In the Chinese game of Daidi (Big Two), a player is 13 cards from a standard, randomly shuffled deck of 52. A novelty of Daidi is that the highest card value is 2.
If your hand has one of each card value (3 to 2, disregarding suit), you are granted an immediate win - this is called a Pure Dragon. If all cards are of the same suit, it is called a Suited Dragon.
If multiple players get a Pure Dragon, the winner is determined by looking at the suit of the 2. If one gets a Suited Dragon, they are the winner (again, check by suit).
Find the expected number of games to be played before one is granted an immediate win, if there are 3 other players.