A shuffle through the gaming mailbag

Q. My wife and her girlfriend play at the same casino. The girlfriend plays strictly 2-cent slots while my wife plays about 80% 2-cent slots and 20% dollar slots. This year my wife earned about 40,000 base points; her girlfriend earned just over 11,000 base points. The girlfriend plays once a week, my wife plays approximately three times per week.

The girlfriend gets five $35 free slot play vouchers and five $35 meal vouchers per month. My wife gets five $15 free slot pay vouchers and no meal vouchers.

They both qualify for the same free gift promotions and they both take advantage of them.

This tells me they have some other system in addition to points to determine who gets what and how much, and it's not based on how much you spend. It's more like, "what can I get away with in comps."

A. In casinos where you redeem points for a set amount of cash, free play, meals or other perks, everything's out in the open. You know how many dollars in wagers it takes to earn a point, and you know how many points it takes to redeem for the comps or cash back you want.

When it comes to direct mail vouchers or online offers designed to bring you back to the casino, thinks get murkier, at least from the player's perspective. There, the casinos are free to use other analytics and metrics to determine the potential value of a customer. Perhaps there's something in your wife's friend's playing pattern that leads the casino marketing department to believe that offering her bigger vouchers will induce extra play.

I will tell you that dollar for dollar, 2-cent slot play is more valuable to a casino than dollar slot play. Let's say you're in a system where $4 in play brings one point, and 100 points can be redeemed for $1. That means for every $400 you bet, you get $1 back.

Now let's say you make $4,000 worth of wagers on a dollar slot that averages a 95% return, and I make $4,000 worth of wagers on a 2-cent slot that averages an 88% payback. We each earn 1,000 points that can be redeemed for $10. But your average loss on the dollar machine is $200, and my average loss is $480.

My loss is $280 more than yours, and I'm more valuable to the casino, but you have the same value in points to redeem. How does the casino make that up? By giving me more in direct mail offers, away from the strict point-redemption schedule.

That's probably not all that's going on in the case of your wife and her friend, but remember the primary purpose of comps is to attract more casino visits by the most valuable players. The casino won't want to overcomplicate the point redemption portion of the plan and make it difficult for players to follow, but it will want to build in flexibility to make sure it can do a little extra for players who help the bottom line.

Q. Everybody tells me single-deck blackjack is better than six decks, but I've never been told why. The proportions of cards are the same.

A. The key is the effect of card removal on the composition of the remaining deck. Removing one card from a single deck changes the percentages in a single deck more than it changes a six-deck pack. That effect means we get more blackjacks and double downs when we play with fewer decks.

Let's say the first card we're dealt is an ace. After all, if we're to get a blackjack the first card must be either an ace or a 10. In a single-deck game, 16 of the other 51 cards are 10 values. That means 31.37% of the remaining cards will complete the blackjack. If six decks are in play, removing an ace means 96 of the remaining 311 cards are 10-values. That's 30.87%, meaning we have a lesser chance of completing our blackjack in a six-deck game than in a single-deck game.

It works the other way, too. If our first card is a 10 value, 7.84% of the remaining cards are aces in a single-deck game, while 7.72% are aces in a six-deck game.

Double downs? Start with 6/5, for example, and 32% of the other cards are 10s in single-deck blackjack, and 30.97% in six-deck games.

The proportion of cards are the same regardless of number of decks only immediately after a shuffle. Once cards are dealt, the percentages change more rapidly with fewer decks in play.