SETUP:
- Standard 52 card deck. Game is O-hell.
- Trump game where any card from one arbitrary suit beats any other card from another suit.
- 3 players, A, B & C.
- A has the lead.
- Each player has one card.
- Hearts is trump, Ah (A of Hearts) is turned up and shown.
- Player A has a 2s (2 of Spades)
- Ace is high
QUESTION: What are the chances that player A will win the hand?
MY ANALYSIS:
- Out of 52 cards, player A knows about 2s and Ah. 50 unknown cards.
- There are 26 cards that a 2s will beat when A plays it. Any Club or Diamond.
- There are 24 cards that will beat his 2s. Any remaining Spade or Heart (trump suit).
- A's chances of beating B seems to be $\frac{26}{50}$.
- What are A's chances of beating B and C: I think it is $\frac{26}{50} \times \frac{25}{49} = 26.5\%$.
Is this how you approach this kind of problem, even while varying the number of cards each player has and the number of players in the game? If it is 4 players and 1 card, then $\frac{26}{50} \times \frac{25}{49} \times \frac{24}{48} $?
Is this an "n Choose k" problem instead?