Quads key to hitting royals in video poker

Jan 27, 2009 5:03 PM
by Lenny Frome, from the GT Archives

We demonstrated recently that the chances of winning in short Jacks or Better sessions were determined primarily by the player’s luck in hitting quadruplets. But, over the longer haul, the quads will average out and hitting a few off the average (of about once per 423 games) will not be so crucial. Then, winning will depend primarily on luck in hitting royal flushes.

To illustrate, let’s assume that a skilled player can play at a rate of 240 games per hour. To play 423 games, therefore, takes a 105-minute session and one quad would be expected. Paying 125 for 5 this winner would account for 6 percent of your total return for the session. If we don’t get it at all, it takes a lot of extra smaller wins (percentage-wise) to make up for that shortfall. An extra quad makes it easy to have a winning short session.

Now consider the royal flush itself. The number of royals we hit, on average, will be determined by the number of hands we receive, which are truly candidates for royals and the probability that they can become royals. There are 2,598,960 unique hands, which can be dealt from a 52-card deck. The candidates for royalty distribute as follows in the pre-draw hands:

In 2,598,960 hands we expect a total of 64.9 royals.


This averages out to one royal for every 40,000 hands, which is about 167 hours of steady play. The hands asterisked (*) do not include ace-10 combos, which are better played as solo aces, nor solo 10s which are better discarded, as we will soon prove.

Since our royals pay 800 for 1 (4,000 for 5), one appearance in 40,000 hands accounts for 2 percent of our overall payback. Failure to appear is difficult to compensate by other smaller winners.

To drive home the point made above and to illustrate the raw power of computer simulation applied to video poker consider the hand:


The expected value, which is the average value of the wins we can get if we consider every possible draw to occur once, is found for (A) holding both the ace and 10 versus (B) holding the ace alone is seen to be:

Expert play always requires that we draw to the cards that offer the highest EV. The solo ace, foregoing the try for the royal, is the better play if we have only the ace-10.

To attain our maximum number of royals, without misplays on any competitive alternatives, we must know the different EV’s associated with the various two-card royals. You may not want to do the math, but there are plenty of strategy guides that will enhance your play, including the ones here on our website.