Aces, aces, and more aces

Item #1.

I've been thinking a bit about a new promotion that Planet Hollywood is running in their poker room. It's kind of a standard aces-cracked thing, but it's unusually lucrative: $200. It runs for three specific two-hour segments a day (10:00 to noon, 2:00 to 4:00 pm, and 2:00 to 4:00 am), Monday through Thursday. (See here for full details.)

I don't mind bonus/jackpot promotions that are basically break-even for me. I don't like ones that end up transferring a lot of the money I contribute to somebody else. How does this one rate on such a scale?

Let's figure it out. PH plays nine-handed games. Pocket aces get dealt once in every 221 hands, on average. At a full table, then, you can expect somebody to have aces about every 25 hands. (This isn't exactly right, because what each player is dealt is not independent of what the others are dealt. But it's close enough for current purposes.) Let's assume that people are slow-playing their aces routinely, inviting everybody into the pot, because the bonus is high enough that it will almost always exceed the average pot one would win absent the promotion. I'm going to assume that you'll average 4-5 opponents in the hand that way. Aces will hold up roughly 50% of the time against that number of opponents.

That means that aces will get cracked about once in every 50 hands or so at a full table. The lucky loser gets paid $200. But the table will have contributed only $50 to the promotion fund during that time. In other words, the casino is paying out four times as much as they're collecting during the promotion hours.

Obviously these numbers are very rough, but they're in the right ballpark. Maybe you could manipulate them to make it only a 3:1 or even 2:1 payout, or maybe it's closer to 5:1. Doesn't matter much for my argument.

My point is that without any serious doubt this promotion requires subsidy from the jackpot collection at other hours (assuming that the casino isn't throwing its own money into the kitty). That means that if you play at Planet Hollywood at hours other than the specific 24 hours per week that the promotion is running, most of the jackpot-drop dollar that you contribute every time you win a pot is being redistributed to the people who play during the designated hours--or at least whatever fraction of that dollar goes to this particular promotion (instead of, say, the high-hand jackpot fund, and I have no idea what those proportions are).

The promotional hours are generally not ones that fit well with my preferred (and, by experience, most profitable) times for playing. Now, maybe the reward is so lucrative that it makes sense to adjust my playing times to be sure I'm there for at least some of those hours and cash in on it. But if I'm not going to do that, then this promotion is a money-loser for me, and I don't like that. I understand that the room is trying to beef up attendance during what have been off-peak hours, and the strategy probably works to accomplish that. But I'm not thrilled about PH using my money to pay those players to fill the seats, just because of when they choose to play.

To make matters worse, there has already been established a cadre of nitty regulars who are there just to collect the jackpot money, and break the rules of the promotion by collaborating to increase the chances of a payout, and to keep it as cheap as possible. They use code words to signal to each other that they have aces, and in response the others in the know will get the pot to the minimum required to qualify, then check-check-check, keeping everybody in, and giving the guy with the aces the maximum chance to get them cracked. Of course, he will reciprocate the favor when one of the others get his turn. This not only grossly distorts the normal play of a hand and is flagrantly cheating, but it increases the number of times a payout is made, thus exacerbating the problem of transferring money from non-promotional hours to the promotional hours. I don't like it.


Item #2.

In the January 4, 2010, issue of Poker Player newspaper, columnist Richard G. Burke presents an interesting table of data that I don't recall having seen before. The question is this: If you have one ace in your hand, and there is another on the flop, what is the probability that you were the only player at the table who was dealt an ace?

The result obviously depends on the number of people dealt in to the hand. Here's what Mr. Burke calculates:

# of opponents/probability of there being no other aces held by opponents

1 / 0.92
2 / 0.84
3 / 0.76
4 / 0.69
5 / 0.62
6 / 0.55
7 / 0.49
8 / 0.43
9 / 0.38

Of course, even if you know the exact probability that nobody else was dealt an ace, you can't know exactly how many might have folded them pre-flop. (What? Fold an ace before the flop??? Am I mad???) But I think it's useful to know that at a typical full table, about 40% of the time nobody else was dealt an ace, which means that about 60% of the time one or more opponents did get one.

Be careful out there.


Addendum

Shortly after posting the above, I checked my Twitter feed and found a message pointing to this thread on allvegaspoker.com, which I hadn't been aware of before. In it, a few people try to estimate whether playing to try to hit this jackpot is a positive expected value overall. That's obviously a different question from the one I'm asking, but it's kind of interesting in its own right.