The "card war" game is played with 2 players and 8 decks (52 cards each, 416 total), the purpose of any player is to score a higher value card, where the values are ordered: ace < two < ... < ten < jack < queen < king. Before the game starts, the dealer draws the top card and removes the following [card value] cards (for example if he drew king then he'll remove the first 10 cards). Now the game begins, player 1 gets a card and then player 2. Each round, whoever has the highest value wins. If both players have the same value, no one wins
What's the probability of player 1 winning at the n'th round, given that the cards that were played are known? My idea is simple, take into account all the possibilities of the cards burned at the beginning and then multiply it by all the possibilities of p1 getting a better value than p2 (of course removing the drawn cards each round from the deck). I was wondering if there was and easier way.