Regression and slot graveyards

27 September 2018

By John Grochowski

QUESTION: I have a question about regression as it applies to gambling, but what leads me into it is baseball.

Whenever a player or team has a hot streak, I read the statheads start talking about regression. When the St. Louis Cardinals went 22-6 in August, I heard they were due for regression. The implication was that they would lose more games to make up for the hot streak.

Isn't the same due in gambling? If there have been 10 black numbers in a row at roulette, don't there have to be some reds to make up for it? Doesn't there have to be enough regression so that the total goes back to normal?

ANSWER: Regression doesn't mean hot streaks have to be followed by cold streaks, or cold streaks have to be followed by hot streaks. There doesn't have to be any makeup time at all.

Instead, regression points to the tendency for events to occur at their normal rate. In double-zero roulette, 18 of the 38 numbers are on black backgrounds. If the ball has landed on black spaces 10 spins in a row, that does not affect future outcome. The expectation is that future results would regress to their normal proportions and would bring black numbers something very close to 18 times per 38 spins — 47.37% of the time.

Given enough spins, hot streaks and cold streaks grow out of normal probability and they fade into statistical insignificance. If there are 10 black numbers in a row followed by 38,000 spins that include 18,000 black numbers, then there are 18,010 black numbers in 38,010 spins.

That's 47.38% — only 0.01% more than normal. No makeup time was needed, just a regression to normal proportions.

In baseball or any other sport, the normal proportions of wins and losses differ with the quality of the competitors. But let's say a team that has a 22-6 month has a performance level that would usually lead to a .550 winning percentage. Then if the next month also has 28 games, a regression to their norms would mean an expectation of about 15 wins and 13 losses, rounded from 15.4-12.6.

A 28-game sample is so small there's a lot of potential volatility in results, and it's well within normal probabilty for the team to win or lose several more games than its norm. There aren't 38,000 games for the streaks to fade into statistical insignificance.

But regression suggests that after a hot streak, the most likely event from that point forward would be for the team to win at its own normal rate. Just as in roulette, regression does not imply the need for a cold streak to follow the hot one.


QUESTION: Every time I go into a casino, there are new slot machines. That makes me wonder what happens to the old ones. Do they go back to the manufacturers? Do they get sold to other casinos? Is there a big slot machine junkyard somewhere?

ANSWER: Changing a slot game does not necessarily mean discarding a whole machine. In most cases, it's only the software that gets changed, and the machine hardware stays right where it is.

The pace at which games are used and discarded has increased in the video slot era. Three-reel games maintained peak popularity much longer than video games do. But even reel slots can be changed on the same hardware with a change of reel strips, new glass to display game title graphics, and a new game chip.

There's no need for a slot graveyard. The machines stay put with no skeletons to be buried.