Sort of glad this thread got re-found;
Originally Posted by AlfieAA
...its good to know that its 1 in 8, but i would like to understand why it is 1 in 8 so i can work out everything else....abit like give a man a fish and it will feed him but give him a fishing rod and it will feed him for life sort of thing....but if it doesnt matter too much then thats cool, i will concentrate on things i do need to learn...thanks
I have never worked thru why it is 8-1 (ish), so let me give it a go;
We see our PP, and there are 50 cards preflop left that we do not know anything about. 2 of those are our gems, so that means we have a 1/25 (2/50) times 3 (flop cards) = 3/25 which works out to about 1/8.333 chance on the flop.
If we get fortunate enough to see all 5 community cards, we can figure we get to improve those original 1/8.333 odds by adding the new calcs of 2/47 (turn) [.042], and another 2/46 (river)[.043]. So, 1/(8.33 + .042 + .043) = 1/9.178 , which in my mind works out to be about 11% (10.9%).
I had always accepted the published formulas without figuring out for myself, and truthfully, I had doubted those published results. But then everyone knows dj is always wrong.....