The probability of Hand is extremely high considering there are over 634,000,000 ways to make a hand. As the easiest hand to play for, many people choose to play for it for the quick score. It can occur almost five times as often as the next better hand, Seven Pairs. Hand scores minus 500 versus minus 1700 for Seven Pairs. Although it is not that high scoring it is important to realize that Hand occurs quickly and is perfect for the times that you need a score and fast.
Look at the next hand, Hand Minor. Hand occurs 7.6 times as often and Hand Minor scores only 1.6 times as much. Give the choice between playing for either of the two; it is almost five times more profitable to play with the easier hand. With Seven Sticks Minor, you see Hand 76 times as often. You score only four times as much. The scoring odds swing in your favor by 19 to 1. This shows you how powerful this hand can be.
If the game were strictly a random collecting of tiles, you would obviously always play for Hand or the even simpler Foot and Open Melds. Of course, it is not strictly a random game, since after the deal, you now have considerable control over the rack you are playing. You do not discard in a random fashion, nor do you pick completely at random, since you have a discard visible to choose each time. Therefore, the chances calculated from the table must be tempered by what you think you can do with your rack. If the initial rack favors one of the low probability hands, consider this as a possibility to play. After all, this is what makes the game so much fun. If you stick only with Hand then there won’t be any true competition in the game, and you may get bored with it.
The table that calculates odds does not include the plays called Open Rummy and Foot. The reason for this is very simple. Both of these plays involve all of the same possibilities as Hand plus the option of laying off tiles on the open melds. There are, they are at least as likely, if not more probable.