Whenever I run across a new book on casino gaming, I usually turn to either the section on Blackjack or Video Poker (if it covers that topic) in order to see if the author knows what s/he's writing about. I received such a book recently and I'll be doing a review of it shortly for our "Product Review" page, but I want to address what this book had to say about why it usually takes about 40,000 hands of play to hit a Royal Flush at a Jacks or Better game:

"When I speak of a payoff cycle, what this means is the frequency with which the machines will hit the various pays, specifically the jackpots.

For instance, on the average, a 9/6 regular Video Poker machine with no wild cards will hit the Royal Flush once every 40,000 hands played. But this does not mean that, like clockwork, each machine will pay the jackpot Royal Flush each 40,000 hands. Remember, the machines are set, by law, to select winning combinations at random. So how can a machine which selects winning combinations at random still pay the jackpot on average every 40,000 hands played? In layman's terms, the computer program has a kind of master control chip which has two main functions One selects the cards which will be dealt at random and the second acts as a master control making sure that winning hands conform to the overall program schedule of payoff frequency. In effect, the master control sort of "rides shotgun" over the random selections (most commonly described as the Random Number Generator). "

Let's stop right here. If there is some sort of "master control" to all this, then it isn't random. (Don't worry, it is. ) But who or what causes a Royal to show up once every 40,000 hands on average? You do. Yes, you the player. That number of 40,000 is very real, but it can be altered, because 40,000 comes about from playing the game in an optimal way. Want a Royal every 25,000 hands? I'll tell you how to do it: change your playing strategy.

Okay, now you think I'm crazy, yet I can assure you that hasn't happened yet. "But", I hear you say, "if you can hit a Royal every 25,000 hands on average, why don't you do it?" My answer is simple; not short, but simple: I can't afford to.

If you play just for the Royal, you'll cost yourself a lot of $$$ in short term play and, when you total it all up, you'll have hit a Royal faster (probably), but you (probably) won't show a profit. That's because you'll have to break pairs, straights and other hands to go for the Royal and, while the Royal has a whopping payoff, missing a bunch of 4Ks, etc. costs $$$. For example, let's say you've been dealt a hand like this

10s Js Jh Jd 3c

A strategy of 'going for the Royal' says to hold just the 10s, Js but that means you're tossing away trips which could turn into quads or a Full House. Yes, you might get a Royal, but the odds there are 1 in 16,215. From an 'expected value' point of view, trip Jacks are worth 21.5125 coins for each 5 bet, whereas the suited 10, J play is worth 1.7854 coins for each 5 bet, if the Royal is at 4000 coins. The difference between the two is 19.7271 coins. If you were dealt that hand 16,215 times and went for the Royal each time, you'd be giving up 16,215 X 19.7271 = 319,800 coins in an effort to win 4000. Sure, the Royal could come on your first try, but it could also come on your 18,000th try. On average, it will take 16,215 tries to get it and that will cost you mucho $$$.

"Oh", you say, "I'd never break trips to go for the Royal, but I'd bust a pair". Okay, with the Royal at 4000 coins, a hand of 10s, Js, Jh, 3c, 5h has numbers that look like this

Hold J, J	7.6827
Hold 10s, Js	2.0870

The difference is 5.5957, so it'll only cost you 80,000 coins to go for the Royal.

I hope I've made my point: How you play affects the frequency of the hands. There is no 'master control' in the machine; you are the master control. Yes, there can be a time when it's correct to break a pair of Jacks to draw to a 10, J suited; it's when the Royal is about 90,000 coins. Seen a quarter VP machine with a $22,500 Royal lately?

Got the concept now? How you play each hand determines how often any particular 'pay' will occur. As many of you know, I play a lot of dollar 9/6 Jacks machines with a progressive Royal. When the Royal is high enough, I'll modify the proper playing strategy to go for it. For example, if the Royal is over $4300 and I'm dealt this hand: Jc Js Qs Ks 5d, I do break the pair to draw to the three suits. The odds are 1 in 108 of making a Royal, but the payoff is worth it, since J, J has an expectation of 7.6827 and the suited J, Q, K has an expectation of 7.7660.

So, from this you may conclude that as the Royal goes up in value, it becomes worthwhile to draw to it more often and you'd be correct. In fact, optimum play for a game with a $5200 Royal would bring a Royal once every 35,136 hands on average which means we'd be giving up something in the sort term, but gain it back (and more) when the Big Banana hits. But my decisions in those situations are based upon mathematical calculations, not hope or hunches. Play correctly and the Royals will come.

See you here next time

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