Sunday, April 29, 2012

Should Poker Players Want Jackpots in Their Games?

This is the second in what I hope will become a series of posts on the things that (good) poker players should look for in an ideal casino game. Regular players in poker rooms hold sway with the casino management, and this series can be viewed as my personal commentary on what I think you should be lobbying for if you are a good poker player.

Entering "jackpot" into the search field on this blog yields many instances of my bemoaning their existence in my games, but in truth my disdain for jackpots has waned recently. (This is decidedly not due to the fact that I've won a substantial amount from jackpots, which many of my casino acquaintances assumed would change my negative opinion of jackpots in general. Talk about results-oriented thinking!) There are many different types of jackpots awarded in poker games at casinos. In Los Angeles, the "Bad Beat Jackpot" is by far the most pervasive, but in Las Vegas, I think the "High-Hand Jackpot" might still be more common. Both usually take $1 out of each pot (sometimes only if there is a flop) and award money to players in rare instances such as losing with a very strong hand (Bad Beat) or just winning with certain types of very strong hands (High Hand).

For this post, I'll be thinking primarily of the "Bad Beat" type of jackpot, which I think is the worse of the two. I'll be looking at how it affects the three main concerns I mentioned in my previous post:

1. Maximizing Winnings.
2. Having an enjoyable social experience.
3. Playing a pure, intellectually stimulating game of poker.

I don't have anything to say about concern #2 here, but some players may have a strong personal preference for or against jackpots. Personally, I don't like them much. Let's look at concern #3 and then #1.

If playing a pure game of poker is your main reason for coming to a casino, you will hate jackpots, especially bad-beat jackpots. For purists, putting finely-tuned poker strategies to work against real opponents is the essence of what makes playing poker worthwhile. It can be a joyous experience to put theory into practice and have it work out. Jackpots destroy this by changing the players' incentive structure, thereby interfering with the logical inferences about your opponents' decisions that characterize a pure game of poker. These disruptions are most evident in Bad Beat Jackpot games during hands where there are two Aces on board, because the easiest way to win a jackpot is for a third Ace to hit the board while one player has the case Ace and the other player holds a large pocket pair. Winning the actual pot becomes insignificant, with players focusing only on making sure they do not miss out on the 1/40 or so chance at winning a few thousand dollars.

There is another, subtler, consequence of jackpots on the purity of the game that is often overlooked. The $1 jackpot fee is taken from each pot, and this affects optimal play. A slightly smaller pot means that it's optimal to play slightly tighter (and, if other players make are making that adjustment, it becomes correct to play more aggressively). This is a minor disruption, but it is made worse by the fact that another $5 is usually being taken out for the casino's rake, and my sense is that each extra dollar taken out is marginally worse than the previous. (Consider, for example, the effect of taking the first dollar out of a $1000 pot compared to taking the thousandth dollar out after already removing the first 999!) In No-Limit Hold'em, which already has a problem of having too little action when everyone in the game is solid, the problem is especially pronounced. A future post may explore the possibility of adding an ante to NLHE games in order to liven them up a bit.

The jackpots introduce opportunities for corrupt practices by players, dealers, and administrators. Honest players now have one more thing to be on the lookout for in order to protect themselves.

When a jackpot is actually hit, the game comes to a screeching halt. Winners celebrate, decks are examined for evidence of cheating, administrators skim off the top of the jackpot (legally and sometimes illegally), ID's are taken out, and forms are filled out for tax purposes. A nightmare for a purist who just wants to sit and play poker.

I hesitate to call myself a purist (after all, it ranks third on my list of concerns), but maybe I am. Certainly, I'm sympathetic to this way thinking, and I consider "game purity" to be the major reason to dislike jackpots. I previously would have told you that Maximizing Winnings is my primary issue with jackpots, but the effect of jackpots on winnings is actually pretty complicated. Let's examine the pros and cons.

Having often argued against jackpots, I'm well-versed in the negatives. The simplest possible analysis is to look at the EV of each dollar paid into the jackpot. In California, I've been assured that the casino is allowed to take 15% for administrative costs, so each dollar returns 85 cents at best. (This is assuming you can trust administrators not to skim off the top.) The money you put in will sit around for months, on average, so the net present value of that money is slightly less than 85 cents. Then, you are expected to tip. (Tipping can be forgone, I suppose, but everyone I know has tipped after their jackpot wins.) Most players tip 5-10%, so our return is now down to about 75%.

Things are still worse than that, though, for several reasons. First, jackpots increase the volatility of our win rate substantially. Second, the deck-checking is unfairly biased towards delaying the jackpot payouts, because they are occasionally cancelled. (Once in a while the deck-check reveals a bad deck and the jackpot is not paid, but is it very rare for a deck to be checked when the jackpot is not paid out. This means sometimes payments have gone into the jackpot drop in hands that would have been voided had the jackpot been won and the deck checked. To be fair, the decks should be checked every time a dollar is paid to the drop, but this is impractical for obvious reasons.) Third, the slightly smaller pots mean tighter play becomes correct, and this can cut into the win rate of strong, creative players. Fourth, when the jackpot is actually won, the game will be delayed, eliminating winnings you expected to have during that time playing poker. These factors are hard to quantify, but I would say that between the EV and volatility issues another 5% of utility is lost. So, we are at about 70% return, assuming there is no cheating or illicit skimming by the casino management.

I've heard a few good arguments for having jackpots amid many weak arguments. The most worthy argument is that jackpots attracts amateur players.  All else being equal, having to play the jackpot drop costs me about $4 an hour and in the long run I get paid back about $3 in jackpot winnings. So, ignoring strategic effects and time delays, it really only costs me about $1 per hour. On the flip side, a single fish at the table is certainly worth much more than this. Even just a slightly weak player can make up for that $1/hour jackpot loss. Moreover, a good player will tend to play hands that have a good chance at making a jackpot, such as high pocket pairs or big Aces. This means that, for good players, the return on investment should be slightly higher than for weaker players. My sense is that this is a very minor effect, but I could be wrong. It is something, at least.

In conclusion, I would say that the only very significant effect of jackpots on any relevant concern is on the purity of the game. Jackpots are unmitigated disasters for game purity. However, your bankroll will benefit if the jackpot scares off the other poker purists. Purists tend to be good players. If your only concern is for making money, the jackpot might actually be helping you in the long run by attracting worse players to the game. Keep in mind, however, that if these worse players are not in the game at any particular time, you would certainly be better off without the jackpot drop.


I did not get into the UMD College Park Applied Math department. I am leaning towards accepting the position in the PhD program in Statistics at UMBC.


Anonymous said...

I like this post a lot. Your criticisms of the jackpot all make sense to me and are well thought out. I always thought the pro bad beat jackpot argument was not that it would attract suckers, but rather that it would make people fear cheating less. I once overheard two guys talking and one said he had played in a home game recently and had four of a kind and lost a big hand. The other guy said something like "That's the problem with home games" as if it were just obviously chalked up to cheating.

Keith said...

Interesting point. I'm not sure if I ever heard that before. I guess it only applies to the bad-beat jackpots. I guess this would still fall under the "attracting bad players to the game" category, if players who are paranoid about cheating tend to be bad players.

The main reason I think jackpots bring players to the game is the excitement of playing the lottery. However, casinos also benefit from the goodwill and loyalty of players who actually do win (and to a lesser extent players who get a table share). Having a bad-beat jackpot in particular tends to directly reverse a potentially highly salient negative experience for the jackpot winner. On the other hand, players who just barely miss a jackpot because of a technicality might be frustrated, but the tendency is to think "I was so close! I can win the jackpot soon if I just keep trying!"