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Best of John Grochowski

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A shuffle through the gaming mailbag

18 August 2011

Q. I have been playing video poker for many, many years and I still have not determined the correct play on Double Double Bonus Poker on the following hand: One pair of 2s, 3s or 4s with an ace kicker. I never hold the ace with a small bonus pair, but recently certain pundits are recommending that the ace be kept with twos and threes.

Could you be kind enough to give me your opinion?

A. Do not hold an ace kicker with a low pair. This is not a close call, and anyone who suggests this play is running seriously contrary to the math of the game.

Certainly, the temptation is there. Should you draw the other two to your pair to complete a four of a kind in 2s, 3s or 4s, that ace kicker gives you an 800-coin bonanza. Without the ace, the quads are worth only 400 coins for a five-coin bet.

Dealt 3-3-7-10-A of mixed suits in 9/6 Double Double Bonus, your average return for five coins wagered is 4.35 coins if you hold 3-3, and just 3.14 if you hold 3-3-A. Drawing the other two 3s to give you a low four-of-a-kind plus kicker is a 1 in 1,081 shot — there are 1,081 possible two card draws, and only one of them is the other two threes.

If you hold just the 3s, there are 16,125 possible three-card draws. Eleven of them will give you four 3s plus the ace kicker. So you'll draw that bonus hand an average of once per 1,739 trials. But 34 draws give you four 3s without the kicker, a nice payoff that come up once per 474 trials when you hold just the 3s. Overall, you'll finish with four of a kind, with or without kicker, once per 358 trials when you hold just the threes, a frequency that makes it well worth tossing the ace for an extra card in the draw.

You're far better off with some flexibility in the hand to draw more threes-of-a-kind, more full houses, more fours-of-a-kind without the kicker than to narrow the possibilities for a long-shot chance at quads plus a kicker.

Q. How does a slot machine manufacturer know the exact return on a slot machine when they sell it to the casino? If they tell a casino it will pay out 92%, is there a program that tells the machine to start paying out when it's below 92%, or stop paying out when it's above 92%?

A. Neither the slot manufacturer nor the casino operator knows exactly what a machine will pay out when it's up and running. Just as with any other casino game, manufacturer and operator know that in the long run, the odds of the game will lead the machine to pay something very close to a targeted percentage.

The manufacturer doesn't program in a specific percentage and tell the machine it must pay out exactly that amount. It just sets the possibilities, and the odds of the game grow out of those possibilities.

Let's make up a really simple example. Say I have a three-reel game, and on each reel there are only two possibilities — a cherry or a blank space. On every spin, you're going to get either a cherry or a blank. There are eight possible outcomes. One is three cherries, one is three blanks, while three include two cherries and three include two blanks.

Now let's say my machine is going to pay off only on three cherries, and for a one-coin bet, it will return seven coins. So one of every eight possible outcomes is a seven-coin winner. The odds of the game will lead the machine to pay out seven coins per eight coins wagered. I can market it to casinos as returning 87.5 percent.

But to satisfy laws and regulations, my game has to have a random number generator. I don't know when the cherries are going to come up. If you get the winners four times in your first eight spins, you've gotten 28 coins back for your four coins wagered, and the game is paying 700%.

What happens then? Does the game have to go into a makeup mode? No. It just carries on with its normal odds.

Let's say that in the next 800 spins, the odds hold up perfectly, and you get 700 coins back. Add in your initial hot streak, and you have 721 coins while wagering 808. The machine has paid 89.2% overall. The longer you play, the closer the odds of the game take it to its expected return.

The machine may never pay exactly its advertised percentage. There will be blips — hot streaks and cold streaks. In the long run, the blips fade into statistical insignificance and the game pays something very close to what the odds of the game say it should.

Recent Articles
Best of John Grochowski
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.

John Grochowski Websites:

www.casinoanswerman.com

Books by John Grochowski:

> More Books By John Grochowski

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.

John Grochowski Websites:

www.casinoanswerman.com

Books by John Grochowski:

> More Books By John Grochowski