did I do the math wrong?

Looks like you didn't quite succeed in making the example you wanted, MBE

[/ QUOTE ]
You're right. In Scenario B, I can't find any strategy that will give you higher EV than 171.58. So the correct answer is to move in preflop.

To make it correct to smoothcall preflop with the 99, you would need more information about your opponent's hand than just knowing it was suited broadway. For example, if you knew it was one of AKs, AQs, and KQs (and you still knew that your opponent was certain to call you preflop if you raised), you could smoothcall preflop and then checkfold on the flop if an A, K, or Q showed up without a 9; otherwise move in on the flop. This simple strategy gives you EV of about 196 by my calculations, higher than the 171.58 you'd get by moving in preflop -- even if you turn your cards face up so your opponent knows precisely what you have. I'm sure that in this revised scenario there are various other strategies that give you even higher EV.

[M.B.E.]

The correct answer is to reraise all-in preflop in both Scenario A and Scenario B. AleoMagus was the first to provide it. And thanks to Bozeman for persuading me that it is correct!

[Al_Capone_Junior]

After hearing Vince's reply and the reply from my buddy Matt Lessinger, I find this very dubious at best. In both cases you clearly must call. What logic wound up convincing you of your conclusion? I read aleo's response but wasn't convinced that Vince and Matt were wrong about thier conclusions.

al

[M.B.E.]

[ QUOTE ]
After hearing Vince's reply and the reply from my buddy Matt Lessinger, I find this very dubious at best. In both cases you clearly must call. What logic wound up convincing you of your conclusion?

[/ QUOTE ]
One of the conditions stipulated in the quiz was this: "if you just smoothcall preflop your opponent is unlikely to make a FTOP-mistake on the flop—in other words, if your opponent flops the best hand he will likely get his chips in the middle, but if you flop the best hand he will likely not pay you off". That condition is essentially what makes it wrong to smoothcall preflop in both cases.

The example is highly artificial; it was intended as a theoretical exercise, not something that might come up in an actual game. Sorry for any confusion!

[Al_Capone_Junior]

I still must question it because he's not making a FTOP mistake by calling preflop in either case if you go all-in. Essentially the exercise prevents the possibility of him making any FTOP mistake on either hand. Because of this, I would rather keep some chips those times I get a clearly unfavorable flop.

al

[Vince Lepore]

[ QUOTE ]
Vince -- happy to see you posting here again.


[/ QUOTE ]
Thank you - M.B.E. If my so called buddy Mason Malmuth had told me about a single table forum I would have shown up sooner. I just started playing these and want to hear how others are doing and discuss some.

The question of which hand benefits from which play is an interesting one. The answer as always is it depends on a number of things.

If you look at this purely as an exercise of two over cards vs a pair it doesn't matter to either hand that the money goes in preflop and the cards are run out. The results will always be the same. But if you take into account playing skill then the better player will benefit from seeing a flop regardless of which hand he holds.

Vince