Understanding Slots
by John Robison
Choices
Does it really matter which bonus box you pick?
One of the most frequently asked questions I receive is: Does it matter which fish (or suitcase, money bag, package, etc.) I choose in the bonus round?
This seemingly simple question is surprisingly difficult to answer.
First, we need to clarify the question. What most people are really asking is whether or not the RNG has already predetermined what the bonus amount will be, regardless of which item they choose. In other words, they want to know if, at the beginning of the bonus round, the slot program polls the RNG to find out what the bonus will be. After they select an item, the slot reveals that corresponding bonus amount, but it also displays what the items they did not choose are worth. Many players feel they had no chance of winning those other amounts, because the RNG had already determined what their bonus would be (therefore, it wouldn’t matter which item they selected; the outcome would have been the same).
But the bonus round does not work that way. Instead, the slot program uses the RNG to assign the possible bonus amounts to the various choices. The item you choose does, indeed, determine the bonus you win. If you had chosen a different item, you would have won a different amount. Nevertheless, despite the fact that your choice determines your bonus amount, your choice still doesn’t matter—at least, not in the long run.
To see why, let’s look at a very simple bonus round:
You get to choose one of three boxes. The amounts of $1, $10, and $100 are randomly assigned to each box at the beginning of each round.
Now, let’s compare four “picking strategies.” In the first strategy, you always pick the first box; in the second, you always select box number two; and in the third, it’s box number three. For the fourth strategy, however, you use a gut feeling, a divining rod, a roll of a die, or some other method to determine which box to pick.
Let’s say we played many, many bonus rounds using each of these strategies and examine our results for each strategy.
In the first strategy, we always picked the first box. Because the bonus amounts were randomly assigned to each box, the probability is one-third that it was worth $1, one-third that it was worth $10, and one-third that it was worth $100. Therefore, one-third of the time, we won $1; one-third of the time, $10; and one-third of the time, $100.
In the second strategy, we always picked the second box. Again, the bonus amounts were randomly assigned to each box, so the probability is one-third that the box was worth a particular bonus amount. As with the first strategy, one-third of the time, we won $1; one-third of the time, $10; and one-third of the time, $100.
In the third strategy, we always picked the third box. As you’ve probably already guessed, our results for the third strategy are identical to those of the first and second strategies. We won each of the bonus amounts one-third of the time.
Now, let’s look at the fourth strategy. In this one, rather than picking the same box all the time, we use some method to determine which box to pick. Obviously, we’re after the one we think is worth $100. We don’t have any useful information we can use to help us pick the box—a gut feeling isn’t really “useful information”—so, we’re once again at the mercy of the random distribution of the winning amounts. That means that, on average, one-third of the time we got $1; one-third, $10; and one-third, $100.
No matter which strategy we use, the outcome is the same. So, even though your choice does determine the amount you win on any particular bonus round, it doesn’t matter what you choose. You get the same long-term results—regardless of which picking strategy you use.
One last—but significant—note: What I’ve described in this column applies to Class III slot machines (the ones you find in Las Vegas, Atlantic City, Tunica, etc.). It does not apply to Class II machines (found in tribal casinos that do not have state compacts) and VLTs (video lottery terminals run by state lotteries). Those machines may indeed predetermine the amount you will win in a bonus round.