Is the name Patrice has given to his bridge section on his web page.
Somehow, this got my imagination running and I wondered… is this true?
A deck has 52 cards, which is split evenly between 4 people (13 cards each).
Then people bid on how many tricks they’ll win.
Then, everone has a turn playing cards, trying to win tricks and make contract.
I decided to not take into account the bidding part. Just the playing of the cards.
My first idea was to try and determine how many hand combinations were possible, then determine how many ways a combination could be played.
That was the idea that is actualyl fun to calculate.
If I remember my stats mathds well, drafting 1 card out of a deck has 52 possibilities. Then, I have 51 cards left, so there’s 51 possibilities for drafting my second card, and so on. So, number of possibilities = 52x51x50x…
1 If I draft the whole 52 cards , it means I have 52! (factorial notation, if my mind serves me well) possibilities, which gives 8.06e67 possibilities to split the 52 cards.
But I don’t want to take into account the order of the cards. A hand with all hearts is the same, no mather in what order you have them!
2 I figure, for a given hand (13 cards), there is 13! ways (orders) for it to be found.
3 So, 52! deck distributions possiblities / 13! hand distribution possibilities = 1.2952932e58 ways to split the deck.
Good. Now, I want to know how many possibilities to play these hands.
1st trick, there’s 13 options for each player. 13x13x13x13 possibilities (13^4).
2st trick, 12 options left. 12x12x12x12 (12^4).
And so on.
4 So I figure there’s 13!^4 ways to play these hands. Wich means roughly 1.5035617e39 possibilities.
So if there’s (3) 1.2952932e58 ways to split the deck in 13 card hands and there’s (4) 1.5035617e39 ways to play the hands,
5 There should be about 1.9475533e97 ways a game could be played. (Or 25% of that, if you don’t want to take into account the possible rotation of the hands around the table).
Which is waaaaaaay much than the 635,013,559,600 ways I read about.
Then I had another way to calculate it.
1a 52 cards, played one after the other. 52!. 8,0658175e67 possibilities.
Could be as simple as that.
Either way, I’m not even close to what I wanted to reach (and I tried a few other ways which all end up with humongous numbers that vary wildly).
How would you go about calculating this?