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Dominion General Discussion / Calculating probabilites of hands
« on: June 09, 2015, 10:49:33 pm »
I played this game with Wandering Winder: http://www.gokosalvager.com/static/logprettifier.html?20150609/log.514b5511e4b0b79c883b5e3b.1433865845040.txt
and we talked about how unlikely my turn 9 hand was. He said it more than 5% chance it would happen during the game. I didn't think so. We didn't really define what we meant though. I had thought more about the first half of the game, before greening let's say. And he hadn't meant that exact hand of course, which would be a lot less likely.
For drawing a hand with no Treasure on turn 9, my chances were 2.17% (on that turn). For drawing it on any turn from 1 to 10, it's 8.72% I think (given my deck buildup).
But the point was drawing the Stables dead. Let's say at least 2 dead Stables.
Calculating the probability of drawing 5 non-Treasures is pretty easy: [total-cards choose 5] / [non-treasure-cards choose 5]
But how do I calculate a more complex hand like at least two Stables and the rest non-Treasure? On turn 9 I have: 4 Stables (S), 9 Treasures (T), and 6 other, (O). I guess it's 3 possibilites: SSOOO, SSSOO, SSSSO.
I hope you mathheads can help.
and we talked about how unlikely my turn 9 hand was. He said it more than 5% chance it would happen during the game. I didn't think so. We didn't really define what we meant though. I had thought more about the first half of the game, before greening let's say. And he hadn't meant that exact hand of course, which would be a lot less likely.
For drawing a hand with no Treasure on turn 9, my chances were 2.17% (on that turn). For drawing it on any turn from 1 to 10, it's 8.72% I think (given my deck buildup).
But the point was drawing the Stables dead. Let's say at least 2 dead Stables.
Calculating the probability of drawing 5 non-Treasures is pretty easy: [total-cards choose 5] / [non-treasure-cards choose 5]
But how do I calculate a more complex hand like at least two Stables and the rest non-Treasure? On turn 9 I have: 4 Stables (S), 9 Treasures (T), and 6 other, (O). I guess it's 3 possibilites: SSOOO, SSSOO, SSSSO.
I hope you mathheads can help.