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# A shuffle through the gaming mailbag

21 July 2011

Q. I usually play Double Bonus Poker, and have always held one face card, choosing one at random when several are dealt, if there is no chance of a straight or a flush. Many times that one will pair up to save my bet. Is this wrong? Does it limit my winning other hands?

A. Strategies vary by specific game and pay table, but it's usually better to hold multiple high cards.

Since you say Double Bonus is your game, let's use full-pay 10/7/5 Double Bonus as an example. Let's say you're dealt king of clubs, jack of hearts, 8 of spades, 4 of diamonds, 2 of clubs. By your method, you'd pick one high card at random and discard the other four cards. The better of the two cards to hold would be the jack, because it leaves more straight possibilities. Straights could be jack, queen, king or ace high. If you hold the king, straights could be only king or ace high.

There are 178,365 possible four card draws, of which 120,401 bring losing hands. Among the 57,935 winners, 43,389 are high-pair hands that pay 1-for-1, there are 8,874 two pairs (1-for-1), 4,102 three of a kinds (3-for1), 764 straights (5-for-1), 491 flushes (7-for-1), 288 full houses (10-for-1), 50 four of a kinds, 5s through kings (50-or-1), 1 four of a kind, 2-through-4 (80-for-1), 1 four aces (160-for-1), 3 straight flushes (50-for-1), and one royal flush (250-for-1, but 4,000 with a five-coin wager).

The average return for all that is 2.198 coins per five wagered.

Now what if you hold both the king and the jack? There are 16,125 possible three-card draws, and 10,053 are losers. You can't get any royals, straight flushes or straights, and the only quads you can get are four kings or four jacks. But you enhance your chances at other hands, especially pairs of jacks or better. There are 5,022 draws that will pair up either the king or the jack, along with 711 two pairs, 281 three of a kinds, 128 straights, 18 full houses and two fours of a kind.

Note the straight probabilities. If you hold just a jack, 0.43% of all draws will bring a pair of jacks or better. Hold king-jack, and that chance almost doubles, to 0.79% of all hands.

Bottom line: Holding king-jack in this situation brings an average of 2.311 coins per five coins wagered, better than the 2.198 for holding just the jack or the 2.109 for holding just the king.

Likewise, holding king-queen-jack of mixed suits is a stronger play than holding just one or two high cards. Make it ace-king-jack, and it's a different story, with king-jack being a better play than ace-king-jack in most games, but with holding just the ace being a better play in big ace-bonus games such as Double Double Bonus Poker. But that's a wrinkle for another time.

Q. I have never had a royal flush and only two four-aces hands. The other day I told an attendant (replacing paper in machine next to me) that I had never seen anyone hit a royal or four aces. The man on my other side said he had done so several times on the same machines. I noticed he was betting dollars and I always bet maximum quarters. Does amount you have chosen to play affect the frequency of winning?

A. The coin denomination does not affect results in video poker. The random number generator that determines what cards you see is the same program in a nickel game as it is in a quarter game or a dollar game or any other denomination.

Some of what you're experiencing is just the normal rarity of the hands. Let's stick with 10/7/5 Double Bonus Poker. We see a royal an average of once per 48,048 hands. That doesn't guarantee a royal within 48,048 hands. Sometimes we'll draw two or more royals within that stretch, but just as often we'll see zero royals within two or three times that many hands. Cold streaks are just a normal part of the game.

I remember once I was talking with a fellow gambling writer and analyst, and I was in the middle of a couple of years without a royal. He asked if I'd been winning money. I told him I'd been winning a little in blackjack, but video poker was putting me in the red overall. He asked the last time I'd had a royal, and I told him it had been more than two years ago. About a month later, I was playing at the old Stardust in Las Vegas, and I drew a royal. Less than an hour later, I drew a second one, on the same machine. Definitely an exciting night.

You never know when they're going to come. It can be a long, long time without a royal. But it's not the coin denomination that's causing the cold streak. It's just normal odds and probability.

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John Grochowski

John Grochowski is the best-selling author of The Craps Answer Book, The Slot Machine Answer Book and The Video Poker Answer Book. His weekly column is syndicated to newspapers and Web sites, and he contributes to many of the major magazines and newspapers in the gaming field, including Midwest Gaming and Travel, Slot Manager, Casino Journal, Strictly Slots and Casino Player.

Listen to John Grochowski's "Casino Answer Man" tips Tuesday through Friday at 5:18 p.m. on WLS-AM (890) in Chicago. Look for John Grochowski on Facebook and Twitter @GrochowskiJ.

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John Grochowski
John Grochowski is the best-selling author of The Craps Answer Book, The Slot Machine Answer Book and The Video Poker Answer Book. His weekly column is syndicated to newspapers and Web sites, and he contributes to many of the major magazines and newspapers in the gaming field, including Midwest Gaming and Travel, Slot Manager, Casino Journal, Strictly Slots and Casino Player.

Listen to John Grochowski's "Casino Answer Man" tips Tuesday through Friday at 5:18 p.m. on WLS-AM (890) in Chicago. Look for John Grochowski on Facebook and Twitter @GrochowskiJ.