Try not to defy law of averages

Jun 27, 2005 2:13 AM

It’s the bottom of the 9th, the bases are loaded with two outs. Your team is down by a run and the pitcher is due up. You look down the bench and need to decide who is going to pinch hit.

Your choices are the All-Star player with a career .320 average but who’s been slumping the past couple of weeks, or the journeyman player with a career .250 average who has been hitting the ball hard.

So, I guess the real question is, do you go with the short-run results or the long-run results?

Many are waiting for the mathematician in me to come up with some magical answer. But it’s a trick question. We’re talking about a real baseball game with real baseball players. The math counts for something, but it can’t be everything.

Who knows what the effect of the pressure will be on each player, or what type of pinch-hitter each player is, or any other aspect of the psyche of his players?

Years ago there was a baseball game called Strat-O-Matic. Basically, it tried to mimic real baseball by using dice and special stat sheets on players. The idea was to capture, as best as possible, the actual results of a player, using dice.

Assuming for a moment that this game did in fact do this, NOW which of these two players will you send up to pinch hit, the All-Star or the journeyman?

When we boil down the career of the All-Star, how he did last week becomes meaningless. When you roll the dice, there will be an approximately 32% chance (representing the batting average of .320) of getting a hit. Sure, even in the fantasy game, there will be ups and downs, but at the end of a season, you can all but bet, he’ll be batting right around .320.

As for that journeyman, he’ll only have a 25% chance of getting a hit. Now the decision is almost a no-brainer. The math is plain and obvious and anyone who tells you otherwise is just, well, wrong!

Sure, if you play this situation out two or three times for each player, the journeyman might win the game more often than the All-Star, but if you had to face this situation or one like it 10 or 20 or 30 times, there is no doubt that the All-Star is going to come out ahead. After all, he didn’t get to be an All-Star for nothing!

Playing video poker is a lot like playing Strat-O-Matic. There are no emotions. Today’s results are not impacted by yesterday’s results. Today’s results won’t affect tomorrow’s results (unless you lose your ENTIRE bankroll!).

Video poker is all about hard, cold math. It was programmed to be that way. You are dealt five cards. There are, in theory, 32 ways to play those five cards ranging from keeping all five to discarding all five.

Each one of those 32 ways has its own expected value telling you the win power of that strategy. The one with the highest chance of winning is the one to play if you want to maximize the overall payback of the machine and maximize your chances of winning.

Sometimes, two choices have similar expected values, but one of them has the potential for a significant payout and people choose to play the one with the lower expected value hoping for the big win. While I don’t condone this, it’s okay to do this if you recognize what you are doing and why you are doing it. This is part of knowing what to expect when you play and is a key component of expert strategy.

But, if someone is going to tell you that the game of video poker is not ruled by math, they are just plain wrong. The machine might just as well defy gravity while it’s at it, as long as it is going to ignore other laws of nature.