機率問題....深夜睡不著隨便打 大家隨便看 沒足球 0rz
不過.....ㄟ.....有時候修個課會比較好懂，很多東西是不太直觀的
我給這串討論串提供一點新的想法(還是有人講過我沒看到?)
「手上每一張非拍賣師的牌打出去之後，剩下的手牌有拍賣師的機率就會越變越高」
妳可能會覺得"幹甲賽，她又沒抽新的牌，為什麼手牌有拍賣師的可能性會越變越大"
這裡就是要用功的部分啦
http://iam.yellingontheinternet.com/2013/09/01/
hearthstone-probabilities-and-the-monty-hall-effect/
http://goo.gl/kIurmn
懶人包請直接看作者幫你寫好的spreadsheet
包妳直接知道"下一張"打出拍賣師的機率有多高
(那是設牌組中只有一張拍賣師的情況下 多的請自己算...
而且越多張拍賣師，機率和直覺算差距越大)
至於這篇文章為什麼會提到monty hall呢
你要注意一個重點
Monty Hall, however, tells you differently. Even though she only has 5 cards
in her hand next turn, she’s been selecting out non-Polymorph cards and
playing them all game. Just as Monty selected out non-winning doors and
removed the pool, making the remaining doors of the ones he could have chosen
more likely to be winners, Jaina has been casting non-Polymorph cards from
her hand, making the ones she’s left in her hand more likely to be
Polymorphs.
monty hall的概念就是每一張非拍賣師的牌被打出來，相當於沒有中獎的門會一直被打開
所以剩下沒打的那些手牌就更有可能是拍賣師，
不要被「他有沒有抽牌/他有沒有換門」給誤導了
而且這樣的機率會比妳想像中的高很多，完全違背沒學過的人的直覺
For now consider the simplest case, where nothing had been cast so far this
game that Jaina would have been likely to Polymorph. Applying the logic from
above, there’s a 50% chance that the Poly started the game in the bottom 15
cards in the deck, and that probability has not been changed by any
subsequent events. There must, then, be a 50% chance that it’s among the 5
cards in her hand. Quite a significant difference from the 25% that seemed
completely intuitive before considering this effect.
兩張的狀況
The other complexity is what I alluded to at the start: the arithmetic is
more complicated with two Polymorphs in the deck (but as I said, the logic is
unchanged). To work the same example with two Polymorphs:
The naive estimate is that out of 20C2 (20 choose 2, referring to
combinations) places the Polys could be, 15C2 choices have them in the bottom
15, so the chance of having one in hand is 1-(15C2 / 20C2), which evaluates
to 17/38, or around 45%.
The Monty-corrected estimate would be that out of 30C2 possible
placements at the start of the game, 15C2 have them undrawn in the first 15
cards, so the chance of having one in hand is 1-(15C2 / 30C2), which
evaluates to 22/29, or around 76%.
打到這邊突然有睡意了 不要怪我沒翻譯
看到機率手癢而已 請各位幫忙補充給看不懂英文的版友看啦 0rz