Holdem Logic Question

10-20 game. All fold to you in the $5 small blind. Somehow you know that the $10 big blind has Q3 offsuit. You can call 5 or raise to 20. You know he will fold if you raise.


If you just call, you know that he will fold on the flop unless a queen or three comes (disregard straights and flushes). He will call all the way with a queen. He will call the flop and turn with a three out there but fold the river if he doesn't hit a queen or three to improve.


Obviously you should flat call with aces kings and queens. But should you call or raise with:


1. AK


2. AQ


3. Q4


4. Q3


5. Q2


6. J3


7. 33

1. AK * CALL

2. AQ * CALL

3. Q4 * RAISE

4. Q3 * RAISE

5. Q2 * RAISE

6. J3 * RAISE

7. 33 * RAISE

Well David, where I come from, WE "CHOP CHOP"

but let's say I am in the hand with someone who doesn't chop....then I would be happy to raise with all of these hands, why would I give my opponnet a chance to get lucky? I'd be happy taking the $10 and move on to the next hand.


But lets say for argument sake that this opponnet is also loose and makes a lot of mistakes on the flop and turn and river.


Well I would smooth call with, AQ, AK

the reason why I would call with AK is because let us say an A or K flops with the Q. A lot of extra money can be made by him making all of these mistakes calling along to the river with a Q and the same holds true for AQ if a queen does flop.


With J3, and 33, I would raise, because the only time I would continue to get action from this person would be if a Q does hit.


I would also raise with Q3, Q4, and Q2, because if the Q does come up and I do get action I will probably be splitting the pot unless I make 2 pair.


This is how I'd play it.

It's probably easy if you do the math, but without having done it I would say:


AK-call

AQ-call

Q4-call

Q3-raise

Q2-raise

J3-raise

33-call

You almost never raise. The point is that if he flops a 3 and doesn’t improve, he loses a bundle, while if he flops a Q you lose the minimum. If neither a Q or 3 flops, you can always raise, getting the same result as a pre-flop raise. So the only hands you need to think about is J3.and 33


For J3. Suppose he loses $30 if he flops a 3. (Not $40 as he can improve), and you lose $10 if he flops a Q. He will flop a Q about 1.5 times more often then a 3, which still leaves you with more profit with a call then a raise.


With 33, he will flop a Q about 2.9 times more often then a 3 (if I did my math right) which still leaves you with more profit with a call.


So, I always call.


Gatlif

I guess the answer might slightly depend on when the BB will raise, but if he is going to play the hand passively (only check & call), then you would call with any hand b/c the fact that he will fold a 3 on the river after dumping 1.5 BBs should be enough to make a profit even with 32.


cu


Ignatius

You should still raise with 33 and J3. With 33, there is only 1 card to make you money. With J3 there are two, but since you will lose when both a Q and a 3 come up, you will still make less than the 0.75 BBs you get by raising.


It's a curious fact that a dominated hand like Q2 will be profitable while the dominating 33 is a clear loser when you see a flop.


cu


Ignatius

Have not read the others...


My basic instinct here is to raise when you do not dominate and call when you do. Domination being when he has 3 or less outs against you.


Raise:

AK, Q2, J3


Call:

AQ, Q4, 33


I am a bit hesitant here though since he will not call the river with an unimproved pair of threes. This means that all the hands basically dominate since he has to hit a Q or trip 3's to showdown so you could simply call with all and then bet all the way if a Q doesn't come (with AQ you would check the flop to let him catch up). Until I think about it more and decide on the latter I'll go with the domination strategy.


Paul Talbot

1. call

2. call

3. call

4. raise

5. raise

6. raise

7. call

If you raise, your expectation is 10 bucks. So, the question is do you make more than 10 bucks on these hands by just calling.


Some basic math appproximations:


When you both hold a Queen, your chances of flopping a Queen are about 1 in 8. Same where you both hold a three but in the case of a three flopping, you can make $30 on the flop and turn the vast majority of the time and just bet him off his hand on the river.


If he only has a Queen out (i.e. when you have 33), he will get there on the flop about 1 in 5.


Thus:


Aq - Definitely just call


Q4 - Definitely just call


Q3 - 1 in 8 times, when a Queen flops, you chop and therefore lose 10 bucks. 1 in 8 times, you let him catch a 3 and then make $30 on the flop and turn. The rest of the time, you make the 10 bucks when he folds on the river (a little more because you can check the flop and let him catch a 3 on the turn). So, definitely just call.


Q2 - Definitely call. You make money when he flops a three and doesn't improve. The 3 will flop slightly more often than a Queen.


J3 - 20 % of the time when he catches a queen, you lose 10 bucks. About an eight of the time when he catches a 3, you will make an additional 30 bucks or therabouts. So, just call but it's close.


33- Raise. Chances of catching a three on the flop are slim. Why give him a free shot at catching a Queen?


Ak - most complicated one to comment on. If he catchs a 3, you will make money by smoothcalling preflop. If he catches a Queen, you will lose a little. Without doing the nitty gritty, I would smoothcall again.


In sum: I would raise with the 33 and that's about it.

The player gives up a lot of money with his strategy. Catching a 3 is GOOD for you since you just keep betting and he's not getting anywhere near the right odds to 'chase' but he will. Catching a Q is bad for you; but since you give him no money when he snags a Q that its not as bad for you as him catching a 3 is GOOD for you; but not by a lot.


Sooooo, you want to play ALL hands against him except those that take away one or two of his 3s.


AQ/Q3: are no-brainers.


AK: looks to me like its reasonable chance to beat a pair of Qs is high enough to overcome the difference in EV when he snags a Q less when he snags a 3.


Q2/Q4: I didn't do the math, but it looks like when you have Q2 he's got 2 good cards to catch (Qs) and 3 bad cards to catch (3s), and over-all that's good for you, especially since you have a realistic chance of tieing him when you both make Qs and a small chance to snag a 2 to beat him. Likewise Q4 looks good.


J3 and 33 look bad since you have taken away the good cards and you are much less likely to beat a pair of Qs.


J4: You didn't ask, but I suspect this unrelated hand is good enough to take a chance with.


A3: curious but I'd suspect this hand is pretty close: he has a 3:2 'out' advantage over you but you make up ground with your 3 card out.


- Louie

You should politely let the person know that you can see his hole cards unless he is a real *******.


There is a such thing as ethical poker...


Just kidding,

-J

Didnt see that he will fold a 3 on the river; thought he would also call the whole way. So just disregard my answer and read skp and Louie's ;-)

First, my initial guesses, before I read others:

Raise the Q3, Q2, J3, call all of the rest.


However, my calculations (assuming I did this right) changed that, i think?


a) Raise nets $15 100% of the time = $15 profit


b) 2/3's time at a minimum, opponent doesn't catch the flop, get same $15 profit from calling $5 pre-flop. If you have a Q or 3, even less chance of him getting past the flop = less chance of getting more than the $15 in blinds.


c) 1/3 time, if you don't have a queen or 3, opponent catches a Q or 3 on the flop, allowing more money to be potentially made or lost.


Without doing the exact math, I assumed the times you beat him when he catches the flop vs. the times you don't were a wash (as in, it's equally likely)


Check raising is not part of the equation here, from what I infer. I also assumed that you wouldn't chase two pair or trips that you know he flopped.


As I read this question, the most you can lose is $35 (call the blind, bet until the river)

the most you can win is $50 extra to the river if you eventually beat his Q. You win $50 1/12 and lose $35 1/12... or win $15 more ($30 total, with the blind money) 1/6 of the time when he catches a Q and you beat him.


70% of the time, he catches the 3, you make $30 if he has only a 3 (no river call). The other 30%, you make $50 when you beat him. Therefore, on average, 1/12 of the time you win $36, 1/12 you lose $35= 1/6 chance of winning $1 more ($16 total)


When 1/3 time he catches a Q or 3 on the flop, you will win an average $8 by calling and beating him, above the $15 from the blinds.


So, at least 2/3 of time, you profit $15 whether you raise or call and you don't get to the turn. At best 1/3 of time, you win $23 by calling and moving closer to the river, when you DON'T duplicate one of his cards

On average, you profit at most $17.66 when you don't duplicate his card and see the flop. You profit at least $15 by raising every hand pre-flop, whether you duplicate or not.

... which leads me to estimate that you should call with AK and raise with everything else?


That doesn't feel right. Someone straighten me out, please. I'm going to eyeball the rest of the responses

Did i make a mistake in assuming that the $15 in blinds is not an investment by me, so it didn't count? As in, I call, investing $5. He doesn't flop. I get back $20, making $15.....


Is that more bad maths?

Here's my shot at it:


1. call

2. call

3. call

4. call

5. call

6. raise

7. raise


NOTE: i'm assuming that if he doesn't flop a pair, he will check behind you if you check, even though Sklansky says that "he will fold on the flop unless a queen or three comes (disregard straights and flushes)." It's illogical for a real player to fold if it's checked to him. This "assumption" is particularly important when I considered my answer for #1 (AK).

Raise only with Q2 call with all the other listed hands.


Jimbo

If you raise, your expectation is 10 bucks. So, the question is do you make more than 10 bucks on these hands by just calling.


Isn't it $15? The sb is in the pot, and raising will always win the pot.

Yes, you are right...oversight on my part...it doesn't make me change my answers though.

No. In fact you're one of the few who got it right. The EV of raising is 3/4 BBs and this is the benchmark you have to compare calling against. If you call and lose, you will at least give up 1 BB in profit b/c you will lose 1/4 BB by completing the small blind (and might lose even more when he sucks-out on you). If he flops a 3 w/o improving, you win 9/4 BBs (1.5 BBs more than by raising). If he flops a Q and you can win a showdown, you win 3.25 BBs (2.5 BBs more)


cu


Ignatius

1. AK - call. if the choice is between continuing on with the hand or not, then anytime you have the best of it, it seems like you should call.


2. AQ - still call. if he calls all the way when the Q hits, you're golden. if he improves, you'll know it, and fold appropriately.


3. Q4 - even though you are a very slight favorite here, i think you should raise and get it over with. the time and variance spent here is not worth playing for the tiny EV here. steal the BB and deal the next hand.


4. Q3 - i say call here. why you ask? well, simply because you're on a freeroll now. anytime you can bait him a bit and then steal a bigger pot is a good thing. he can't outdraw you (disregard straights and flushes).


5. Q2 - raise. unless you feel like seeing a flop and hoping he'll chase and then toss. doesn't seem worth it though.


6. J3 - raise. no reason to chase him down. even though you know what he has. seems like a wsate of time for a minute advantage.


7. 33 - call. hope for a 3. really hope for a Q on the river.

Let's first see what the answer is if you hold something like J4. Notice that if you call, you will win $10 if a queen or three doesn't flop. The same $10 you could have won by raising. Therefore, we only need to figure out whether we would average winning more than $10 given a queen or three does flop. When a queen flops, we lose $10 (actually a tad less). When a lone three flops, we win $40 about 80%, lose $40 about 10%, and lose $20 about 10%. Thats an average of plus $26. With J4 in our hand a lone three flops only slightly less often than a queen, so can simply average out plus 26 and minus 10. Doing that means that we average winning about eight bucks if we call with J4. A bit worse than if we steal $10 preflop. However we are not taking into account flops like QJ4, JJ3Q, or a flop like J42 where we would let a card come off and possibly trap. Overall I think it is very slightly wrong to call but Louie Landale was right to call it close. (JT suited is probably a call. Maybe someone can work it out.)

Without actually calculating it, I think it is clear that AK has enough advantages over J4 to swing things. An ace or king may flop with a queen. If it flops without a queen or three, you let him catch up. If a queen flops by itself, your implied odds let you chase, bringing down the $10 loss from folding. Thus you shouldn't raise with AK.

Anyone who would raise with any hand containing a queen has serious problems. It would be wrong to raise even if the queen was exposed in a folded hand! In that case you would win $26 EV almost three times while losing $10 twice (since there are three threes but only two queens left). That's about eleven dollars in expectation. But if it is your hand with the queen, it is so much better. Even if you have Q2, you tie almost every time when a queen flops. So you no longer subtract twice ten dollars. It is of course that much better yet for the other queens.


Obviously if J4 is close, J3 must be a raise. Now you win $26 only twice when you call, while losing $10 three times. An expected profit of about seven bucks instead of the ten dollar blind. A3 is closer because you can trap when an ace comes, so Louie is right again. But I think it is still a fold.


With two threes in your hand you will win an average of more than forty bucks when a three flops. But you will lose almost ten bucks when a queen flops and that will happen three times as often. After four relevant flops you will be ahead less than twenty bucks. Five bucks a hand. Thus it is absolutely critical to raise with this hand, much more critical than any other.


Finally I would like to say that this is not just a math problem. I thought of it because it pertains to strategy in middle size games. In such games it is common that the player in the big blind will fold many hands to a preflop raise but botch those same hands badly, post flop, if he is not raised out. One of the reasons Abdul Jalib's admonition to almost always raise or fold when first in, is bad advice for these games.

I'm not sure I understand how this is relevant to actual play.


Much of your expectation here comes from knowing exactly what your opponent's hand is. Because of this, many of the calls seem like they become raises if you add the possibility of making mistakes postflop. In addition, the BB will have position on you throughout the hand.


Can you clarify?

Craig Howald

"Finally I would like to say that this is not just a math problem. I thought of it because it pertains to strategy in middle size games. In such games it is common that the player in the big blind will fold many hands to a preflop raise but botch those same hands badly, post flop, if he is not raised out. One of the reasons Abdul Jalib's admonition to almost always raise or fold when first in, is bad advice for these games."


What exactly are "these games?" And how is one to know that your opponent would be holding such a hand like Q3 and play it like you described? It seems to me like your shunning of Abdul's advice is predicated on a contrived example.


I did not use any math at all to come up with my answers, which, I'm happy to say, I got all of them right! I used logic, pure and simple. The AK one got me thinking, I must admit. The rest were easier.

If there is a rake you always raise.

David,

Evidently I assumed more restrictions than you were looking for in your original quiz.

I didn't realize that the Q3 would call check-raises, or bet if we didn't.


Also, you said nothing about winning $60 ($10 from blinds, $50 flop/turn/river) when the 3's improve by the river and you STILL beat them.


As for raising the Q hands.... aren't I just going to split most of my Q hands (except for AQ), therebye rendering no gain and only risk from letting them in on the flop? This includes the Q4, since it probably is overkicked by board as much as Q2...


Another point- "J3 must be a raise. Now you win $26 only twice when you call, while losing $10 three times"

So, the presumption is that you won't chase, even though you know that the player has only a pair of 3's with a Q and they won't call on the river if they don't improve, handing you the pot?

why would a3 flop less often then a Q ?

Unless I'm counting wrong, with six outs your odds to hit are 3.1 to 1 if you see both turn and river; but your implied (expected) odds are a straight 3 to 1 at best--and this is only if you expect your opponent with a pair of Queens to bet *and* then to call a raise if an A or K falls. That is, once the flop comes with a Q but no A or K, you decide to chase, hoping to win $90 (if he will bet into you and call your raise when you hit on the river) versus a cost to draw of $30.

Wooooaaaah, Nelly.


You can calculate and play these hands with precise positive EV much MORE because you KNOW what he has and you KNOW how he'll play it, and much LESS because he'll play it poorly. Your calculations become impractical and your EV drops quite a bit if you were to give the player any one face card and any one small card (not to mention all the other hands he can have to play poorly): 55 is a winner against Q3 but a loser against J6 and 97s.


I therefore suggest that this example is POOR support for your last paragraph. Support for your last paragaph would need some specific features of how such a player may play poorly after the flop and a general notion which which of your starting hands tend to play very well vis-a-vis the sorts of mistakes such a player is likely to make.


Since I'm sure such advise does exist I'm sure your last paragraph does have merit; but it sure would be nice to see some specific examples that can be put to real use in these real games. Hint.


- Louie