Ask the Slot Expert: I lose more, but my wife gets better rewards

When my wife and I get our fliers from the casino, she always gets a larger dollar amount than I do. I know at times I have spent more dollars and yet I get screwed in the end — what gives? The explanation of ADT was very vague and complicated.

Casino rewards can seem arbitrary when you compare your rewards with someone else's. This confusion usually arises because you're not comparing the right numbers that go into determining rewards.

Let's compare two players at a roulette table. One person plays for two hours, bets $10 per spin, and loses $200. The other player walks up to the table, makes a $200 bet on black, loses it when red comes in, and walks away from the table and out of the casino.

If you were running the casino, which player do you think will be more valuable to you? To whom would you give more benefits?

Both players lost the same amount of money, but their playing styles were very different. The hit-and-run player took a chance on making a quick hit. Win or lose, he was going to make that one bet and leave.

The first player, on the other hand, came to play. There's a very good chance he will play back any money he wins.

In determining rewards, casinos don't look at how much you won or lost — after all, if you won, does that mean you'd get no comps? Instead they look at how much they expected to win from you, average daily theoretical (ADT). You might also hear this called "theo" (theoretical win).

We calculate ADT by multiplying the house edge in the game you're playing by the amount of action you gave (i.e., the total of your bets). In my example, the theo for the hit-and-run player is 5.26 percent of $200, or $10.52. To calculate the theo for the two-hour player, let's assume there were 30 spins per hour at the table. Two hours times 30 spins per hour gives us 60 spins. At $10 per spin, his total action is $600.The theo for the two-hour player is 5.26 percent of $600, or $63.12.

In my example, both players played the same game. The games people play can affect their ADT because different games have different house edges.

Compare two players playing $5 per spin on slot machines. One is playing a penny slot and the other is playing a dollar 9/6 Jacks video poker machine. The penny slot player's ADT will be higher (maybe much higher) than the video poker player's ADT because the house edge on penny slots is so much higher than that on 9/6 Jacks (6-10 percent versus 0.5 percent). The lower house edge on video poker paytables — even poor video poker paytables — explains why video poker players have to give more action than slot players for the same rewards.

I think if you compared your play instead of your losses, you'd find that your wife plays longer or plays higher house-edge games — or both — and that explains why she gets larger rewards.

You wrote:

The result of a spin in Washington State is determined by a central computer. When you hit the Spin button, the central computer conceptually chooses a scratch-off ticket from the pool of electronic tickets remaining and uses its electronic quarter to scratch-off the coating to reveal your result. The central system then sends the results to your machine. When the central computer runs out of tickets in the pool, it unwraps a new packet of tickets and starts over.

Consider the game of craps. Suppose that instead of actually throwing dice, a deck of 36 cards depicting the 36 possible combinations of two six-sided dice was used to determine the result of a game. "Rolls" are generated by dealing the top card off the deck until the deck is exhausted, at which time it is shuffled. (Because of an arcane law forbidding the use of dice to determine the result of a game of chance directly, some California casinos actually use this method, though I understand their decks contain multiple 36-card sets and are not dealt to the last card.)

Question: Would having the RNG of an electronic craps game shuffle a deck of 36 cards when necessary and "deal" the cards sequentially produce results identical to having the RNG select two integers from 1 to 6 for each "roll"?

Answer: No. The card-dealing method guarantees that all 36 combinations of the two dice will occur in exactly their theoretical proportions; the dice-throwing method only ensures that those proportions will be close to their theoretical values after a large number of throws. In practice, of course, the results generated by the two methods will be close enough to be considered equivalent...after a large number of (actual or card) rolls.

The same difference is present between Washington State's use of virtual scratch tickets and the use of a continuously running RNG in other venues to generate results. The long-term payback will essentially be the same, but -- and this is my point -- the scratch ticket method is safer for the runner of the game because 1) the house advantage can be calculated exactly and 2) the variance can be set by how many tickets are in a packet (i.e., how many plays are in a "long run").

Many players don't realize that volatility affects both sides of a bet. Volatile games yield large bankroll swings for both the player and the casino. The differences between the two are, of course, that the casino has a much larger bankroll than the player and the casino plays long enough to get to the long run.

I once attended a seminar given by a slot director who was involved with the development of Bally's Blazing 7s machine. He said that the machines were very popular -- and profitable -- in their test runs in Reno. When they were installed in Las Vegas (at the Tropicana, I think), the casino complained that they were losing a lot of money on the machines. Players were hitting combinations of 7s right and left. After a while, the initial hot streak favoring the players became a smaller and smaller part of the overall performance of the machines, the casino's win got closer and closer to the amount calculated from the machines' long-term payback, and the rest, as they say, is history.

The house advantage on a Class III, RNG-based slot machine can be calculated exactly, but because the result of each spin is determined at random, it might take millions or tens of millions of spins for a machine's actual payback percentage to zero in on its calculated long-term payback percentage. The fewer spins a machine has had, the farther away its actual payback percentage can be from its long-term payback percentage. It's not unusual for casinos to show a loss on machines for the first few days or weeks they are in operation. But don't worry. The casino has the bankroll to see it through the cold streaks.

RNG-based machines use sampling with replacement. Every outcome is possible on every spin with the exact same probability. Machines that mimic scratch-off tickets, on the other hand, use sampling without replacement. The probability of hitting any particular outcome changes as the tickets for that outcome are used. Certain outcomes can become impossible once all of the tickets with them have been used. For the operator, as you point out, the long run is achieved not in millions of spins, but every time a pool of electronic tickets has been exhausted. If Blazing 7s had used a scratch-off pool, the machines in Las Vegas would have been profitable much, much sooner.