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# Gaming Guru

### Oops!

16 July 2003

One of the nice things about mathematics is that when you're right about something there is no question about it; you can supply a proof of your assertion.  The flip side of that coin, however, is the fact that when you're wrong you're wrong and there is nothing you can do about it but own up to your error.  Well, there was a mistake in my July 6, 2003 article entitled Four Card Poker Paradox.  Somehow, I don't know how it happened, two of the numbers in Figure 3 got switched, leading me to the conclusion that when Straights outrank Flushes that the Flush frequency is smaller than the Straight frequency.  Not true!  The numbers were calculated correctly but were switched in a printout.  The correct conclusion is that when choosing four card Poker hands from five card hands that Straights should outrank Flushes since their frequency of occurrence is smaller.  The corrected table follows.

 Type Hand Frequency Four of a Kind 624 Straight Flush 2072 Three of a Kind 58,656 Straight 105,960 Flush 110,464 Two Pair 123,552 One Pair 1,047,552 High Card 1,150,080 Total - 2,598,960

Four From Five Frequencies when Straight > Flush

Sorry for the misinformation but at least the record has been set straight.  See you in a couple of weeks (hopefully with accurate information).

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