You already know how to figure out what tiles that you need and how to memorize the tiles so that you can get them, but what are the odds like as the hand progresses? The chances of picking a tile obviously increase as the hand goes on, but how you play it is what will differentiate a beginning player from an expert player.
After the deal, all the tiles are unknown to you obviously. Since you hold 14 tiles, after the first draw, the chances of the needed tile being picked from the pile are 1 in 46, regardless of the number of players. Those aren’t very great odds. This presumes that both tiles of the same number and color will fill your meld. However, if you are using one on your rack, the odds increase to 1 in 92 which is even worse for you.
On the second draw if you have not seen the tile appear as a discard or on the table, the chances improve to 1 in 45 with one opponent and 1 in 44 with four players. If everyone continues to draw only from the drawing pile, the odds on the 12th draw are 1 in 37 with one oppo9nent and 1 in 32 with two opponents, and 1 in 28 with three opponents. Of course the game is rarely played with each player only drawing from the drawing pile. Therefore it is important to keep track of the number of tiles left in the drawing pile. That is why they are stacked in piles of seven so that you can quickly look to see how many remain and therefore calculate your chances of picking the tile that you want.
Your chances are figured from the total number of tiles that are unknown to you. This includes the tiles in the pile plus all unknown tiles on opponent’s racks. The number of tiles on your opponents’ racks will be the number of players multiplied by 14, minus the number of tiles on your rack, and then minus the number of tiles on the table. It may sounds confusing, but once you get used to the equation it is very easy to figure out your odds of picking the right tile you need.
With only two players, it is possible to have a chance to pick every tile in the deck, either on your original rack, from the pile, or from each discard of your opponent. Unless one of you draws a lucky rack in the early hand, you will soon be able to develop a pretty good idea of where each tile is. If the game continues without either of you going out, the drawing pile will eventually become very small. By this time you have had the opportunity to figure out pretty accurately what tiles your opponent is holding. Again, it is extremely important to keep track of the tiles that have been played because it is these hands that separate the good player from the random player.