It was early summer sometime in the early nineties. I had thumbed from Salt Lake City to Glenwood Springs, Colorado to work day labor. The jobs paid twice as much in the Colorado mountain towns than they did down in the city. I made $8 to $10 an hour and was paid in cash everyday. My intent was to jump start a bankroll to play $1 to $5 7-Card Stud Hi-Lo Split 8 or Better in Cripple Creek, Colorado.
I pulled this trick off more than one time. It went like this: Bank a few hundred dollars in Glenwood Springs or Frisco....Hitchhike to Cripple Creek on a Friday....Set my tent up in the campground....Go to playing stud hi-lo....if everything works out alright, keep playing poker....if it doesn't work out hitchhike back to Glenwood or Frisco and make some more buy-in money....sooner or later I will get through the window.
In Glenwood, or any other town I was working day labor, I would hit the library quite a bit in my spare time and read gambling books. As I recall, under the Dewey Decimal System, 795.4 was where the gambling books were always located. It was there at Glenwood that I found a book that I believe was called The History of Gambling. One of the chapters covered how Galileo was the first mathematician of note to work out the probabilities of dice throws.
The story went that sometime in the early 1600's a dice gambler came to Galileo with a problem. This gambler had been propositioned to a particular type of dice game. This is how the proposition went: The Hustler (propositioner) proposed that they play a game with three dice. They would roll the dice and any time the total was nine the Hustler would pay the Dice Gambler. Any time the dice totaled to ten the Dice Gambler had to pay the Hustler. The Dice Gambler accepted the proposition.
Slowly but surely the Dice Gambler lost a lot of money to the Hustler. But he couldn't figure out why he was losing. This is speculation on my part but faulty math probably led the Dice Gambler to thinking he had the best of it. He was probably figuring something like "There's 3 six-sided dice so 3 X 6 = 18. Half of 18 is nine so I have the median number. And I have an extra way to win by rolling three-of-a-kind, my opponent can't do that.
But after getting his clocked cleaned the Dice Gambler took the problem to Galileo. Who knows how long it took Galileo to solve the puzzle, but he did get back to the Dice Gambler with an answer. There were 27 combinations on the dice that added to ten, but there were only 25 that added to nine.
I was sitting at the bus stop yesterday and got to thinking about the nine and the ten. I had never sat down and figured out what those combinations were. This is one of my favorite tricks, doing a math problem when someone else has given only the answer(as long as they are right). It will confirm I did the math right if I come up with 25 and 27 combinations, respectively. So I set about doing it at the bus stop, and also on the bus. I didn't stop until I had figured out all 216 (6X6X6) combinations. This is how many combinations there are depending on what number you throw:
3 = 1
4 = 3
5 = 6
6 = 10
7 = 15
8 = 21
9 = 25
10 = 27
11 = 27
12 = 25
13 = 21
14 = 15
15 = 10
16 = 6
17 = 3
18 = 1
Here are the combinations that make a nine:
6-2-1, 6-1-2, 2-6-1, 2-1-6, 1-6-2, 1-2-6
5-3-1, 5-1-3, 3-5-1, 3-1-5, 1-5-3, 1-3-5
5-2-2, 2-5-2, 2-2-5
4-4-1, 4-1-4, 1-4-4
4-3-2, 4-2-3, 3-4-2, 3-2-4, 2-4-3, 2-3-4
3-3-3
For a total of 25
Here are the combinations that make a ten:
6-3-1, 6-1-3, 3-6-1, 3-1-6, 1-6-3, 1-3-6
6-2-2, 2-6-2, 2-6-6
5-3-2, 5-2-3, 3-5-2, 3-2-5, 2-5-3, 2-3-5
5-4-1, 5-1-4, 4-5-1, 4-1-5, 1-5-4, 1-4-5
4-4-2, 4-2-4, 2-4-4
4-3-3, 4-3-4, 3-4-4
For a total of 27
Only the nine and the ten are action rolls in the game. All the other rolls, like 3 thru 8 and 11 thru 18 are no action rolls. The Hustler figured to average a two bet win per 52 action rolls-an edge of a little over 3.8%.
Galileo certainly was a fascinating person. The Dice Gambler was not too sharp. But the Hustler (propositioner) in the story also fascinates me. This hustle was invented at least several decades before the branch of mathematics known as Probability Theory was founded. Did the Hustler invent this dice hustle? Or was it taught to him by someone else? Is it just a 400 year old hustle? Or was it invented long before that? Was it passed down from generation to generation? Who knows? I can only imagine. But one thing is for sure. A long time ago, and far far away, an enterprising dice hustler set out to figure out the combinations of dice throws. He discovered that the ten had 27 combinations out of 216, while the nine only had 25. Then he found a way to capitalize on his newfound knowledge. And that is what professional gambling is all about.
