A. Without considering the progressive jackpot or the sequential royal payoff, 9-5 Double Double Bonus Poker, in which full houses pay 9-for-1 and flushes 5-for-1, returns 97.9 percent in the long run with expert play, while 8-5 Double Double Bonus returns 96.8 percent. Neither of these is a game for advantage players.

Adding a sequential royal gives a very small boost to the 8-5 game, making its overall payback 97.02 percent. The reason that a large jackpot has such a small effect on the payback percentage is the rarity of the hand. On average, one royal in every 120 royals is in sequence (i.e., 10-J-Q-K-A). There are five positions for cards on the screen. Multiply 5 times 4 times 3 times 2 times 1, and you’ll get the number of ways the cards can be ordered.

In 8-5 Double Double Bonus, we’ll draw a royal flush in sequence about once per 3.7 million hands. If we’re playing 500 hands per hour, that’s about 7,400 hours worth of play --- look at it as a small miracle if you hit one. Some sources put the frequency at one sequential royal per 77,980,800 hands, but that assumes five-card stud poker, with no draws. Double Double Bonus, like the vast majority of video poker games, is five-card draw poker.

The progressive jackpot on non-sequential royals makes more difference to the overall payback percentage. Figure on adding a bit more than about 1 percent to the overall payback percentage for every 2,000 coins above the base of 4,000 paid for a royal, given a five-coin wager. At 5,800 coins --- $1,450 on a quarter machine --- 8-5 Double Double Bonus with a sequential royal jackpot is a 98.0 percent game, just edging past the 97.9 on 9-5 Double Double Bonus.

Which should you play? It depends on what you want from the game. The non-progressive game’s 9-for-1 return on full houses will give you a somewhat better chance at extended play. The sequential/progressive game with a large enough jackpot to match the overall payback percentage will be a bit more volatile, with more of its return tied up in rarer hands, but give you a chance at a bigger bonanza.

There’s really nothing to do there but walk away. The casino misread your play and barred a non-advantage player. That’s not something that’s going to help their bottom line. But they have the right to do it.

In Nevada, courts have held casinos to be private clubs who can bar any player for any reason. They don’t have to prove to anyone’s satisfaction that you’re a card counter or advantage player. Other states have their own regulations, but in most, the principle is the same. The casino doesn’t have to deal to you, and can bar you from the premises. New Jersey is an exception. In a case brought before the state Supreme Court in 1979 by Ken Uston, the court ruled casinos in New Jersey may not bar card counters. The casinos can use other methods to stifle advantage players, such as frequent shuffles and bet size limits on individuals.

When a casino asks you to leave, it’s best just to cooperate, walk away, and not let the situation escalate.

A. I’ve seen one, back in the 1990s when I was first writing a weekly gambling column for the Chicago Sun-Times. One of the casinos on my regular rounds was Harrah’s Joliet, about a 45-minute drive southwest of Chicago.

For a brief time, Harrah’s offered a field bet that paid 3-1 when the roll was either 2 or 12. The field pays even money if the roll is 3, 4, 9, 10 or 11. It also pays on 2 or 12, with some casinos paying 2-1 on either of those numbers, for a 5.56 percent house edge, and some pay 2-1 on 2 but 3-1 on 12, for a 2.78 percent edge.

When this casino decided to pay 3-1 on both 2 and 12, it created a wager with zero house edge.

New craps players who take the time to learn about the game are warned off the field bet. Frank Scoblete includes it with his "Crazy Crapper" bets that no one should make. That’s right on the money in nearly every case. In the 5.56-percent version of the bet, the house edge is too high. Even with the 2.78-percent version, the house edge is nearly twice as high as the 1.41 percent on pass or come with no odds, AND there is a decision on every roll. At wizardofodds.com, Michael Shackelford says it takes an average of 3.38 rolls to decide a pass line wager, so the effect of making even the "good" version of the field is to lose about seven times as much money per hour as making pass bets of the same size.

Nevertheless, for a brief few months at one casino, the field was not only the best bet at the craps table, but the best bet in the house for unskilled players.