| Well, I came close to eating crow but fortunately I did mention in my article that one could produce different numbers by having the player choose the best four-card hand from 5, 6, or 7 cards (although I tempered the remark by indicating that a player would not be happy turning a Full House into Two Pair). So, crow is not on my bill of fare since both of the aforementioned games deal five-card hands and have the player (or dealer) select the best four-card Poker hand from the five. Let's see what this does to the frequencies. How many Straight Flushes (including Royals) are there? Well there are four suits and the straights in each suit occur as A-J down to 4-A so there are eleven of them. The A-J can be paired with any of the 48 remaining cards; the other 10 can be paired with only 47 of the remaining 48 since, for example, putting a suited J with a 10-7 Straight Flush would produce a J-8 Straight Flush rather than the desired 10-7. Hence there are 4 x 48 + 4 x 10 x 47 or 2072 Straight Flushes. There are 13 four-card Four of a Kinds and any one of the remaining 48 cards can be paired with each to make a five-card hand, so there are 13 x 48 or 624 of these. There are 13 choices of ranks for a Three of a Kind and for each such choice there are four ways to pick the three from the four. Picking 2 of the remaining 48 (1128 ways) we have the number of five-card hands containing a Three of a Kind is 13 x 4 x 1128 or 58,656. Now here is where things get interesting. The two games mentioned above rank hands as follows: Game #1: Straight Flush Four of a Kind Flush Straight Three of a Kind Two Pair One Pair High Card The first Global Gaming Exposition, or G2E as it is called, was held in late September 2001, a few days after the dastardly attacks in New York and Washington. The keynote speaker was Whoopie Goldberg. I imagine that other attendees, like myself, were curious as to how this funny woman would approach that task given that the country was in such a state of shock and sadness. I can tell you that she handled things with grace and was indeed very funny. To assure that I got a seat for this event I arrived early. I found a seat easily near the rear of the hall; in fact there were a couple of empty seats next to me. A minute or so after I got seated an attractive woman asked me if I was saving those seats for someone and I promptly plopped my program on the seat next to me and told her the seat was hers. Typical of my luck with women, she told me she needed two seats since her husband was coming. So I appropriated the two seats and she made her way down the row and sat down next to me. We chatted for a couple of minutes and, sure enough, her husband showed up. We shook hands and he sat down with us. The guy looked familiar to me but I couldn't place him. A minute or so later we exchanged business cards and then it became clear that a few years earlier I had listened to him speak about Video Poker in an Atlantic City conference. It was Bob Dancer and I had been talking to his wife, Shirley. I was delighted to meet him in person and especially delighted to meet Shirley because, as you know, she is frequently the subject of Bob's Video Poker stories. I can tell you that Shirley is every bit as charming and outgoing as Bob's articles describe. Bob Dancer is a nice guy and speaks modestly of his Video Poker talents. When I told him that whenever I play Video Poker I have to go back and study the strategy charts again because they fade from memory when I am back at home computing rather than competing. "Yes," he said, "so do I." Sure Bob! I mention all of this because having met the Dancers in person made the reading of Bob's new book Million Dollar Video Poker, Huntington Press, 2003 seem like the story of personal friends. Then again, maybe it seemed that way because it is so well written. Whatever the reason, I thoroughly enjoyed the book. Let me begin by telling you what the book is not. It is not a book about how to play proper Video Poker strategy. Bob, together with his friend Liam Daily, does have such books available to players, but that is not what this book is about. In a sense though, it is a "how to" book. Not how to play Video Poker but how to be a professional gambler. |
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