As you already know from the American version, calculating the odds on each of the possible hands in the Israeli version is a daunting task. There are over 6 trillion hands that can be made. This can be very important to the player in determining whether or not to play for any specific hand or hands that may be developing on the player’s rack.
In these 6 trillion ways to calculate the hands, it does not even include the hands that are duplicates of each other. In other words, if a run of red 1, 2, and 3 is included, it is only counted once, even though it can be made up eight different ways with the duplicate tiles. In many hands, the run can obviously appear twice. It is nearly impossible to account for differences in odds resulting from exchanging each tile for its duplicate. Included in the table is a list of the scores for each hand, again without jokers.
Many hands haven’t even lent themselves to mathematical analysis. Reasonable speculations can be made about their possibilities though. For example, Piccolo 41 Odd and Piccolo 41 Runs are both easier to obtain than Piccolo 41 Groups. Piccolo 41 Sets are probably harder to get. Minor 51 Runs is less than Minor 51 Groups, which is less than Hand Minor 51. All three are probably easier to get than the Piccolo hands since they include the lower-count Piccolo hands which are played as Piccolo of course. Grand Odd, Single color Odd, Mosaic, Little Wave, and Big Waver are all very low probability hands. Little Blitz or Big Blitz should occur approximately once out of every 5000 to 7000 hands.
Two colors are easier to obtain than Four Colors obviously, and they both score more frequently than Three Colors. This is because Two Colors can be scored with two, three, or four runs, of lengths between three tiles and eleven tiles. Three Colors can be played with only three runs. Four Colors is played with four runs, but after you have formed your first two you still have two colors left for the third run and one for the fourth, whereas with Three Colors, after two runs you have the possibility of working with only one color. With Three Colors you also must form at least one longer run than you have to form with Four Colors.
These are all examples demonstrating the complexities for forming many of the hands which are not immediately obvious from looking at the form of each hand. Playing the suggested solitaire game is a good way to get a practical feel for what the table is saying. Intuition may tell you that it should be easier to form Odd hands than hands with groups and runs. After all, you don’t have to match up tiles to form an Odd hand, do you? Of course the chances of forming at least some runs and groups with 14 tiles are extremely high. Therefore, it is far more difficult to prevent their formation, and the Odd hands are of low probability.