The question came up during a game of Skull King.
We were playing the first round and each of the 6 players received a single card.
With the 12 of red I drew the conclusion that I should mention 0 (not winning my hand, as opposed to 1 which is winning). In this game the person wins if he plays the highest card in this round.
A deck of card consists of 66 cards.
Out of those 66 cards, 22 can beat mine (13 red, 1-13 black, 5 pirates, 2 mermaids, 1 skull king = 22 cards). It is also worth mentioning that I will have to start the round, which means the color i play (red) will be trump. For that reason any yellow and blue card won't win against mine.
What is the probability that I will lose this hand as intended?
- Is there an easy way to calculate that?
For those who are interested, you can find the official rules under the following url.
Best Answer
Btw, if I feed what you have written as it is, Wolfram returns an impossible probability of $\approx 1.84$
Anyway, the easiest way to compute:
P(you don't win) = $1$- P(you win) $= 1 - \dfrac{\binom{43}5}{\binom{65}5} \approx 0.8835$
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ADDED
An alternative way to compute it is
P(you don't win) $= 1 - \left(\frac{43}{65}\cdot\frac{42}{64}\cdot\frac{41}{63}\cdot\frac{40}{62}\right) \approx 0.8835$