A shuffle through the gaming mailbag

Q. The other day I was playing Double Joker's Wild on a video poker machine and was dealt a natural royal flush. Would you by any chance know the odds of being dealt a natural royal flush from a 54-card deck?

A. With a 54-card deck, there are 3,162,510 possible five-card denominations, and four possible natural royal flushes, no wild card. That makes your chances of a dealt royal 1 in 790,527.5 -- considerably longer odds than the 1 in 649,740 on a non-joker game.

Just as in any other draw poker game, your overall royal flush chances depend on your drawing strategy. With expert strategy that nets a 98.1% return on the full-pay version of Double Joker, you'll draw a royal about once per 44,931 hands. You'll also draw a wild royal, including at least one Joker, about once per 2,876 hands. For a five-coin bet, you'll get a 4,000-coin jackpot on the natural royal, and 500 coins on the wild royal.

The rest of the pay table, assuming a five-coin wager, brings you 250 on five-of-a-kind, 125 on a straight flush, 40 on four-of-a-kind, 25 on a full house, 20 on a flush, 15 on a straight, 10 on three-of-a-kind and 5 on two pairs. I've never seen a Double Joker game that starts the pay table any lower than two pairs. Some single-joker machines pay off on a pair of kings or better, but with two jokers, you're looking for higher-ranking hands.

Q. I have been playing slots for the past four years and I have noticed that virtually all of my big wins ($500+) happen within the first few spins. I have not been able to "force" a machine to win by playing long periods at the same machine. Given this, I am now of the opinion that if you play a machine more than four or five spins and don't win you are wasting your time and money.

The obvious question is, how would a machine know you are a new player, it's your first spin, etc.?

The RNG should have no concept of one session to the next, the only thing that might change is the player's card changing or credits added (money in). Any thoughts?

A. There is nothing in the games or their programming that would make big wins come up more frequently early than late in a session.

I think there is some selection bias, in that everyone has an early portion of their session, but the "late" part comes up only if they're getting enough money back to keep playing.

If you were to keep track over a long time, you would find that the frequency of big jackpots in spins No. 1-10 is no higher than the frequency in spins No. 101-110, or 551-560, or any other 10-spin segment you'd care to designate.

Q. My dad is an old horse player, and he and I are having an argument. He says the racetracks give you better odds than the casinos. I say some casino games might have worse odds than racing, but mostly the odds are better in the casinos. Can you settle the argument?

A. In horse racing, a percentage of every wagering pool is held out for prize pools, the track operator, the state and other taxing bodies. The remainder is divided up among winning bettors. The amount that's held out of the wagering pool before distribution to bettors is the equivalent to the house edge at casino games.

That amount varies depending on the type of wager and the jurisdiction. On single-horse wagers on thoroughbred races -- win, place and show -- Illinois and New Jersey hold out 17% and California 15.43%, just to take a little coast-to-coast sample. On two-horse wagers such as exactas and quinellas, the takeout rises to 19% in New Jersey, 20.5% in Illinois and 20.18% in California.

Only the worst bets in casinos have house edges that high, such as the 16.67% on any 7 in craps or the 24.1% on the special symbols on the Big Six Wheel. Mostly, we see narrower edges such as 1.09% on the banker bet and 1.24% on player in baccarat, or 1.41% on the pass line in craps, or half a percent or so, depending on house rules, against a basic strategy player in blackjack. Even on the slots, house edges hover around 5% on dollar machines and 10% to 14% on penny games.

However, casino players make many more bets per hour than horse players. It's easy to make 500 bets an hour on a slot machine, and at a full seven-player blackjack table you're going to play 50 or 60 hands an hour. I recently spent a day at the races, betting every race on a nine-race card. Those bets were spread out over about 3 and half hours.

Casinos have much lower house edges than do racetracks, but make a living by taking far, far more bets per hour.