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By John Grochowski

John Grochowski is a blackjack expert and a well-known and respected casino gambling columnist. His syndicated casino gambling column appears in the Chicago Sun Times, Denver Post, Casino City Times, and other newspapers and web sites. Grochowski has written six books on gambling including the "Answer Man" series of books ( He offers one-minute gambling tips on radio station WSM-AM (890) and podcasts are available at Send your question to Grochowski at


Q. I've stayed away from craps in favor of blackjack and video poker for a long time, but I'm starting to get back into it. I have an old copy of the Mensa book on casino games, and it describes a combination where the player has an edge. Can you shed any light?

A. I checked my old copy of "American Mensa Guide to Casino Gambling," and found a combination that was not quite as you described it, but just as unlikely. The claim isnít that the bet will give the player an edge. Itís that the overall house edge is lower than the house edge on any of the component wagers. Thatís not possible.

The combination is meant to be used at casinos that pay 3-1 on the field when a 12 is rolled. Make a $5 place bet on 5, $6 place bets on 6 and 8, and a $5 wager on the field, and the Mensa Guide says the house edge is 1.136 percent.

All the individual pieces of this combination have higher house edges than 1.136 percent. House edges are 4 percent on the place bet on 5, 1.52 percent on the place bets on 6 and 8, and 2.78 percent on the field when rolling a 12 brings a 3-1 payoff.

Problem is, the Mensa Guide assumed fresh money on every wager on every roll of the dice but thatís not how we calculate house edges. We assume a bet that is played to a decision.

Take the place bet on 6. Per 36 rolls, 25 of them make no difference. The only ones that matter in settling the bet are the six ways to roll 7 and the five ways to roll 6. Letís say weíre betting $6 a pop. For those 11 decisions, we risk $66. On the five we win, we win $35 plus keep our $30 in wagers, leaving us with $65. The house keeps $1. Divide that $1 by the $66 risked, then multiply by 100 to convert to percent, and you have the 1.52 percent house edge on placing the 6.

Now letís do it the Mensa way. If we assume weíre betting fresh money on every roll, then we donít put $66 at risk, the wager total soars to $216 per 36 rolls. We still lose the same $1, but now we divided it by $216 in wagers, and get a house edge of 0.46 percent.

If the Mensa guide was consistent in evaluating the house edge, and the same conditions used in calculating house edges in the combination was also used on the component place bets, then it should list edges of 0.46 percent on 6 or 8 and 1.11 percent on 5. And the house edge on the combination is higher than that on the place components, and lower than that of the field bet. The combination does not reduce the overall house edge.

Evaluated in the usual way, with place bets left on the table until a decision is reached rather than replaced by fresh money on every roll, the house edge is 2.5 percent --- lower than the edge on the field or the place bet on 5, but higher than the place bets on 6 or 8. Thatís the way it has to be. The house edge on any combination is a weighted average of the house edges on the component bets.

Q. On video poker games like Double Double Bonus Poker with the big pays on four Aces, does the machine deal fewer Aces to make it up? I know about random numbers. Is this like a slot machine where fewer random numbers are assigned to the top jackpots? Are there fewer random numbers for the Aces?

A. Actually, we draw four-Ace hands MORE often in games with the big Ace payoffs, because we hold more Aces. Dealt Ace-Ace-4-4-3 in Double Double Bonus Poker, we hold just the Aces. In Jacks or Better, we hold both pairs. Another example: Dealt Ace of clubs, King of diamonds, Jack of hearts, 7 of spades, 3 of clubs in Double Double Bonus, we hold just the Ace, while in Jacks or Better, without a super-sized pay on Ace quads with a low-card kicker, we hold King-Jack instead.

Our strategy makes a difference in the frequency of final hands. But the random number generator just keeps dealing the cards as if they were from a real 52-card deck, with no change in the odds of drawing any given card.

The random number generator is not programmed with fewer Ace numbers. Nevada regulations require video games using cards to give every card an equal chance of being dealt. Thatís also true in most other gaming states. There are a few --- and my colleague Frank Scoblete has pointed out that New Jersey is among them --- that would allow a more slot-like approach to random numbers. But as a practical matter, manufacturers have insisted that players are getting the same video poker game regardless of whether theyíre playing in Nevada, Mississippi, New Jersey or any other state.

Q. OK, I know you can't count cards against a continuous shuffler. But what about playing a betting progression? Does that help at all? Is a non-counter any worse off against a continuous shuffler than in other games?

A. Raising or lowering your wagers without knowledge of the composition of the deck does not change the house edge. In that respect, betting progressions do not help regardless of whether the shuffle is continuous.

Progressions will yield more big winning sessions than flat bets will. The flip side is that they bring more frequent small losing sessions when small wins are followed by losses at larger bet sizes. On balance, the house edge holds up.

There is one aspect in which a continuous shuffler hurts a non-counting progression player: More hands are dealt per hour when there are no shuffle breaks. When youíre spotting the house an edge, a faster game helps them, not you.

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