A new slot machine and blackjack basic strategy

30 March 2014

By John Grochowski

QUESTION: I have a question about a new slot game I found. It has three different bonuses, and they’re kind of color-coded. There are purple bonus symbols on the first three reels, green on the second, third and fourth, and blue on the third, fourth and fifth. You need all three purples to launch one bonus, all three greens for the second and all three blues for the third.

The bonus symbols come up pretty often, and there are almost always a few on the screen, but getting the three matching ones is tough. The purple bonus is the best one, but it comes up the least, and the blue comes up the most. Since every bonus symbol has a set of three reels, it seems like they should hit about the same amount. Can you explain why they might be different?

ANSWER: I don’t know the game you’re describing, nor have I seen any that use a mechanic quite like it. So I’m going to have to generalize a little bit.

All casino games are based on math, and the designer/programmer would have to build any difference in bonus frequency into the math of the machine. Let’s try a example of how this could be done. I’m going to assume one payline to make this easy. A game programmer would deal with more complex math to account for multiple positions in the slot window on each reel.

Let’s say each of the five reels has 100 symbols. We’ll assume that 20 of the 100 on the first reel are purple bonus symbols. The second reel has both purple and green, so let’s assume 10 purple and 20 green. The third reel has all three colors. Let’s say 10 of each. On reel No. 4, we’ll assume 15 greens and 15 blues. And we’ll put 30 blues on reel No. 5.

For each three-reel set, there are 100x100x100 possible combinations, which comes to 1 million. For three-purple combinations, we multiply 20 on the first reel by 10 on the second by 10 on the third, for a total of 2,000 combinations. That will lead to the purple bonus once per 500 spins. There are 20x20x10 all-green combinations, or 4,000, and it occurs once per 250 spins. And there are 10x15x30 blue combos, or 4,500, which is once per 222 spins.

The programmer does not have to put the same number of bonus symbols on each reel. And the math on the real game would be more involved than this. But you can see that making bonuses occur with different frequencies is something well manageable for game designers.


QUESTION: Please explain to me something about basic strategy in blackjack. When I was learning, my friend told me always to assume the dealer had a 10 face down. He told me that was your guideline as to when to hit and when to stand anytime you had 16 or less. If the dealer had a 5 up and you assumed he had a 10 down, that’s 15, and another 10 would bust him, so that’s a standing hand.

I’ve played that way for years, and nobody every said anything. Last month, I was playing and somebody spoke up after I stood on a 12 when the dealer had a 2 up. I noticed one guy shake his head a little. I didn’t let it bother me, but a little while later, the same thing. The dealer had 2, I had 12 and I stood. The same guy shook his head again.

So I asked him what was wrong. He said basic strategy says you should hit 12 against a 2. Is that right? Why?

ANSWER: Assuming the dealer has a 10 down is not a perfect guideline. Ten is the most frequently occurring card value, but 10-values -- 10s plus face cards -- make up only 30.8 percent of cards in the deck. Nearly 70 percent of the time, the dealer will NOT have a 10 face down.

Instead, basic strategy is a balancing act. How often will the dealer bust? How often will he improve the hand. How often will YOU bust or improve the hand?

If you always stand on 12 vs. 2, you lose about 65 percent of the time. If you hit, you improve that to 60 percent losses -- the hand is still a loser, but you lose less. On some hands, that’s the best you can do.