Four Aces

Four Aces is a card game Ryuji played with Jonouchi for a bet.

Ryuji's version

 * This game is played with 4 "ace" cards, which the challenger sets face-down and shuffles in the table.
 * The player picks any 2 of the face-down aces. His goal is to pick either 2 red aces (diamonds and hearts) or 2 black aces (spades and clubs). By picking 2 aces of the same color, the player wins; otherwise, the challenger wins.

Ryuji tricks the player to think this is a fair game, with a 50-50% chances. However, this is a bar bet. It works like this:
 * Ryuji tricks the player by using the term "choose 2 cards at the same time", which makes it looks like the player has 50% of chances.
 * However, one must think of it as picking one card at a time; after the first card is picked, there are 3 cards remaining, and out of them, only 1 has the same color as the one the player picked. So, the actual chances of winning in this game are only 1/3.

Yugi's version
Noticing that the game is not fair, Yugi challenges Ryuji using alternative conditions:
 * A joker card is added to the aces.
 * Both players take turns picking one of the 5 face-down cards.
 * Whoever picks 2 aces of the same color first, wins.
 * If a player picks the joker, they lose.
 * Other results end in a "draw".

At first, Ryuji thought Yugi has set him in another bar bet, but then he realizes this is a fair game. Any other result would end up being a "draw", so the player who picks the joker first loses. The chance is 1/5 for the first player, and since both Yugi and Ryuji had the chance to start, the game was fair.

Ryuji vs. Jonouchi
Ryuji plays as the challenger, and shuffles the aces face-down. Jonouchi picks the two aces in the middle; they turn out to be one ace of hearts and one of clubs, so Ryuji wins. They play again, with Ryuji shuffling the aces face-down one more time. Jonouchi picks the left-most ace and the 3rd ace from left to right. They turn out to be an ace of clubs and an ace of diamonds, so Ryuji wins again.

Ryuji vs. Yugi
Yugi starts, and picks the ace of hearts. Ryuji picks the ace of spades. Yugi picks the ace of clubs. Ryuji picks the joker, so Yugi wins.

They play once more, with Ryuji starting this time. Yugi picks the aces of clubs and spades, while Ryuji picks the ace of diamonds and the joker, so Yugi wins again.