Straight Flush
Join Date: Sep 2005
Location: IRC Chat Room
Posts: 5,406
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Fun fact: the number of combinations of hole cards for pocket pairs is based off of triangles, while the number of combinations of hole cards for non-pocket pairs is based off of rectangles.
There's a series of numbers called the Triangular Numbers, which is just based around stacking cans or something in pyramids like you would as a kid:
T1 is the first triangular number, T2 is the second, and so on. If you notice, T1/T2/T3 are 1/3/6 which are the numbers that correspond to the number of possible pocket pair combinations if there are 2/1/0 of the respective card removed from the deck. What you can extrapolate is that if a deck of cards had 5 suits instead of 4, the pocket pair combinations would be based off of 10-6-3-1-0 instead of just 6-3-1-0. Similarly, if it had 6 suits, it would be 15-10-6-3-1-0, and so on.
So for non-pocket pairs, imagine you have 3 Aces and 4 Kings available in the deck. Then you do 3x4 and get 12, which is a rectangle that's 3 by 4:
***
***
***
***
or
****
****
****
and so on. Same thing for the rest of the non-pocket pair combos. Like say you have 2 King and 3 Queens, then you'd have this rectangle:
**
**
**
or this one
***
***
which both give you 6 combinations.
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