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# Gaming Guru

### Pay Tables Do Not Reflect True Odds

6 March 2004

The payout table on a Jacks or Better machine makes one wonder what kind of abacus was used during the invention of the game. Now, mind you, I'm not complaining about the 99.6 percent payback it offers the expert players. I'm simply puzzled that the pay table does not reflect the true odds for each of the winning hands.

Why should a full house pay 8- or 9-for-1 while the straight pays 4-1 and the flush 5-for-1, when we'll make more full houses (1 in 87 hands) then either straights or flushes? We'll make about the same number of straights as flushes, so why the premium on those flushes, when they both come up about once every 90 hands?

At the upper end of the pay table, things are even more confused. The 25-for-1 payout on quadruplets is a mite light when compared to the full house when we recall that those quads occur only once for every five full houses!

However, the worst of all is the relatively rare straight flush, which put in an appearance once every 9,610 times (on average, not on schedule) yet pays only 50-for-1 - about 1/10 its true odds compared to a full tub. Unfortunately, most players are very uncertain about how to play that potential straight flush, so it is even more rare an occurrence that was stated above.

Consider the following hand:

 AH 2H 3H 4S KC

Do we play this hand by:
(A) Drawing one card to the four-card straight?
(B) Drawing two cards to the three-card straight flush?
(C) Drawing three to the A-K?

Expert players always hold those cards that offer the greatest chance of making the most coins back when all possible draws are considered. We would expect the draws to distribute as follows:

 Case A Case B Case C Unique Draws 47 1,081 16,215 Royal Flush @800 0 0 0 Straight Flush @50 0 1 0 Four of a Kind @25 0 0 2 Full House @ 8 0 0 18 Flush @5 0 44 0 Straight @4 4 11 64 Three of a Kind @3 0 9 281 Two Pairs @2 0 27 711 Jacks or Better @1 3 129 9,200 Non-Winners @0 40 860 10,117 Total Payouts 19 524 7,737 EV (payouts / draws) .40 .48 .47

Expert play always goes to the highest EV. That's why, in the above example, drawing two cards to the three-card straight flush is the correct play. The three-card straight flush is a superior hand despite its being open on one end only.

Even good players would be misled by its seemingly weak appearance. That's why expert play requires good instructions.

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Lenny Frome
Lenny Frome spent 40 years in the aerospace engineering business before moving to Las Vegas. During the ensuing 10 years, he became one of the most prolific gaming authors, having written 8 books, countless tip sheets and nearly 1000 articles for a variety of gaming magazines.

Lenny's ground breaking work in the area of Video Poker earned him the title of the 'King of Video Poker'. He also wrote on a variety of other gaming topics including Spanish 21, Let It Ride, Keno and others.

Besides being an author and columnist, Lenny was the premier Gaming Consultant at the time of his passing in 1998. He helped develop paytables for Let It Ride and Three Card Poker, and consulted on literally hundreds of other gaming projects.

His son, Elliot, now follows in his footsteps, as a gaming author, analyst and consultant. Their website, and a complete catalog of all their products can be found at www.vpheaven.com. Feel free to drop Elliot an e-mail at compuflyers@prodigy.net.

#### Lenny Frome Websites:

www.vpheaven.com
Lenny Frome
Lenny Frome spent 40 years in the aerospace engineering business before moving to Las Vegas. During the ensuing 10 years, he became one of the most prolific gaming authors, having written 8 books, countless tip sheets and nearly 1000 articles for a variety of gaming magazines.

Lenny's ground breaking work in the area of Video Poker earned him the title of the 'King of Video Poker'. He also wrote on a variety of other gaming topics including Spanish 21, Let It Ride, Keno and others.

Besides being an author and columnist, Lenny was the premier Gaming Consultant at the time of his passing in 1998. He helped develop paytables for Let It Ride and Three Card Poker, and consulted on literally hundreds of other gaming projects.

His son, Elliot, now follows in his footsteps, as a gaming author, analyst and consultant. Their website, and a complete catalog of all their products can be found at www.vpheaven.com. Feel free to drop Elliot an e-mail at compuflyers@prodigy.net.

www.vpheaven.com