Still, without fate points, I have taken many parties to level 20+. Striking dice is very efficient. The best part is it retains all the integrity of the game, as the odds to get the same number are the same they were when first rolled. I would like to see the curve on how effective it really is by some math geek.
Depends on whether striking the die is actually equivalent to a reroll, or if it sometimes just bumps the die so it turns by one or two sides (in which case there is a much reduced chance of getting the same result).
Also depends on when you choose to do it. For example, if you always choose to strike the die when a 9 comes up, but no other number, the chance of the first digit being 9 drops from 10% to 1%. The odds of the other leading digits increase accordingly, from 10% to 11%.
The average roll will be (ignoring open-ended and assuming randomness on a strike):
Normal roll: 50.5
Replace 9's: 46
Replace 8's: 42.5
Replace 7's: 40
Replace 6's: 38.5
Replace 5's: 38
Replace only 0's: 51.4
Replace 9's and 0's: 49.6
Replace 8's and 0's: 46.1
Replace 7's and 0's: 43.6
Just replacing 9's, the chance of open-ended up drops from 5% to 1.4%.
Replacing 0 and 9, the chance of open-ended up drops from 5% to 0.5%.
So replacing a 0 brings up the average a bit but does reduce the chance of open-ended up.
In practice, I assume a player will think about what is the threshold for a bad result. If the enemy needs a 90 to hit, then obviously they don't want to reroll an 8. If the enemy needs a 70, it's probably better to reroll 7+. So the system is probably more favorable to them than the numbers alone suggest.