"It's definitely due"

A couple of weeks ago I was playing at Harrah's. The Harrah's properties in Nevada (well, most of them, anyway) have a linked system for bad-beat jackpots, so that when it hits at any poker room in the system, everybody logged in at all of the properties gets a piece of it. Of course, the winner and loser of the hand get the biggest chunk. The threshold qualification for it drops over time as the pot gets larger.

At the time, the jackpot amount was something like $75,000 with a requirement, as I recall, that four-of-a-kind nines had to be the losing hand. The dealer was explaining the rules to a new player. The player noted that the jackpot was quite large. The dealer responded, "Oh yeah, it's definitely due to hit."

This was very similar to a comment I heard at Mandalay Bay in February, when one of their royal flush high-hand jackpots had swollen to unusually large proportions. A woman at my table commented that she had switched her play to Mandalay because the jackpot was "due" to hit very soon.

I don't understand how people can play so much poker and still be completely out to sea about the most rudimentary concepts of probability.

It is certainly true that over a long period of time one will find an average amount that is in a bad-beat or high-hand jackpot when it is hit. But if an unusually long time goes by without a qualifying hand, so that the jackpot money grows larger than average, that does not mean that it is "due" to hit. A qualifying hand is no more likely to be dealt on the next shuffle, or within the next 24 hours, than it was the week before.

The probability of a jackpot hand occurring is precisely the same every time the cards are dealt. It is exactly the same the very next hand after the jackpot has hit as it is when months have gone by. If we assume for the sake of simplicity that a given card room deals the same number of hands every day, the probability of having a qualifying hand is exactly the same today as it was yesterday and will be tomorrow, completely independent of when or if the jackpot was last awarded.

Think what would have to be true for it to be otherwise. There would have to be some central respository of information about all of the hands that have been dealt, and somebody (one of the lesser poker gods who couldn't get a plum assignment, perhaps?) would have to be constantly reviewing them, noticing that they hadn't seen, say, a royal flush in quite a while, which entity would then have to actively intervene in the shuffle to arrange it to happen. If you believe that things like that happen in this universe, then you have bigger issues than being mentally ill-equipped to play serious poker.

The cards have no memory as to what arrangements they have been in in the past, nor any consciousness to use such information, nor any means of organizing themselves into particular configurations as a result of a decision based on that information. This isn't like some slot-machine jackpots, which are programmed to have a guaranteed big payout within a certain time frame or before they reach a certain capped amount. Poker hands are random and fully independent events. The probability of a certain type of high hand or bad beat occurring remains exactly the same every time a deck comes out of the Shufflemaster.

If you find yourself saying, or even thinking, that such a jackpot is "due," get thee to a remedial math class. You need a refresher in the basic concepts before you play another hand of a game for which a decent grasp of probability is indispensible.