Heck, It's still morning and I haven't had my second can of Diet Coke yet.
I know it's getting involved, but I hadn't specified the TWO cards to start with. Yes you are correct, if I was only looking for two specific cards.
It like saying, what are the chances of drawing a Royal Flush, which starts out, with the player needing any 20 of 52 cards. Sounds easy 38%! (it's the chances of getting a 10-j-q-k-a) OF course the next card is 4 in 51, 3 in 50, 2 in 49 and 1 in 48. Because the suit has to match now.
That's not taking into account that if someone is playing poker, there will be other cards dealt, and if all the cards one needs are still in the deck, the odds of getting what you need, get better as each wrong card is removed.
I'm not going to do the numbers, because it's been done (correctly I must add) a number of times. Lets just say around one in 53,000 chance, off the top of my head.
If anyone finds a _GOOD_ book on dice and probability, please send me an email. The only one I found doesn't address Indian Dice, AKA Bar Dice, odds. I start to lose my mind (for numbers! No comments) when it's six random objects, that keep changing numbers, instead of a deck of cards which is random but finite and constant to some extent.
Seems that it's a Mid-West thing and people West play other games. If you haven't ever been in a saloon in the Middle states, the first slam of the dice will wake you up and you wonder what the heck is going on.
It's even in the statutes in WI that it's legal to play dice games (bar dice is the reason) for drinks and food. (but not for money)
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