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# A shuffle through the gaming mailbag

10 May 2012

Q. My dad retired to Vegas and every time I visit him (two or three times a year) we play hours and hours of video poker. We almost always play Double Double Bonus. We play single play, Triple Play or Five Play.

I would without a doubt call my dad an expert player. The one area we disagree on is when we are dealt three to the royal along with a pair of aces. I always argued to hold the three suited cards and he always wants to hold the pair of aces and, of course, hope for the four of a kind with the kicker.

There was one time we held the aces in a five-hand machine and we would have pulled the royal on one of the hands. Ever since then I won't let him hold the aces when we have three to the royal. Can you solve our dilemma by giving us the real odds?

A. The best play is to hold the aces. I'll break it down in a couple of different scenarios. First, if the three-card royal does not include the aces -- for example, aces of spades and clubs, with K-Q-J of hearts. Your average return per five coins wagered is 9.64 coins per five wagered for holding the aces, but only 7.37 for holding the suited K-Q-J.

If one of your aces is included in the three-card royal, the margin is even bigger for holding the aces. For example, with A-Q-J of hearts with an ace of clubs and a six of diamonds, average return is still 9.64 on the aces, but only 6.86 on the three-card royal. The number on drawing for the royal falls when the three suited cards include an ace because the ace is a limiter on the number of straights that can be drawn. Straights in that situation can only be ace-high, where as with K-Q-J, K-J-10 or K-Q-10, they can be either ace- or king-high, and with Q-J-10 they can be ace-, king- or queen-high.

Three cards to a royal is a good starting hand, but you'll draw the royal only once per 1,081 trials. Four aces with a kicker is worth half a royal, and you'll draw that once per 1,344 trials when you start with a pair of aces, AND you'll get the 800-coin four aces, no kicker once per 489 trials. You'll get four aces one way or the other once per 358 trials, so overall you'll get aces three times as often as a royal. You'll also get more frequent threes-of-a-kind when you start with the ace pair, and you leave open chances at a full house, which you can't draw when starting with three to a royal.

Weigh all that against the 1 in 1,081 shot at drawing a royal, and the balance is in favor of holding the aces.

Q. I've been practicing the Hi-Lo count (for counting cards in blackjack) on the computer, and the software I use shows an error rate of a little less than 2%. I'm not comfortable with that, and am working to improve. Still, I use the count in casinos, and have been doing pretty well, actually making a little money. I assume I probably have the same error rate in the casinos as on the computer, so why am I not losing money?

A. There are at least a couple of possibilities here. First, you didn't say how much you've been playing. You might just be having a short-term run of good luck. Even when the house has the edge, players have winning streaks.

Second, you haven't specified what the mistakes are. Some mistakes are more costly than others. Some hands are closer calls than others. The closer the call, the less it hurts your expectation when you make a mistake.

If your 2% error rate reflected that you were consistently standing on 16 vs. 7, that would hurt you a lot more than if it meant you were standing on 16 vs. 10, a close-call hand. If you were a tad too slow to adjust strategies with the true count -- waiting until plus-4 instead of plus-3 to take insurance, or waiting till minus-2 instead of minus-1 to hit 13 vs. 2 -- those could show up in your error rate, but hurt your expectation by only a tiny amount.

It's possible the error rate means you're not getting everything possible out of the Hi-Lo count, but are still playing a winning game. It depends on what the errors are.

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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.