"Unbelievable"

I put in an unusual (for me) early afternoon poker session today at Treasure Island. The TI is a delightful little place, definitely among the best of the small poker rooms. It is unbeatable for friendliness, service, innovations, and overall quality of dealers. But I've had kind of a curse there, losing more than I win. Before today, I had played 12 times in cash games, winning only 4 of those days, with a net loss of $929. It has been puzzling me for a long time why this particular room stands out from the rest of the Las Vegas poker rooms as such a prominent statistical anomaly. But once in a while, I head back there to see if I can break the curse. Today I tripled my $100 buy-in in one hour, and took the unusual step of quitting early to lock up the "W." This is now two winners in a row there, so maybe, maybe, I'm seeing what statisticians call "regression to the mean"--that is (to oversimplify), an unusually good or bad streak will tend, over time, to end and revert toward the long-term average.

Anyway, about halfway through my time there today, one player displayed a sufficiently high degree of ignorance about pot odds that I thought it was worth commenting on here.

He had just sat down at the table with $100. This was his first hand at our $1-3 NLHE game. He raised to $10 and had four callers. The flop was A-J-x with two spades. He bet $15, and chased away all but one opponent. The turn was an offsuit blank. He bet $35 and got called again. The river put out a third spade, and our hero pushed in his last $40. His nemesis called. The bettor showed A-J; he had flopped top two pairs. The caller had 4s-5s, for a baby flush.

This is the point at which the subject of this post threw up his hands and said, "Unbelievable!" This was followed with a cursory, insincere "Nice hand" to the guy who was stacking up the chips.

As I've said, I don't give lessons at the table, but if I did, I would have told our new player that he needed to do his math better.

Let's not debate whether one should call even a smallish raise from an unknown player who just sat down, when you have small suited connectors. Personally, I would wait until I had more information on a new opponent. But it's certainly not outright foolish, because you can sometimes make a big profit, as happened here.

Now we're on the flop. There's about $50 in the pot. The new player bet just $15 into four opponents with a double-suited flop. If one of these opponents had hit a flush draw with that flop, he is being offered a pot of $65 for a $15 call, or 4.3:1 on his money. Of course, he's not guaranteed to win even if he makes his flush, because of the board pairing and giving the first player a full house, or somebody else hitting a bigger flush. But even accounting for that, 4.3:1 payback when his odds against making his hand with the next card to come are only about 4.2:1 (out of 47 yet-unseen cards, 9 will make his flush and 38 won't, and 38:9 is 4.2:1) is not a bad deal, if you assume that he'll win more from this new player than what is now in the pot if he hits.

Now consider the situation on the turn. The drawing player had to call a $35 bet for a chance to win what was now a roughly $115 pot, which is about 3.3:1. If he could know that his opponent had flopped top two pair, he would probably expect to get the remainder of that stack if he hit his flush on the river, because players with top two pairs tend to be pretty stubborn with it. So if we add the new player's last $40 to the potential winnings, the "implied pot odds" jump to $155 for that $35 call, or 4.4:1, while the odds against hitting are only 4.1:1. Again, it should be a profitable call to make.

In other words, his opponent made pretty reasonable decisions at every point along the way. There was not one thing even a little bit "unbelievable" about either his decisions or how the cards fell.

One way to think about good "big-picture" strategy in poker is that your goal is to induce opponents to make mistakes, either mistakes in guessing what you're holding or mathematical mistakes of putting too much money into the pot for what their payback could be, weighted by their probability of winning. This new player didn't do that. If instead of $15 he had bet, say, $40 on the flop (about 80% of the pot size), and this opponent called, then he would have induced a mistake, because if these two players repeat this same scenario a thousand times, the bettor will win a whole lot more money than he loses.

Alternatively, the original bettor, after being called for $15 on the flop, could have reasonably guessed that his opponent was on a flush draw. Then, when the turn card didn't bring the third spade, he could have pushed in his remaining $75, thus requiring the drawing player to pay $75 for an approximately 1 in 5 chance of winning a $155 pot, horribly incorrect odds for trying to make it. And if the turn card had instead been one to make the flush, the original bettor could shut down, and limit his loss to $25.

Even after making two bet-size errors on the flop and turn, the new player still could have salvaged something of the situation on the river. After getting called twice, he must guess that this opponent flopped either a flush draw or something that had him beat, like a small set. He should not have bet the river, no matter what came. (I'd make an exception if he got lucky and made a full house on the river with an A or a J.) If the last card does not complete the potential flush, he will probably only get called by a player who had flopped three of a kind, and had him beat all along, making this a "zero-equity" bet. (See http://pokergrump.blogspot.com/2008/01/that-guy-didnt-bet-his-full-house.html.) And if the last card does complete the possibly flush, he should save his last $40 instead of throwing it away.

In fact, the only thing unbelievable about this hand was that this new player to the table made three critical errors, and still thought that the outcome--the loss of his entire stack of chips--was "unbelievable." Nope; it was not only believable, it was entirely predictable.


Oh, and the photo at the beginning of this post? That's Danette, the day shift supervisor at TI. If she looks familiar, it's because she's one of the dealers on NBC's "Poker After Dark," GSN's "High Stakes Poker," and FSN's "Poker Superstars." (See http://blogs.nbcsports.com/poker/2007/01/unsung-heroes-part-1.html.) She's also a frequent contributor to the forums at http://www.allvegaspoker.com/. Despite several email exchanges, I had never managed to catch her on duty when I played at TI, until today. Delightful young woman, and even more fetching in person than on TV. To top it all off, she knows and cares about details of poker rules, and there ain't nothin' sexier than that! (Don't get any ideas, guys--she's married and has kidlets at home when the dealing's done.)