Thursday, August 17, 2006

Poker Strategy 202

I'm going to stretch the bounds of "fair use" quite badly and post an entire problem hand from a book a borrowed from Gil (Jacobs, Byron with Jim Brier, How Good Is Your Limit Hold'em. Hassocks, West Sussex, UK: D&B Publishing, 2005), which he purchased at the Gambler's General Store last time we were in Vegas together, about this time last year. I'd provide links for all of that above, but I'm composing this offline and so can't look up URL's.

This wouldn't normally present a "fair use" problem because it's a single problem hand, but the entire book consists of exactly twenty-four problem hands, so I am in effect publishing an entire chapter, accredited but without permission. I'm going to play with the order of the text a bit, in effect re-editing it, but all the words below are verbatim from the book, excepting my typos.

The reason I do this is that I'm on sort of a crash program to improve my game. I want to be beating midlimit games for a reasonable income as soon as possible. And this is the sort of hand that gives me trouble. (I actually scored a 63 out of 100, which is a passing grade—but it's a D−.) Since I want to discuss the hand, I think I need to post the hand—even if some hypothetical jury of the future might find I went beyond "fair use."

(Someday when I'm feeling ambitious I might look into making this test "takeable," having radio buttons that score you automatically. I don't know how to do that, but I could learn, and it would be a good project.)

Hand 2: Caught in the Headlights

This is a ten-player $15/$30 game. You are in middle position with A♠K♠. The cut-off is Madness, a loose and rather aggressive player. The big blind is TheRabbit. TheRabbit is a delightful player to have in the game—loose, passive and utterly transparent. He is also rather timid—not the kind of player to make pressure plays.



It is passed around to you. There is $25 in the pot and it is $15 to call.

Question 1. Do you (a) fold (b) call (c) raise?

Scoring 1. (a) [fold], 0 (b) [call], 1 (c) [raise], 5

Analysis. Calling (and hoping to re-raise) is possible with the absolute premium hands such as AA and KK. However, with AK suited you are really hoping to get heads-up or in a three-way pot where your hand has some chance to win even if it doesn't improve. Limping is more justifiable with weaker hands such as QJ suited and KJ suited.

You raise.

Hypothetical Play: Madness calls and TheRabbit now raises. There is $115 in the pot and it is $15 to you.

Question 2. Do you (a) fold (b) call (c) raise?

Scoring 2. (a) [fold], 0 (b) [call], 5 (c) [raise], 4

Analysis. TheRabbit's three-bet from the big blind suggests a very strong holding. You have position over him and seeing the flop for just one more small bet is preferable to getting frisky with a raise. Nevertheless, you have a very big hand and raising is not really a mistake.

Actual Play: Madness calls, as does TheRabbit.


The flop is Q♠10♣4♣. You hold A♠K♠.

TheRabbit checks. There is $100 in the pot and it is $15 to bet.

Question 3. Do you (a) check (b) bet?

Scoring 3. (a) [check], 2 (b) [bet], 10

Analysis. Checking might get you a free card, but it also tells the world that you don't have a great deal. Betting is a far superior play as the flop is rather scary for mediocre hands such as small pairs. Even against a pair you could have as many as ten outs, which would give you approximately a 40% chance to improve to the winning hand by the river.

You bet.

Hypothetical Play: Madness raises and TheRabbit three-bets. There is $190 in the pot and it is $30 to you.

Question 4. Do you (a) fold (b) call (c) raise?

Scoring 4. (a) [fold], 10 (b) [call], 2 (c) [raise], 0

Analysis. An incorrigible optimist would see ten outs here, approximately 6-to-1 pot odds, and conclude that it is an easy call. This simplistic assessment is fraught with difficulties. TheRabbit, who we know to be highly timid, has now three-bet out of position, and Madness likes the look of his hand too. Your only clean out is a jack, and even the J♣ is tainted as it puts a three-flush on board and sets up redraws, even if it doesn't give someone a flush at once. It is time to resign gracefully.

Actual Play: Madness folds and TheRabbit now check-raises you. There is $145 in the pot and it is $15 to you.

Question 5. Do you (a) fold (b) call (c) raise?

Scoring 5. (a) [fold], 0 (b) [call], 10 (c) [raise], 20

Analysis. You have an easy call as even if you have only seven outs (if TheRabbit has AQ or KQ) you are getting pot odds of nearly 10-to-1. However, raising is a far better play. Unless he has an absolute bone-crusher, your three-bet will probably put the frighteners on TheRabbit and get him to shut down. This creates the opportunity to take a free card on the turn or pursue your semi-bluffing strategy. The extra small bet is a cheap price to pay for this.

You raise.

Hypothetical Play: TheRabbit now caps and you call. The turn brings Q♠10♣4♣2 and TheRabbit bets out. There is $250 in the pot and it is $30 to you.

Question 6. Do you (a) fold (b) call (c) raise?

Scoring 6. (a) [fold], 10 (b) [call], 2 (c) [raise], 0

Analysis. TheRabbit is telling you that he has a very big hand. Please listen. TheRabbit might be a timid player but he is not stupid. He can see that you may easily have a hand as strong as AQ, but he is telling you that he doesn't care. It is now very likely that your only out is a jack, and the pot odds aren't there to chase it.

Does this mean you made a mistake by three-betting on the flop? No—that is just an illusion. The play cost you an extra $30, but if you had played the hand passively you would still have called the turn with apparently reasonable pot odds, and thus would have spent the $30 there instead.

TheRabbit's response to your three-bet generated the important information that you are way behind in this pot, and enabled you to get away from the hand. Had you played it passively, you may very well have lost even more money if an ace or king came on the river and you called or even raised. When you are facing a player who you are sure will only bet with a very good hand, it is okay to apply pressure and then back off if he plays back at you. This method is more problematic against tough, aggressive opponents as you cannot always be sure where you stand when they give you heat.

Actual Play: TheRabbit calls.


Hypothetical Turn: The turn is Q♠10♣4♣10♠. You hold A♠K♠.

TheRabbit checks. There is $190 in the pot and it is $30 to bet.

Question 7. Do you (a) check (b) bet?

Scoring 7. (a) [check], 7 (b) [bet], 10

Analysis. You have now picked up a flush draw so, unless TheRabbit has a huge hand, you have umpteen outs—possibly as many as 21. The 10 is a great scare card, and it is a good idea to pursue your semi-bluff here, since a bet may even persuade TheRabbit to fold a mediocre queen. Although it is not likely that TheRabbit will muck, it is possible. It is certainly well worth making a bet with a small negative expectation in order to give him the chance to go seriously wrong.

Actual Turn: The turn is Q♠10♣4♣8. You hold A♠K♠. TheRabbit checks. There is $190 in the pot and it is $30 to bet.

Question 8. Do you (a) check (b) bet?

Scoring 8. (a) [check], 10 (b) [bet], 3

Analysis. The 8 may have helped TheRabbit. If he has QJ or Q9 he has picked up a gutshot draw (if he holds Q9 he is not to know that a jack will give you a higher straight) or with Q8 he has made two pair. Even if he hasn't improved, he will have no reason to suspect that the 8 has helped you. Thus a bet is unlikely to get him to fold, and he may even raise. Taking a free card is the best option.

You check.


The river is Q♠10♣4♣8J♣. You hold A♠K♠.

TheRabbit now bets. There is $220 in the pot and it is $30 to you.

Question 9. Do you (a) fold (b) call (c) raise?

Scoring 9. (a) [fold], 0 (b) [call], 4 (c) [raise], 10

Analysis. Well, he could have a flush, but it is not likely on the play. TheRabbit is not the kind of player to check-raise you on the flop with a drawing hand. He sees no reason why you should have a 9 in your hand and is betting his hand for value.

You raise and TheRabbit calls. Your straight takes the pot from TheRabbit's two pair with QJ♠.

Question 10. The river card, 8, put four to a straight on board. Therefore did TheRabbit make a mistake by betting his two pair on the river: (a) yes (b) no?

Scoring 10. (a) [yes], 10 (b) [no], 2

Analysis. The four to a straight is a red herring as it is hard to see why you should have a 9 in your hand. However, your play is consistend with having a flush draw yourself, and this would have come home on the river. TheRabbit's bet is a classic river mistake in that he is making a bet which is unlikely to be called by a losing hand.

TIP: One of the most common scenarios in hold'em is that you raise pre-flop with your lovely big cards and then . . . miss the flop completely. It is difficult to play accurately with just overcards, as you can rarely be sure where you stand. However, mastering this element of the game is critical to your success.


100 Excellent. You handled your overcards very well.
90–99Very good.
80–89Good. You probably need to think harder about when to push
with your overcards and when to back off.
60–69Never mind. Handling overcards is tricky.
below 60 Poor.

Where I Go Wrong

Question 2 (preflop). Jacobs sets up that TheRabbit is a weak player. Therefore, I discount his three-bet from out of position. A four-bet might get rid of Madness, and allow me to take the flop heads-up with a hand that's probably best. If my cap doesn't get rid of Madness, that's okay too, since my ace-king looks to be better than his hand, too. Since I proably have the best hand, I want the pot as big as possible. Jacobs doesn't really see capping as wrong, but he deducts a point because he sees calling as a better option. I'm about 80% sure I disagree with him. On the one hand, we're talking about one point in a problem hand, so it's not that big a deal. On the other hand, I put real money at risk when I play. If I'm making a mistake, it costs me real money. If I were to cap, I might lose one bet when I'm wrong, and win one to two bets when I'm right.

(The math: Assume Madness would always call one more bet, and would fold to two more bets, let's say one-third of the time. So, if I call, my three bets are up against six. If I raise, TheRabbit should always call, which is one bet, and Madness puts in an average of 11/3 bet. Madness' most likely holding is something like AT, QJ, or a purely speculative hand like 66 or 89 suited. So, averaged out, let's say I'm a 2:1 favorite over his hand, so he'd outdraw me 1/3 of the time. So on the flop, I win 4/3×2/3 = 8/9 of a bet from Madness from my raise, plus TheRabbit's bet if I'm right that I'm beating him. Therefore: Raising might cost me one bet or win me 18/9 bets.)

So, on balance, I conclude I don't have to give up the extra point for "missing" question 2.

Question 5 (TheRabbit has check-raised the queen-high flop). Okay, this is the one I really don't get. Jacobs strongly prefers reraising. I'm having a lot of trouble with this. Not only don't I have a hand, but TheRabbit's strong play suggests to me that he won't be folding before the river, so I can't win the pot without making a hand. Given that I'm probably drawing, I want to do so cheaply.

Jacobs has a point that reraising the flop sets up a free-card play on the turn, and if TheRabbit is indeed a weak player I might get it, but I'm still drawing. I have seven outs and the pot-odds to call, but if I'm less than 50% to win at this point then any extra money that goes into the pot at this point benefits my opponent, not me. The raise makes sense from the free-card angle, then, to keep my drawing price low.

However, Jacobs also says a reraise makes sense in order to set up a semi-bluff later. This, I totally don't get in this context. TheRabbit is a weak player who likes his hand a great deal. For a bluff to work, he has to be willing to lay down the hand. I absolutely don't see that from him.

Maybe I don't lose the whole ten points I lost by answering "call"—but I lose most of them for missing the free-card angle.

Question 6 (he caps, I call, he bets the turn when a blank comes). Okay, here I deserve to lose the points. I engaged in "test-taking strategy" and answered "call" because Jacobs seemed to want to go to war with the hand. I nearly have the odds to try for the Jack—maybe that's why Jacobs gave me two points for answering "call"—but on balance a fold is clearly correct.

Question 7 (he calls, and the 10♠ falls on the turn, giving me overs, a gutshot, and a flush draw on a paired board). Jacobs prefers betting, although he doesn't take a lot of points off for checking. I checked because I don't see TheRabbit folding his hand, and I'm still drawing. Even if I truly have 21 outs (i.e., TheRabbit has Q2 with no spades) I'm still not a favorite to make my hand by the river. Assuming TheRabbit won't fold, extra money going into the pot at this point doesn't benefit me. However, I want to see the river card. So, a check costs me zero or one bet, while a bet costs me one or two bets. I prefer the check.

That said, TheRabbit might fold. If he indeed has a weak Queen, I've shown enough strength to get him to think he has kicker problems, and possibly fold. If I really have 21 outs, and there's a reasonable chance TheRabbit will fold, then I like a bet here. Otherwise, I don't.

Question 8 (he calls the flop, and the 8 falls on the turn). Now Jacobs favors a check, basically on the premise (well, Jacobs is British, so the "premiss") that the Eight could have helped TheRabbit, so risking a raise is unwise. QJ and Q9 would indeed be reasonable holdings for TheRabbit, but the gutshot shouldn't particularly scare me. Few boards don't feature a possible gutshot of some sort by the turn, and in any case he's beating me with his Queen if he indeed holds one of those hands. QT would be just as reasonable a holding, but for some reason Jacobs wasn't worried about that in Question 7.

On balance, while the Eight could have helped him, there's no reason to think it helped him so much that it changes the balance to a check. My belief now is that questions 7 and 8 should be answered the same way (either bet both times, or check both times). For some reason, though, when I originally read this problem hand, I answered exactly wrong to both questions.

I think Question 5, and Questions 7 and 8 together, that those are the crux of the hand, the places I went the most wrong. It's here I'd like to hear others' thinking on the hand.

Question 10 (should TheRabbit have bet the river). I was taken in by Jacobs' red herring, asking about the straight when TheRabbit should have been worried about the flush. I agree with Jacobs' reasoning even though I answered this wrong originally.

I'm interested in others' reactions to this hand. My email address at right is changed to a working address, even if I have comments turned off on the blog. (I hesitate to say that, even, since I got some real asshole comments on my blog back when they were turned on.) But if you have constructive criticism of my game, I'd like to hear it. Unimproved Ace-King is a tough one to play, and it concerns me to see that I (may) have got this so wrong. I'm interested in other analysis.