# Paytables a must in video poker

Sep 18, 2007 12:58 AM

Last week, I said I would explain how the payback of any video poker game could be determined based on the paytable, which must be in plain sight, either on the machine’s glass or on the monitor itself.

This is required in most jurisdictions by law. If you can’t find the paytable for a video poker machine, don’t play it!

I didn’t mean to imply that you could calculate the payback of the video poker machine in your head based on the paytable — although it is possible to get a rough estimate similar to another paytable you are familiar with. Thanks to computer programs, the payback of a machine can be calculated once the paytable is known.

You can then buy a book or a tip sheet and bring it with you to the casino to figure out the paybacks of your favorite type of game. There are even some websites that list virtually every imaginable paytable and its payback.

So, how is the payback computed? First, we start with each of the possible 2,598,960 different pre-draw hands. This is the number of ways that 5 cards can be dealt from a 52-card deck, where the order of the cards doesn’t matter (generally speaking, we don’t care the order of the specific 5-cards). Each of these pre-draw hands can be played 32 different ways — 1 way to draw 5 cards, 5 ways to draw 4 cards, 10 ways to draw 3 cards, 10 ways to draw 2 cards, 5 ways to draw 1 card and 1 way to draw 0 cards.

Each of these 32 ways are analyzed to determine how many winning hands (and of what rank) would be formed if all of the possible outcomes were played. So, if we draw 3 cards, there are 16,215 possible outcomes that might range from a Royal Flush to a High Pair. Next, the payout of each winning hand is multiplied by the number of outcomes of that rank hand.

If we determine it is possible to wind up with 120 Straights, we multiply 120 times the payout of a Straight (4 units in the case of a full-pay jacks or better). We sum up the total units returned for each of the 32 ways, and divide this number by the number of total possible outcomes to arrive at the expected value for that combination of pre-draw hand and specific draw.

The expected values of each of the 32 ways is then compared, and whichever way has the highest expected value is the best to play that pre-draw hand. We sum up the expected values of each of the 2,598,960 hands to arrive at the overall payback for that paytable.

I realize this all probably sounds easier to me than it does to most of you. The good news is that you really don’t need to know how it is done; other than it is based in sound mathematical principles. For those of you who are interested in how the payback is derived, it also can show how as the paytable changes. Not only will the payback differ, but which of the 32 ways is the best way to play the pre-draw hand. This is what causes the strategy movement that occur when the paytable changes.

It is important for you to memorize the paybacks of some of the more popular games with higher paybacks. More accurately, it is probably more important to memorize the paytables of the popular high payback games so you can search for them in the casino. It may be nice to know that your favorite game is a 95.6 percent payback, but that won’t help your wallet. Better to know which paytables to look for when looking for the 99-plus percent games. The nice part is that the casinos put this information right there in plain sight!