A Surprising Quiz Answer

Ever since my little rush of playing lots of one-table satellites yielded some good rewards in larger tournaments, I've kept playing them, and had a very interesting hand come up the other day. This is neither a "bad beat" nor a "brilliant play" story, by the way. I found it interesting because my gut instinct regarding who the favorite was likely to be turned out to be slightly wrong, although I'm still OK with my decision (you're allowed to write in and tell my why you don't like the decision, though).

Here's the situation: We're fairly early in a one-table $200 buy-in one-table no-limit hold'em (NLH) tournament; 10 players started, and one has been eliminated. My chip position is still average, as is my key opponent's. I'm under the gun with the 7 7, and decide to limp in. A player in middle position raises, but it's only a tiny raise: double the big blind. The blinds and I call.

The flop comes 6 5 4, which is certainly one of my better flops, although nothing like the powerhouse that a flopped set would have been. There had been about $200 in the pot preflop, and after the blinds checked, I bet $225.

If you play much online poker, you know that the action can get pretty wild and wooly in the early going. I have lots of theories about this. Some of it stems from impatience (the "double up early or go do something else" theory), some of it from inexperience (there are lots of people coming into poker these days), some of it from misunderstanding current literature, and a lot more for reasons only "The Shadow knows."

With the preceding paragraph for a setup, you don't have to be a rocket scientist to have guessed that the original raiser popped me back: He moved all in. The situation, then, is this: The blinds quickly get out of the way, and I can try to claim a pot containing about $1,250 by calling about $750.

The possibilities I face (cast your ballots in this Let's Make a Deal-type selection process) are:

Door No. 1: My opponent has made his small raise with a small pair and now has a small set. The bet is certainly the right size; he doesn't want me to draw at a straight or a flush, but if I'm going to try it, he's going to make me pay too much to do it, and people call online with all kinds of crazy hands. This door's scenario seems fairly unlikely, though. Small pairs like that usually either limp or raise a bit more. With small pairs, you want either one opponent (giving you a chance to hold up against overcards) or six (providing you the opportunity to get paid off handsomely when you make your set). Raising twice the big blind isn't enough to create an isolation situation, but it might reduce the number of opponents to a suboptimal three or four. If it turns out this is the scenario I'm facing, my straight draw combines with my shot at a bigger set to make me about a 2-1 dog.

Door No. 2: My opponent has two big cards and is just trying to buy it, figuring that if a limper made one small pair, he won't call. In a regular tournament, that's reasonably likely to be true; the bet is imposing. It's less likely online, because players tend not to lay medium hands down (indeed, I have seen players call huge bets with astoundingly poor hands), which makes naked bluffing much harder to do (that doesn't stop people from doing it, of course). In this situation, I'm about a 4-1 favorite; the overcards can hit, but they have only two chances, not the five they would in a preflop situation, and I can still make a straight or a set.

Door No. 3: My opponent has a big suited ace, like the A 10 or something of that sort. It certainly fits the small preflop raise, because he can get away from it easier to a big reraise. Of course, it could be the A K or the A Q, which for all practical purposes are the same hand for me and my two sevens (board overpair and open-end straight draw), although, again, I'd expect a slightly bigger raise with one of those hands. If I am facing one of those hands, my sevens are leading the non-pair, but two of my redraws (the 3 and the 8) are disasters, because they make the flush while making my straight.

Door No. 4: My opponent has a bigger overpair; even eights are possible because of the gutshot for the straight. If this is the situation (and it's certainly possible, although, again, I'd expect a slightly bigger preflop raise), I'm about a 3-2 dog, which makes the pot odds just about right for a money game, but not so exciting for a tournament, where I'm not anxious to play all of my chips for roughly correct pot odds as an underdog.

OK, cast your votes for what my opponent had. Don't peek. Don't make any assumptions based on my knowing what my opponent had: My opponent could have voluntarily shown me his cards if I laid my hand down.

To add a bit more space between the question and the answer, I'm going to discuss one more possible hand that doesn't quite deserve its own door: pocket threes. Although that hand does offer straight possibilities, it's an underpair to the board, not an overpair, a very considerable difference, and it's certainly not much of a raising hand preflop, especially a tiny raise (I have seen players over-raise with it, in hope of picking up the pot then and there, or isolating just one opponent, but for the same reason fours, fives, and sixes aren't hands likely to be merely doubling the big blind, threes shouldn't be doing so, either). I'd be about a 4-1 favorite there, too. I guess you can't rule it out entirely, because a number of online players play no-limit like limit (they just hit the "raise 30" button), but I'm not giving it its own door.

All right, that last paragraph was long enough to protect you from your wandering eye. You figured it out, didn't you? I thought you would, because in only one of my four examples did I not offer calculated odds for the situation: The right cards are "behind Door No. 3," in this case, the A Q.

Different parts of the quiz will interest different folks, but I find the odds for Door No. 3 the most interesting. Who do you think is the favorite there? I have a pair, one card that will give me a set (the other 7 gives my opponent the flush), and six cards that give me a straight. My opponent has two overcards and a flush draw.

Don't cheat by going to your poker software and figuring out the answer. Make your best guess. Ready? It surprised me: It's a coin flip, with my opponent actually owning about a 1.5 percent edge. Naturally, if I know my opponent to hold those cards, I'm willing to play a coin flip when I'm getting pot odds that good.

Next quiz question: What should I do? I'm pretty unhappy with Door No. 1, thrilled with Door No. 2, reasonably happy with No. 3 (not overjoyed, because I'd prefer a bigger edge than that when playing for my whole stack, but happy enough so that if this had been a brick-and-mortar casino (B&M) tournament and my opponent had flashed his hand, I'd have played), and not happy with Door No. 4, even though the money odds are fine.

This is a tournament, albeit a small-money tournament being played in a situation in which I can find another tournament in 10 minutes. I'd prefer not to play my stack for a coin flip early. If I get that unexpected glimpse at flashed cards (possible only in a live game, not an online tournament), I probably let the hand go. My rate of return on these tournaments is pretty good. Playing on with $750 is not a big disadvantage.

So, what did I do?

Because I titled this piece "A Surprising Quiz Answer," the first question you should ask is, "Did you know that if you were up against the nut-flush draw, that situation was a coin flip?" The answer to that one, I'm sad to say, is no. I figured that if that was the situation, I was probably about a 4 percent favorite (which actually turns out to be almost exactly the case if I had been holding the 7 as one of my sevens). That's not being wrong by a ton, but it's still off. The real danger was if I'd been much more wrong: Suppose the situation meant I was actually a 15 percent dog? Then, my decision might – might – change. I haven't presupposed a glimpse at my opponent's cards here, and of course in an online tournament, I can't get one.

I feel compelled to state that in a B&M tournament, neither I nor you should be trying for a glimpse of an opponent's cards. Leaning back in your chair, even a little, is just cheating, folks; sorry if you don't like to hear it characterized that way. End of morality lecture.

Ultimately, I wound up deciding that the chances of it being Door No. 1 (the small set) weren't very good. The chances of it being Door No. 2, the random overcards, like K-Q, were actually much higher. The player was expecting to win with his bet. The chances for it being Door No. 3 were probably the highest of the four, I think, although I was expecting to see something like the A 9, not the A Q (not that it would have mattered). People who play raggy nut-flush-possibility hands like to get the pot a little bit bigger, so that players will chase them down if the flush or flush draw hits. The chances of encountering Door No. 4 (the better overpair) were, I think, fairly close to the same as for Door No. 2, in an online tournament. My very fast analysis of the chances was:

Door No. 1: 5 percent

Door No. 2: 25 percent

Door No. 3: 40 percent

Door No. 4: 30 percent

For educational purposes, that's all that matters. To keep the e-mail limited to debates about analysis, yes, I called. I was in big trouble only in the Door No. 1 scenario, and that seemed least likely. The sevens didn't make a straight, but they didn't have to. The turn and river were blanks, and I doubled through. I finished in the money, but I don't remember if it was second or third.

The matters I'd like you to think about are (you can write with your thoughts if you'd like, but mostly I want to get your thinking):

1. How surprised were you to learn that the nut-flush draw and overcards were actually a teensy, tiny favorite over the made pair and open-end straight draw?

2. How surprised were you to find out that a "small" matter of my holding one of my opponent's sevens changed my status from a 1.5 percent dog to a 4 percent favorite?

3. What's your own online experience "take" on my analysis of what my opponent was likely to be holding? Remember, now, this is a $200 buy-in NLH tournament, and I (you) have no notes about a random opponent.

My estimate for what hands my opponent is likely to be holding in a one-table B&M tournament are quite different, and that's an analysis for another time, although it wouldn't be a bad subject for you to spend some time thinking about, either.

The analysis changes considerably if this isn't the start of an online tournament, but the final table of a reasonably big-money live tournament, where considerations like ladder climbs change multiple aspects of the analysis immensely. Of course, the chances of reaching a 10-player final table where everyone has virtually identical stacks aren't very high.

There's also a reasonable possibility that I (you) may have some information about how my (your) opponent plays at such a B&M final table, but that kind of information is so important that it changes the question even more than the ladder-climbs issue does. Let's stick to one set of questions at a time!

Andrew N.S. Glazer, "The Poker Pundit," is Card Player's tournament editor, and he writes a weekly gambling column for The Detroit Free Press. He is the author of The Complete Idiot's Guide to Poker (Alpha Books, September 2004), Casino Gambling the Smart Way (Career Press, 1999), and Tournament Poker With the Champions (Huntington Press, spring 2005). He is a consultant to www.PartyPoker.com, and welcomes your questions.