Long Video Poker Play Raises the Chance You'll Hit, Not That You'll Win

I hit a royal at 25-cent video poker the other day. It returned 4,795 coins -- $1,198.75 -- for a $1.25, five-quarter, bet.

The hand started with the jack, king, and ace of hearts. Holding these and pulling the 10 and queen involved no great skill. They did take considerable luck. The chance of a royal, going into a round, is one out of 40,160. The chance of starting with the three cards I did, and pulling the two I needed, was one out of 1,081.

The casino I'd brought to its knees has several similar poker machines. Most return 4,000 coins for royals. A few pay 4,795 coins. Naturally, I shop for high jackpots -- especially when I know other factors are equal. In this case, looking before leaping was worth an extra $198.75. Of course, hitting a jackpot on one game doesn't mean I'd have won a penny, never mind $1,000 or $1198.75, on another. Or that I should have played the $5 slots that time. But these are philosophical issues best pondered after calling 1-900-PSYCHIC on a dark and stormy night.

In reel-type slots, higher jackpots typically imply lower chances of being hit. This isn't true for poker, where probabilities of hands depend strictly on random selection from a known deck. This permits use of returns posted on the machines to calculate payoff percentages and other statistical characteristics of each game.

It turns out that for the machines in question, those with jackpots of 4,795 coins return 97.17 percent to players. The versions with jackpots of 4,000 coins return 96.77 percent. But putting too much stock in such payback percentages can be misleading. Few solid citizens get enough rounds over a reasonable period of time, let alone a single session, for values influenced by effects of infrequent events to really mean much.

A common video poker strategy is to play until a session bankroll runs dry or one of the high-return hands hits. Make believe someone will cash out on a machine with nothing wild, after getting four-of-a-kind or better. Here are the returns for five coins played on the machines in question: four aces, 400; four twos through fours, 200; four fives through kings, 125; straight flushes, 250; and royals, either 4,795 or 4,000 depending on the machine selected.

For either version, hitting only full houses or less has an 86.53 percent return. This figure can be used to estimate the average number of rounds a given stake should allow, while waiting for one of the bell ringers (and, I can tell you first-hand, it isn't much of a bell). A starting bankroll of 60 units -- $75 in a 25-cent machine playing five coins at once -- should last for 438 rounds. This is long enough to expect at least one four-of-a-kind. But it isn't as good as it first may seem, since the hit would pay only 125 coins ($31.25) in most cases, 200 coins ($50) in others, and 400 coins ($100) for the premium rank. And, don't confuse statistically expecting a hit with actually getting it.

The hill gets steeper as it gets higher. A bankroll of 1,280 units, $1,600 in a 25-cent machine playing five coins at once, is needed to persist for an average of 9,475 rounds. This is long enough for the math mavens to say that you expect at least one straight flush -- paying 250 coins ($62.50). You may not be overjoyed to learn the figures for a royal, but here they are, anyway. A bankroll of 5,400 units, $6,750 in a 25-cent machine, has an average survival of 39,994 rounds. This is about enough to expect at least one royal -- paying 4,795 or 4,000 coins ($1198.75 or $1,000, respectively).

So you can't count on playing long enough to get over the hump. You have to be lucky and hit early. I did it loading $20 into a quarter machine. And $6.25 was left when the royal hit. So I made $1,192.50, not factoring in my earlier video poker career. The main fly in the ointment of triumph, beside the aforementioned debilitated bell, involved the winners' limo for the ride home. When I asked about it, they told me the uniformed chauffeur would be waiting at the Greyhound terminal in 20 minutes, and not to be late. I guess the poet, Sumner A Ingmark, was right when he said: