--- In vpFREE@yahoogroups.com, Cogno Scienti <cognoscienti@...> wrote:
>
>Aces up are 19008 out of the 2,598,960 possible hands.
>
>
This is the type of math I had to learn when I got into the gambling game. I'm a high school dropout that never even took algebra. But necessity is the mother of invention. I had to teach this stuff to myself past the age of 39 If I can do it anyone can. Trust me, being able to do this kind of math will set you free in the gambling world. Because once you learn it you will no longer be playing follow the leader. You will be the leader.
How did Cogno come up with 19008 as the number of five-card combinations representing Aces Up in a 52 card deck? Others may be able to do it faster but here's the uneducated way. I may be slow but I can get the job done.
There are 4 cards in each rank. How many combinations in that rank make a pair? To be dealt a pair you would have to catch any one of 4 cards then any one of 3 cards. 4 X 3 = 12 permutations. When you catch a specific pair, say 2 of diamonds and 2 of clubs it can come in two different orders. You could catch the diamond first and the club second or the club first and the diamond second. So we divied 12 by 2 which = 6. That's the number of pairs in a rank.
When catching Aces up we know that one of the pairs we're dealt will be Aces and the other pair could be anything from Kings down to deuces. So the equation looks like this:
6X72X44 = 19008
The 6 represents the combinations representing the pair of Aces. The 72 represents the number of pairs in the other ranks....12 ranks X 6 pairs. The 44 represents the number of sidecards one would catch with the hand....this number is easily derived; when you catch two pair the fifth card has to be a card of a different rank than the two pair. 52 minus 8 = 44.
Aces up is the most prevalent two pair hand. The equation for Kings Up is 6X66X44 = 17424. Queens up 6X60X44.... and so on down the line.
