# Deal or no deal?

Jun 11, 2007 2:26 AM

The game show Deal or No Deal is all about settling for what is offered vs. taking the risk to win even more. Do you take the \$100,000 when the \$1,000,000 case is still out there?

When I watch the show, I can’t help but always try and figure out the expected value of the remaining cases. I just add up the dollar amount of the remaining cases and divided by the number of cases left.

It should come as no surprise that until there are only a couple of cases left, the amount offered is well below the expected value. The show would be a little boring if everyone took the first offer because it was a fair one.

Video poker players have to make a similar decision on virtually every hand. There are, of course, some key differences. First of all, being on the game show is pretty much a once in a lifetime opportunity and affords the player the chance to win what could be a life-altering amount of money.

Decisions like this tend to wind up being more emotional than mathematical. We’ve all played the lottery where the odds may be 50 or 100 million to 1 to win \$25 million. A very poor payback, but for that amount of money, we’re willing to take the chance.

In video poker, any player can pretty much play an unlimited number of hands, so the emotional aspect can be removed. No one hand is going to allow the player to win such a large amount of money (unless you’re playing \$5 machines and up). As a result, we let the mathematics rule.

The second significant difference is that on the game show, the show really doesn’t care if the player wins the \$1 million once in a while. They make their money from the commercials and the sponsors. The more drama, the more viewers. The more viewers, the more they charge for commercials.

So, the goal is drama, and they get the drama by trying to get the contestant to stay in as long as possible, knowing that more often than not, the result will be heartbreak.

In video poker, most hands are worthless after the initial deal. When I say that, I mean that only a small number are sure winners after the first five cards. Roughly 20% of initial hands are a High Pair or better. This means that for 80% of the hands, the player is choosing the best possible way to play the hand, knowing that there is at least some chance the result will be that he wins nothing. This is really not a very risky proposition. He’s really not risking anything further.

Of the 20% of hands that are a pair of Jacks or better, the overwhelming majority is played as the winning hand. Again, very little is being risked. The player knows he has a sure winner, and is just hoping to improve the hand when possible.

There are, however, times when the player should say ”˜No Deal’ and risk the sure winner for the chance at an even better hand. While they are not commonly occurring, the difference in expected value is great, and they are hands that afford the Player chances to win big.

By saying Deal, you may have a short-term victory and the expense of the long-term. Let’s take a look at some of these cases for full-pay jacks or better.

The ultimate near miss is the 4-Card Royal Flush. With an expected value of better than 18, we throw away every sure winner except the Straight Flush. This means we throw away Straights, Flushes and High Pairs — even if it is an Inside draw (10-J-Q-A).

This is the ONLY hand that we break apart a Straight or a Flush for. We do NOT throw away Straights or Flushes to go for a 4-Card Straight Flush. We do, however, throw away a High Pair to go for a 4-Card Straight Flush — again, even if it is an inside draw (8-9-10-Q-Q).

In full-pay jacks or better, we do not throw away a High Pair to go for a 3-Card Royal. However, if you are playing a progressive and the jackpot reaches a sufficiently high level, this is another time the sure winner would be tossed in order to go for the big prize.

Just as important as knowing when to say ”˜No Deal’ is to know when to say Deal. In all other cases (for full-pay jacks or better), you keep the sure winner.