VIDEO POKER

How Often Do You Win a Hand?

Several authors, including myself, have told you several times that the strategy for playing the multi-line games is exactly the same as when you play the single-line games (assuming the same pay schedule.) We have also told you that 9/6 Jacks or Better returns 99.54% when played perfectly on a single line machine or a multi-line machine. What we told you was true --- as long as we are looking at the long term.

Liam W. Daily pointed out to me, however, that whether or not you win an individual hand matters a lot on how many games you are playing at once.

Take an ordinary sort of hand like 2d 5s 6h 7c 8d and assume you are playing a game without wild cards where straights return 20 coins for your 5-coin bet. The obvious play is to hold 5678. You will win if you draw any 4 or 9. There are 8 such cards out of the 47 still in the deck. 8 chances of success out of 47 come out to 17% --- a little better than 1 in 6. So 17% of the time we win a net of 15 coins (the 20 coins we win minus the 5 we bet) and 83% of the time we lose our original bet.

In Triple Play, though, it is different. Since we are betting a total of 15 coins (5 on each line) and a straight returns 20 coins, we will end up being a winner for the hand if one or more of the three possible straights come in. This will happen 43% of the time. Same hand, yet the probability of whether or not we win on it is very different.

In Five Play, since we are betting 25 coins, we need to collect two or more straights in order to win. This happens 20% of the time. In Ten Play, we need three of the 20-coin straights to make up for our 50-coin ante, and this happens 23% of the time. In Fifty Play, we need to connect on 13 or more straights in order to win, and this happens 7% of the time. And at Hundred Play, we will only get exactly 25 straights (which will give us our money back) 1.2% of the time, and we will only make money 1.5% of the time.

I find this interesting. How can we say the overall odds of winning are the same and yet have such different chances to win any particular hand? Seems to be a contradiction. The explanation lies in the fact that these numbers only consider HOW OFTEN you win rather than HOW MUCH.

Consider our hand in Triple Play. You will get 0 straights (losing 15 coins) 57% of the time. You will get 1 straight (winning 5 coins) 35% of the time. You will get 2 straights (winning 25 coins) 7% of the time. And you will get 3 straights (winning 45 coins) about a half percent of the time. The average return on the 15-coin bet will be 10.2 coins ( meaning you will lose 4.8 coins) whether the 15 coins were bet on a single line game or a Triple Play game.

I was sitting next to a man playing 50 Play and he asked me about his chances for success on just such a hand. I don't have these numbers memorized, so I got back to him the next day and told him that 13 out of 14 times he would lose money starting from this hand on this game. He responded, "I thought so. I almost NEVER win. So that's why I throw everything away. Who knows, I might collect on a royal! After all, I have 50 shots at it!"

Bad logic. Completing a royal on the redraw from this position is 380,000 to 1 against you (or over a half million to one against if one card is an A, K, Q, J, or T). Even having 50 shots at that is still extremely unlikely. Most of us will never have a "royal on the redraw" in our lives. Basing your decisions on such a possibility rather than a realistic look at the probabilities is an expensive way to play. Since this guy was playing 50 Play for dollars (which means $250 per play!), his decision to throw everything away was costing him $165 each time he did it.

That's it for this week. Until next time, go out and hit a royal flush.