Stay informed with the
Recent Articles
Best of Donald Catlin

# Grit Your Teeth and Go For It

1 August 2004

I was recently in Las Vegas and stayed at the Las Vegas Hilton. The Hilton has some 9/6 Jacks or better machines and, as usual, I was giving one of them a try. Every now and then one is dealt a pat hand, that is, there is already a winner in the hand and I was dealt just such a hand. But what a hand! I was dealt the TC, JC, QC, 3C, AC. I held a pat Flush and a four-card Royal. How would you play this hand? Let's take a closer look.

After the initial deal, there are 47 cards remaining in the deck. If we toss the Three of Clubs then there are seven clubs that will give us back the Flush, one card that will produce a Royal, three cards that will give us a Straight, and nine cards that will give us a Pair of Jacks or better. That leaves 27 losers. The expected return breaks down as follows:

 Result Probability Payoff Product Royal 1/47 4000 4000/47 Flush 7/47 30 210/47 Straight 3/47 20 60/47 Jacks or Better 9/47 5 45/47 Losers 27/47 0 0 Totals 1 -- 4315/47

The number in the lower right cell is our expected return when tossing the 3C; it is 91.808 units. The expected return by keeping the Flush is 30 units so it is clear that the correct decision is to go for the Royal; the decision isn't even a close call. On the other hand, the return from all of the possible non-Royal draws is a mere 6.7 units. Oh yeah, I forgot to mention that the machine I was playing was a triple action dollar machine (located near the hallway to the restaurants and convention facilities). This meant that I had a sure \$90 if I held the 3C, a \$75 profit over the \$15 the hand cost me. Tempting, but you'll never get that elusive Royal if you don't go for it. So I made the correct play, gritted my teeth, tossed the 3C, and went for it.

Well, somewhere folks are singing, somewhere people scream, but there is no joy in Hiltonville for Catlin drew a Queen. See you next month.

Recent Articles
Best of Donald Catlin
Donald Catlin

Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

#### Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers
Donald Catlin
Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

#### Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers