ATC Quant Card Simulation

In this game simulation, players are dealt a single card without replacement from a well-shuffled deck. Only first player dealt a card earns points in the game. If player 1's card is not greater than player 2, player 1 gets 0 points and the round ends. If player 1's card is greater than player 2's card, player 1 gets a point, and then compares the card to player 3. If the card is greater, player 1 earns a points and moves to player 4. If the card is less than play 3, player 1 earns 0 points and the round ends. What is the probability that player 1 earns 0 points?