AJs hand quiz

[AdamL]

You raise utg with A /images/graemlins/diamond.gifJ /images/graemlins/diamond.gif and get two callers.

Flop:

10 /images/graemlins/diamond.gif2 /images/graemlins/heart.gifJ /images/graemlins/spade.gif

You bet. Both opponents call.

Turn: K/images/graemlins/club.gif

You bet. Next player raises. 2nd opponent folds.

You?

[MarkD]

Call. I don't think it's close enough to bother doing the math.

[DiamondDave]

I almost always fold second pair when raised on the turn in a relatively small pot by a typical opponent in a low-limit game.

In 15/30 and 20/40 I run into more people who do the raise-the-turn-and-check-it-down-if-I-miss routine with combo draws. Tricky guys earn their river calls, but there is no reason to pay off straightforward players who raise the turn because they can beat one pair. Especially when your outs may be tainted.

[MarkD]

Count your outs, count the size of the pot, and if you are still convinced that folding the turn is correct convince me.

[sfer]

Folding is a disaster.

[LA_Price]

You have four outs for sure and possibly up to 9 outs if you count with the 3 Aces and 2 jacks(maybe even more if the bettor has JT or T2). Getting around 8:1 on your call I think folding would be wrong.

[AdamL]

Should you call a river bet if you don't improve on the river?

Also, would calling the turn still be right if the T /images/graemlins/diamond.gif on the flop was instead a 9 /images/graemlins/diamond.gif? (Hence removing the gutshot)

You'd still have 5 outs to what would probably be the best hand. That requires about 8.2:1 to call, and you're getting about that much.

[Danenania]

I'd call turn, call river. Between your outs and the chance you're still best calling down should make you money. A lot of players would do this with hands like QT, QJ, etc.

[DiamondDave]

Let's talk about outs. Hitting a Q on the river gives you (and anyone else with an ace) the nut straight. Hitting an ace on the river gives anyone with a Q a straight and gives you a payoff hand. Hitting a jack will allow you to draw out on one pair of kings, kings and tens, etc. But you may be up against top two or a set (or a straight), so the jack may not be an out.

I might consider calling if the pot were gigantic. But it isn't, not for a typical low-limit game. There will be a better opportunity to invest your chips in a few minutes.

[Guy McSucker]

[ QUOTE ]

There will be a better opportunity to invest your chips in a few minutes.


[/ QUOTE ]

The question is not whether there will be a better opportunity soon, but whether this opportunity is a +EV one.

Guy.

[DiamondDave]

"The question is not whether there will be a better opportunity soon, but whether this opportunity is a +EV one."

In the absence of metagame considerations, you are right. But I don't think the situation here is even close to +EV.

[Danenania]

Well, it's nice that you think that, but it will take a little more than your opinion to get me to fold this.

[Doombolt]

The real question here is what are your probability estimates for the hands the raiser could have; from there the calculation is straightforward. I think the most likely holdings are AQ, KQ, KJ, and KT. Less likely holdings are AA, AK, AJ, KK, QQ, QJ, QT, JJ, JT, and TT. (If you have some profile information on the raiser, you can probably eliminate many of these hands from consideration.) We'll ignore total bluffs for now, and players who cold call UTG raises with K9s or worse.

I'll make the following rough probability estimates (feel free to revise them and recalculate):
KQ: 20%
KT: 20%
AQ: 15%
KJ: 15%
JT: 6%
AK: 5%
QT: 4%
QJ: 3%
AA: 2%
AJ: 2%
KK: 2%
QQ: 2%
JJ: 2%
TT: 2%

For the following EV calculation, let's suppose we bet out if a Q or J hits on the river, call down on A, and fold otherwise, and the preflop raiser follows a similarly basic river strategy. The pot as of the start of river betting is 8.75 BB. I won't make second-order corrections like a river ace being slightly more or less likely due to information gleaned from the betting.

KQ: 3xA @ -2 BB, 3xQ @ +8.75 BB, 2xJ @ +8.75 BB, 36x @ -1 BB; EV = 0.0398 * 20% = +0.0080 BB
KT: 3xA @ +7.75 BB, 4xQ @ +8.75 BB, 2xJ @ +8.75 BB, 35x @ -1 BB; EV = 0.9261 * 20% = +0.1852 BB
AQ: 2xA @ -2 BB, 3xQ @ +3.375 BB, 2xJ @ -3 BB, 37x @ -1 BB; EV = -0.8381 * 15% = -0.1257 BB
KJ: 3xA @ +7.75 BB, 4xQ @ +8.75 BB, 1xJ @ -3 BB, 36x @ -1 BB; EV = 0.4375 * 15% = +0.0656 BB
JT: 3xA @ +7.75 BB, 4xQ @ +8.75 BB, 1xJ @ -3 BB, 36x @ -1 BB; EV = 0.4375 * 6% = +0.0263 BB
AK: 2xA @ -2 BB, 4xQ @ +3.375 BB, 2xJ @ +8.75 BB, 36x @ -1 BB; EV = -0.2045 * 5% = -0.0102 BB
QT: 3xA @ -2 BB, 3xQ @ +8.75 BB, 2xJ @ +8.75 BB, 36x @ -1 BB; EV = 0.0398 * 4% = +0.0016 BB
QJ: 3xA @ -2 BB, 3xQ @ +8.75 BB, 1xJ @ +8.75 BB, 37x @ -1 BB; EV = -0.1818 * 3% = -0.0055 BB
AA: 1xA @ -2 BB, 4xQ @ +3.375 BB, 2xJ @ +8.75 BB, 37x @ -1 BB; EV = -0.1818 * 2% = -0.0036 BB
AJ: 2xA @ +3.375 BB, 4xQ @ +3.375 BB, 1xJ @ +3.375 BB, 37x @ -1 BB; EV = -0.3040 * 2% = -0.0061 BB
KK: 3xA @ -2 BB, 4xQ @ +8.75 BB, 2xJ @ -3 BB, 35x @ -1 BB; EV = -0.2727 * 2% = -0.0055 BB
QQ: 3xA @ -2 BB, 2xQ @ +8.75 BB, 2xJ @ +8.75 BB, 37x @ -1 BB; EV = -0.1818 * 2% = -0.0036 BB
JJ: 3xA @ -2 BB, 4xQ @ +8.75 BB, 37x @ -1 BB; EV = -0.1818 * 2% = -0.0036 BB
TT: 3xA @ -2 BB, 4xQ @ +8.75 BB, 2xJ @ +8.75 BB, 35x @ -1 BB; EV = 0.2614 * 2% = +0.0052 BB

Net EV: +0.1281 BB

So I think this is a pretty clear call, as long as the raiser isn't extra-likely to have AQ.

[DiamondDave]

"Net EV: +0.1281 BB"

This is approximately the size of a tip.
Next hand.

[Doombolt]

[ QUOTE ]
"Net EV: +0.1281 BB"

This is approximately the size of a tip.
Next hand.

[/ QUOTE ]

Tips add up. Online, I'm keeping all the "tips" I possibly can.

In B&M play, though, depending on the size of the tip your consideration becomes important. Keep in mind you'll only have to pay the tip less than 20% of the time here, though (since you're losing more than 80% of the time).

[MoreWineII]

Call me crazy, but I'll take any +EV I can get, even if it's only "the size of a tip".

[MarkD]

In the face of a very solid and thorough analysis proving that you are wrong you come back with, "This is approximately the size of a tip." Why the hell are you on this board if you don't want to learn?

[DoubleJ]

I am just starting out in poker and I am interested in how you arrived at the positive expected value that you did. If you have any time to reply to this message and clue me into where I would learn more about these calculations or where you got these numbers, that would be great.

[DoubleJ]

Through reading the replies, I've noticed that a lot of people have commented on how many outs you may have to hit your hand or what the precise statistics of your opponent having a certain hand are. I think all of these considerations are important, but here is my take on this hand, so please excuse me if its too novice but I'm here to learn.
I would mainly worry about KQ which I think may just be strong enough perhaps to call a raise with in later position from an utg caller; although I've come to trust Sklansky and most experts that you need a better hand to call a raise with than you usually would raise with yourself. Anyway, I would assume you are recognized as a solid player, although the other players at your table may only play their cards. What type of player is your opponent? If your opponent is aggressive and has position, can you put him on KQ on that flop, if so, why would he not raise on that flop to semi bluff with the overcards and the open end? It's possible he has overcards because most players i've ran across at my low 3/6 games (i'm just starting out) wait until the turn to fire at the pot with their huge hand. You just need to know your opponent in this situation. How many preflop raises have you seen them call and have you seen any weaker hands of theirs in a showdown on a raised pot preflop? The point is, who is your opponent? Everything you can remember, then you can make your best play.
Let me give some other thoughts on this. Looking at the board, why would he call the flop and bet the turn? That's your question. Is he capable of playing Q9 to a raise preflop? Would he hold AQ? Would he wait until the turn to fire bullets with his set?
I would argue he does not have AQ because there is no flush draw, so absent the board pairing on the river, he will be holding the nuts at the river. I think this is very important. Why would he give away his strength and force the third opponent to cold call two bets when he could suck him in and gain more bets. But, its still possible he holds a strong hand such as a set because he would need to raise the turn in order to get any Q drawing to the open end to make a tough decision as to cold call two bets and to force you with AJ to pay for the inside straight draw if he has you on AJ that is.
If he is a loose/aggressive player, I think you almost have to call because he mayjust be playing that scare card to get you out. But, with thatsaid, there are many reasons to fold. There's not much he can have, IF he's a solid player, that would not beat you. Remember, he had to call a preflop raise from someone utg. So, AK, AQ, pocket 2's, 10's, J's, Q's, K's and Aces have you beat. Any K has you beat. And there's not much to semibluff in that spot except for any Q but what hands with a Q would he play against the utg raise? AQ beat you, KQ beat you, QQ beat you. You hope for QJ and Q10 so that's it right there. Of all the hands a solid player could call your utg raise with, only two marginal ones would lose to you. Of course many other hands lose as well but QJ and Q 10 fit the criteria of what he may call on the flop and raise on the turn without being able to beat you.
So you are down to a choice. Does he have a legitimate hand? Is he capable of a marginal hand or would he try for a pure bluff on a scare card. Unless you read him very well for nothing or have him as very loose/aggressive, I say lay it down and save the bets for a better spot, maybe next time without playing AJ UTG at a full table in a small stakes game.

Disclaimer--I apologize for the length of this post, I am merely trying to learn and get some good feedback. Thanks

[DoubleJ]

I already replied to your post once, giving away I know nothing of what you were mentioning, but I am very interested. How much does it improve your calculation if you know for sure your opponent does not have AQ? I say this because as I mentioned in my post on this AJ quiz, I am almost positive the opponent does not have AQ. I just can't think of any reason for that opponent to raise with AQ on the turn in the position he is in since it makes more sense to call the turn to induce the third opponent to chase as well and then still have the nuts at the river. I still think a fold is in order, but then again, I don't understand the calculation that you did. From my perspective, I just don't see many hands that your opponent can call to an utg preflop raise and not hit something to beat you with that board, not to mention there's not much to semi bluff in that spot on the turn, or at least I don't think there is. Anyway, any feedback would be great.

[Doombolt]

[ QUOTE ]
I am just starting out in poker and I am interested in how you arrived at the positive expected value that you did. If you have any time to reply to this message and clue me into where I would learn more about these calculations or where you got these numbers, that would be great.

[/ QUOTE ]

The process I used was:
1. Make an estimate of the likelihoods of various hands my opponent may hold. Any reads you may have on the opponent are very useful here. (For example, if you know your opponent cold calls with AQ but few worse hands, instead of a positive EV situation you have an easy fold. Conversely, if you're sure your opponent wouldn't raise with AQ, you don't want to fold because you can count on 5-9 outs.)

2. For each possible hand you put your opponent on, estimate its individual EV for you on the river. There are 44 possible river cards (52 minus your two cards, your opponent's two cards, and the 4 cards on the board), we'll treat them as being equally likely. (This isn't precise, since the betting will typically give us at least a little information about what cards are probably left in the deck. But it's almost always a good enough approximation.)

For example, if the opponent has KQ in the above example, there are three Aces, three Queens, two Jacks, and 36 other cards among the 44. With an ace you call down and lose to the straight, losing two big bets; with a queen you bet out, your opponent calls down (we're pretending the effects of bluffing more or less cancel each other out, to make the computation tractable), and you gain 8.75 big bets; with a jack you bet out, get called down, and gain 8.75 big bets; with any other card you fold/lose at the showdown, losing one big bet. Thus, your EV for calling if your opponent holds KQ is:

(3 * -2 big bets (Aces) +
3 * 8.75 big bets (Queens) +
2 * 8.75 big bets (Jacks) +
36 * -1 big bet (other)) / 44 cards =
(-6 + 26.25 + 17.5 - 36) / 44 = 1.75 / 44 = 0.0398 big bets

Calculate in this manner for all your opponent's possible holdings, sum the weighted (according to your hand likelihood estimates) EVs, and you get your final result.

[DoubleJ]

Thank you for taking the time to post the process for calculating the expected value, it was a valuable lesson.

[DiamondDave]

[ QUOTE ]
In the face of a very solid and thorough analysis proving that you are wrong you come back with, "This is approximately the size of a tip."

[/ QUOTE ]

The methold Doombolt used to estimate EV is very useful, but I'm not comfortable with some of the assumptions he made.
(For instance, why was no probability assigned to your opponent holding pocket deuces?)
But I don't want to go into what I think Doombolt did wrong. Instead, I'd like to thank him for his contribution to this thread.

[ QUOTE ]
Why the hell are you on this board if you don't want to learn?

[/ QUOTE ]

I DO want to learn. Very much.

The reason I posted was to point out that I view the betting decision in question as a pesky one. Calling will increase your variance quite a bit relative to a very optimistic assessment of the EV you might earn. (Which, if it's a 4/8 game and Doombolt's assumptions are correct, is about the size of the customary $1 tip.) And if the assumptions upon which you are basing your decision are a bit off, making the decision to call may actually increase your fluctuations and have negative EV. And that would be a disaster.

In a loose low-limit game you can afford to make some folds that are slightly weak-tight because your opponents make huge mistakes so often. Turn bets don't need to fly off your stack in pursuit of an estimated 0.12 big bets in expected value.