The mystique of slot machines - part 2

Last week, I started a look at the mystique of slot machines — a mystique that is mainly due to many players not understanding how the games and issues surrounding the games work.

Let's look at a few more frequently asked questions.

Q. I've read that slot machines are random, and I've read that they have programmed percentages. How can they be both random and programmed?

A. Let's start off by pretending we're flipping a coin. Results are random, right? In the long run, about half are going to be heads, and about half are going to be tails, but you can have winning streaks and losing streaks on either side.

Now let's say you're betting 50 cents on each flip. Each time you lose, I take your 50 cents. Each time you win, you keep your 50 cents, and I pay you 45 cents in winnings.

On the average, 20 flips will bring you 10 heads and 10 tails. You'll risk $10, and you'll have $9.50 left. The average expected payback is 95%.

So now you have a game in which results are random, but which also has a "programmed" payback percentage.

That's analogous to the way it works on the slots. The programmer sets the possibilities, and they will appear in a random fashion. In the long run, each possible combination will come close to the expected average number of appearances. And just as in our coin flip example, the payouts will be something less than would yield an even game.

Q. You've written that table games usually have lower house edges than slots. But I saw a gaming commission report online that listed table game hold percentages three or four times higher than on the slots.

A. Hold percentages are calculated differently on slots and table games, creating a statistical illusion. The unwary often are fooled. A televised special report — I don't remember if it was on CNBC or MSNBC — got it wrong a few years ago. Marilyn vos Savant once got it wrong in her "Ask Marilyn" column. A casino marketer got it wrong in a letter he sent to me many years ago.

The confusion comes because slot machines track every wager, and table games don't. Hold percentages on slots are the percentage of all wagers kept by the house, while table hold percentages are the percentage of all BUY-INS kept by the house.

When I slide $100 into the bill validator on a slot machine. I win on some spins, lose on more, and continue to play. Let's say I've had about average luck on a dollar machine, and before I lose my $100, I've had enough winning spins to make $2,000 in wagers. In the end, I lose 100/2,000ths, or 5%, of my total wagers. That 5% is the slot hold percentage for my play.

Now let's say I sit down at a blackjack table, and push $100 across the layout to the dealer, who then gives me $100 in casino chips. I bet $5 a hand, and I win some and lose a little more. A couple of my $5 chips bring smaller denomination tokens when I win 3-2 payoffs on blackjacks. I stick around to replay my winnings until I've made $2,000 worth of bets, and find I've lost $14. So I go to the cage to cash in $86 worth of chips.

What is the casino's hold on my table action? It's $14 of my $100 buy-in, or 14%.

Look at that carefully. I've wagered the same amount of money at table and slot, and walked away from the table with most of my money while losing it all on the slot. Yet the hold percentage is higher at the table.

That's one of the basics of casino math. Slot hold percentages and table hold percentages measure different things and cannot be used to compare one to the other.

Q. Why do I get cash back and buffet comps when I play slots, but no cash and fewer comps when I play blackjack?

A. The house edge is higher and the games are faster on the slots. If you're playing $5-a-hand blackjack at a full table at about 50 hands an hour, you¹re risking $250 an hour. The house assumes it has about a 2% edge — the real edge differs with player skill — making your expected loss about $5 an hour. The house will issue comps based on that.

If you're playing a 25-line penny slot, even if you're betting only 1 cent per line, at a moderate pace of 500 plays per hour, you risk $125 per hour. House edges on slots vary from casino to casino, but we can use 13% as an average figure on pennies. Your expected loss per hour becomes $16.25.

Note that even betting one penny per line, the slot player is much more valuable to the casino than the $5 blackjack player — more valuable than even a $15 a hand player. That's why slot players get more in comps.