Poker Variations

Cost of Variations

Today, it seems as if new video poker appears daily. While that statement is probably a gross exaggeration, new versions of the cards game do crop up more frequently now, and each new variation vies for the players'' money with different enticements. Some of these don’t last much past the "trial" stage due to very low payback or playing difficulty; after a brief try, most players avoid them. Occasionally a machine might fade away due to very high payback (e.g., over 102%) because the pros eat it up and the casinos remove it from their floors. Others survive either because of unique character or because the payback is still near or over 100%, or both.
If you encounter a new variation, how can you determine whether its payback is sufficient to warrant giving it a try? My new analysis/trainer program, Optimum Video Poker allows you to easily make changes in a game’s payoff table and quickly analyze the game to see how the changes affect the game’s payback.

Poker Payback

The tables in "The Payoff Schedule" sections show the probability of each final hand (assuming perfect play). To estimate the cost or benefit of a variation, it is necessary only to multiply the change in the payoff by the probability of occurrence and add the product to the total Average Payback. But note that the product is often a negative number because the payback has been reduced. Some examples will help to clarify the procedure. Player look first at the Jacks-or-Better payoff schedule. If the schedule is as shown in "The Payoff Schedule - Jacks-or-Better" except that the royal pays 4,700-for-5, what is the total payback? Well, that’s 94O-for-l, an increase of 140, which we multiply by the probability (.0000248), giving .00347, or about .35%. Adding this to the basic game’s 99.54% payback with perfect play yields 99.89% payback. As usual, we must deduct about .02% for human play.

Variations on Game

Another variation might be to reduce the full house to 8 but increase the flush to 7 (making it an 8/7 machine). If we subtract .01151 and add back .01102, we have a net reduction of .00049 or about .05%. This is a small loss, and we could probably recover most of that (or maybe even realize a net gain) with proper strategy modifications.
Another fine change is to reduce the payoff on quads to 20 instead of 25-for-l. Multiplying the difference of five by the probability of .002363 reveals a very significant 1.18% reduction. The Frontier on the Las Vegas Strip used to offer a bonus coupon when you cashed your paycheck. If you hit any four-of-a-kind on Jacks-or-Better with the coupon, the payoff was doubled, adding 5.91 % for over 105.4% total payback! Due to a $100 limit, a dollar machine didn’t give the full $125 double pay, but this still added 80% of 5.91 % for an expectation of about 102% in the short term!
As we have noted before, a bonus on a certain set of quads, such as four sevens, must take into account the frequency of that particular final hand. We have seen that four sevens (or four deuces through four nines) will occur about once in every 13.44 sets of quads, but even assuming one in 13 or one in 14 would not cause too big an error for a quick approximation. In Joker Wild (kings or better), four deuces through four queens will occur with about equal frequency, and in online poker game Deuces Wild any set of quads (other than four deuces which is a separate category) will have about the same frequency of occurrence.