In my opinion, 3 Strikes would be better if it weren't so hard, and if it involved more "baseball" analogy. To the first point, what makes the game hard, and long-and-drawn-out, is trying to put the number you've drawn in the right space on the board. Even if you don't draw a strike, you realistically only have a one-in-four or one-in-five chance of guessing the right position for the number, at least at the outset. (Foul balls, if you will). And the more draws you have to make, the greater the chance of just striking out.
My suggestion for this game is to give the player three "balls". By that I mean, the player gets three free "placements" of the number he/she draws. When the player has used his 3 free placements, then the player has to guess the right space for the remaining draws before striking out.
I would assume the player would begin by using his/her "balls" at the very beginning, but maybe not if he/she were certain of the first number in the price, say.
Two problems with my suggestion, which I think could be overcome. One, the set would have to be modified to count "balls" as well as strikes. Two, the producers would have to develop a clear and quick way to explain the "ball" rule. I don't think it would be any more complicated than Drew saying "do you want to guess, or use one of your balls?"