Those pesky slot odds

29 December 2016

By John Grochowski

QUESTION: My brother and I have been playing slots for donkey’s years, and we’ve been having the same argument about what “random” means all this time.

He says that if you have a reel with nine 7s and one lemon, that means for the game to be truly random a 7 should come up nine times out of 10. I disagree. I say the game can be random, but still have the lemon come up more often than the 7.

Can you elaborate?

ANSWER: Let my start by saying the answer here applies mainly to three-reel stepper slots. On video slots, gamemakers can design reel strips as long as they need to be to place symbols in the desired proportions.

On slots with mechanical reels, making the odds of the game work to bring about the desired frequency of payoffs and jackpot size makes it necessary to make the reels behave as if they have a different proportion of symbols than the really do.

That’s done with a random number generator and virtual reels. If 90% of the symbols are 7s, as in your example, and the designer wants 7 to come up only 10% of the time, then only 10% of the random numbers are assigned to the 7s.

To stay with your example, the designer has to work with a reel that has nine 7s and one lemon. One way to change the proportions while keeping results random is to work with a set of 100 numbers. The programmer can tell the game, “Any time the RNG generates number 1, show the first 7. If it shows 2, show the second 7.”

The programmer can go down the list and assign one number to each 7. Then he can assign the remaining 91 numbers to the lemon.

Results are random because you never know what number the RNG is going to spit out. On any given spin, the chances of each number being generated are equal – there is a 1 in 100 chance of it landing on 1, 1 in 100 of landing on 53, 1 in 100 of landing on 97 and so on.

However, because 91 numbers have been assigned to the lemon and only one to each 7, there will be a 7 on the payline only 9% of the time and a lemon on 91%.

Results are random, but the odds defined by the random number associations will lead to far more lemons than 7s on the payline.


QUESTION: The casino where I was staying had two-deck blackjack games, but blackjacks paid 6:5. It also had six-deck games where blackjacks paid 3:2. Which is better, fewer decks or getting the bigger blackjack payoff?

ANSWER: Getting the bigger blackjack payoff far outweighs the number of decks.

You didn’t tell me what other rules were in play at the table, but let’s assume equal rules other than the number of decks and the blackjack payoff. We’ll define games where the dealer hits soft 17, you can double down on any first two cards including after splits, may split aces only once but may split any other pair up to three times for a total of four hands.

Under those conditions, the six-deck game with a 3:2 payoff on blackjacks has a house edge of 0.64% against a basic strategy player. With two-decks and a 6:5 payoff on blackjacks, the house edge soars to 1.83%.

I can’t emphasize enough how bad 6:5 payoffs are for players. Avoid 6:5 games like the plague.