Saturday, July 14, 2012

Riviera success, Tropicana fail

A few months ago, a friend of mine who lives in Australia wanted to organize a couple of get-togethers for people who, like him, participate in an online poker forum. He comes to Vegas for about six weeks every year. After consulting with potential participants about when they might be in town, he picked two dates, June 24 and July 8, both Sunday evenings. Between those two dates, nearly everybody who was interested in coming could make at least one of them.

I volunteered to make arrangements for small private poker tournaments. Because I live in town and know the poker rooms pretty intimately, I thought I was in a good position to pick spots. The poker room manager of the Riviera piped up on the forum, actively offering his facilities at a discounted rate, so that was half of the decision easily made. I could have done both nights there, but wanted to spread the business around a little, because I thought that people attending from out of town might not have seen other poker rooms and would appreciate the variety.

The first event at the Riviera was just perfect. They were great hosts and took really good care of us, taking pains to be sure that we all had a wonderful time. I could not have been more pleased. If you're ever have occasion to have a private poker tournament, I recommend that you put the Riviera near or at the top of your list of venues to consider.

The Tropicana, however, is another story. I spoke to the poker room manager by telephone in late April, explaining what we were looking for. He promised that he would come up with a proposal for a tournament cost and structure and get back to me. He did, several days later.

My first warning sign of trouble was that he clearly had me mixed up with somebody else for whom he was also negotiating a private poker event. He had the date wrong, he had the number of expected participants wrong, and he remembered that we had wanted to have pizza available, which is something I had not requested. But after getting those items corrected, he gave me his proposal, and I accepted it: July 8, 8 p.m., total of $75 buy-in. The tournament was to be followed by low-stakes cash games, and he promised (just as the Riviera had) to lower the usual rake for any cash games we started. I told him that exactly what games we played would depend on the preferences of those who showed up, but that something like the dealer's-choice mixed game that they regularly offer on Monday nights might be interesting to our guests. He said that would be fine, and if we did that, we could make it either $2/4 or $3/6 limits.

So it appeared that all was in place. Early Sunday I sent him an email as a final confirmation that all was in place. I did not get a reply (still haven't, in fact), but I didn't worry about this. I just assumed that the room manager had the day off and thus didn't see the message. In retrospect, I should have seen that lack of reply as more of a red flag than I did.

Just before 7:15, as I was getting ready to leave home, the first people to arrive were sending messages via Twitter that the staff of the poker room had no idea what private tournament they were talking about. Some small misunderstanding, I thought. So I quickly printed out a copy of the email the poker room manager had sent me containing the details and stuck it in my pocket as I headed out the door.

When I got there, it was as the others had said. The guy behind the desk knew nothing about it. Furthermore, he had in the interim called the room manager, who had claimed to know nothing about any private tournament. They had just one dealer on duty, running their one and only cash game.

I called the room manager. He said that there had been a flood in his office that destroyed his computer, and he had lost all of his emails for the last few months. I was highly skeptical of this story. (I related it to those who had arrived, and one of them quipped, "So he's telling you that the dog ate his homework." Yep--that's about it.) But he said that they always had dealers on call in case they got busy, and they could have someone there in about 20 minutes, and he would take $5 off of the house's portion of the tournament entry fee to help compensate for the misunderstanding. Fine--that was easier than trying to organize going somewhere else at the last minute.

The dealer arrived, sat into the cash game, and the one that had been in the cash game ran our single-table tournament. But when it was over, we were told that we couldn't open another cash game as we had planned; the dealer who ran our tournament was already on overtime and they couldn't keep him there any longer.

A few of us decided to go over to Bally's and play there instead. Others went their separate ways.

The whole thing was a disorganized mess from that second phone call on. I was embarrassed, because I had promised everybody that all was in place, and the failure made me look bad. (Admittedly I could have been more aggressive about rechecking before the appointed date to make sure that all was set. But I assumed that I didn't need to, that this guy was a professional at running his room, and that when he promised to be ready for a private poker tournament at a certain date and time, he would be.)

So what I said about giving consideration to the Riviera if you need to find a venue for a private poker event? Do the opposite for the Tropicana. Put them at the very bottom of your list, unless you relish the idea of your event being ignored and forgotten.

Dogs playing poker

Can this be beat for sheer adorableness? I say no!

Deuce-Four wins a tournament

See last hand described here:

Thursday, July 12, 2012

Poopcorn must die

Now, see, I'm laughing out loud just typing out that post title. Sadly, only one reader will find it as funny as I do.

I was playing a few SNGs with Josie tonight, and IM-chatting with her on the side, when I had occasion to type that phrase. As I looked at it there on my screen, I thought, "There must come into existence a blog post with that title. It's too good to waste." I lamely suggested to Josie that she write one, but I don't think she will. So it falls to me.

The problem is that the story that generated the phrase, well, it just isn't very interesting, nor is it very funny. If I bothered to type it out, you'd all read it and think, "That's it?" Which is probably what you'll think when I end up leaving it a mystery, too. Oh well. Nothing I can do about that.

I guess you'll just have to take my word for it: Poopcorn must die.

Wednesday, July 11, 2012

Probability of a bigger pair

Ed Miller's column in the June 27 issue of Card Player magazine is about bet-sizing tells. He walks the reader through a hand that he played while holding Q-Q, showing how opponents' bet sizes helped him deduce what hands he was up against. I have no quibbles with his reasoning. In fact, it's a highly worthwhile piece, and the sort of insight that makes me never want to miss his columns.

I do, however, have a quibble with an incidental point tossed in along the way. In explaining why he elected to just call rather than reraise when faced with an opening raise from a nit under the gun, he says:
[T]here are still five unknown hands behind me. There's about a one percent chance each player has either A-A or K-K, making about a five percent chance in total that one of the two hands I'm most afraid of is lurking behind me.
(Note: this is just one of the reasons he cites for not reraising, not the only one.)

At first I wondered why he was making a distinction between the players who have already acted and those yet to act. After all, A-A or K-K is an ugly problem for Q-Q no matter where on the table it is being held. But I think I see what he means. If he were in the big blind, and thus last to act on the raise, and nobody had reraised yet, then he could quite confidently assume that nobody was holding A-A or K-K, unless it is the UTG nit.

Or put it another way: Before there is any action, there is a fixed probability that any other player has been dealt a pocket pair higher than Q-Q. But people so reliably raise and reraise with A-A or K-K that when they fail to do so, we can safely revise downward that estimated probability.

What is the a priori probability that somebody at a ten-handed table has been dealt A-A or K-K when I'm holding Q-Q? It turns out to be a ferociously complicated mathematical problem, one that I could never solve on my own. Fortunately, though, somebody a lot smarter than me has already worked it out, and you can see both the process and the result here:

The table containing the solution is at the bottom of the page. The answer for Q-Q is 0.0841. That is, if I see Q-Q in my hand, and I have nine opponents, about 8.4% of the time one of them will be holding a pair bigger than mine. That does indeed work out to a round estimate of about a 1% probability that any particular one of them has the goods. And that's a useful rule of thumb. Before there is any action (action constituting additional information to throw into our estimation math), each player in a full ring game has about a 1% chance of having been dealt a pair higher than my queens.

If I'm in the big blind and nobody has raised, then probably nobody has a bigger pair, unless they're trying the ol' limp/reraise thing. Also, if I open-raise from under the gun with my Q-Q and get only callers with no reraise, I can go to the flop reasonably confident that nobody has A-A or K-K. But really, that fact has everything to do with what we know from experience about how people play, and little to do with the math. The conclusion would be equally true if the a priori probability of somebody holding a bigger pair were 80%, or 0.8%, rather than the actual 8%.

But I think there's a problem with how Ed applies the math to the situation he describes. Once a nitty player has opened for a raise from under the gun, we no longer have the baseline 8% chance that somebody at the table has A-A or K-K. The probability now has to be estimated to be vastly greater than that. Exactly how much greater depends, obviously, on exactly how nitty this particular nit is. If he is the extreme case and will only raise UTG with exactly A-A or K-K, then our previous 8% probability goes to 100%. Of course, it's not often you'll have a player with a range that narrowly definable, so it usually won't go up all the way to 100%. But it's surely a damn sight higher than 8%.

If the nit does, in fact, have A-A or K-K, then the probability that any other player at the table also has A-A or K-K is much lower than the roughly 1% apiece that we would otherwise be using as our rule of thumb. Using the next column in Alspach's table, we see that the a priori probability that two players have been dealt pocket pairs bigger than my queens is only about 0.2%--a negligible quantity. The implication is this: The fact that a nit put in an UTG raise means that the probability of a bigger pocket pair being out there is much greater than the baseline 8% (as just discussed), but also that nearly all of that probability resides in the nit, not in the players who will be acting behind me.

It is thus no longer true that each player behind us still has a 1% chance of holding aces or kings. Our estimate of the probability that any one of them has A-A or K-K must be greatly reduced from its baseline ~1% by the fact of having observed that UTG raise from the nit. Put most simply: As the probability that the UTG nit has aces or kings goes up, the probability that anybody else at the table has aces or kings goes down.

Now, this is where it gets a little weird and mind-bendy. Because two things are simultaneously true: (A) The probability that any player is dealt A-A is independent of whether any player is dealt K-K.* (B) Alspach's calculation of a 0.2% probability of two players having A-A or K-K is no longer valid once we actually know that one player has one of those hands. The 0.2% is valid only when we have no information except for having seen our own Q-Q.

This is analogous to questions such as the probability of a roulette wheel hitting 00 twice in a row. It is 1/38 x 1/38 = 0.026 x 0.026 = 0.0007. But if we spin and the ball falls in that 00 slot the first time, now the probability of seeing 00 twice in a row greatly increases, to 0.026. Of course, the probability that the second spin will be 00 has not changed one smidgen by virtue of the result of the first spin, yet the probability of seeing two 00s in a row has changed.

So it is with the A-A and K-K. If we know that the UTG player surely or almost surely has A-A or K-K, we have to throw out the window the Alspach table numbers. They no longer apply. The 8% probability (that exactly one player has A-A or K-K when I have Q-Q) is no longer valid because we have strong reason to believe that this specific shuffle of the deck did, in fact, result in one of those 8% events. And the 0.2% probability (that two players have each been dealt A-A or K-K when I have Q-Q) is no longer valid both for that reason, and for the reason that once the UTG nit is known to have A-A or K-K, two of those eight cards are no longer available to be given to other players.

The knowledge (or at least high suspicion) that UTG nit has one of the two premium pairs is akin to opening the sealed box in which Schrodinger's poor cat has been confined. It is now known to be either alive or dead, not in some hybrid or probabilistically indeterminate state.

Mind you, I don't claim to have worked out the math so as to be able to tell you exactly what the new, revised probability is that each of the five players yet to act has a pair bigger than Q-Q, in addition to the one that we presume is hiding under the nit's card protector, but it is definitely not well estimated by the 1% rule of thumb. It must be substantially lower than that. Exactly how much lower depends entirely on the degree of confidence with which we can assign A-A or K-K to the open-raising nit.

*Note: I realize that that is not quite true, because as soon as two aces are in a player's hand and no longer in the deck from which the dealer is pitching cards, the concentration of kings in the deck rises slightly by virtue of card subtraction, so the probability of K-K goes up slightly. But it's a tiny difference.