Normally, A Pokemon can get one of two quick moves and one of three charged moves. You always get a move of the actual movepool, never legacy.
(1) Change of Quick move
Invest one TM. You get the other Quick move for sure
(2) Change of Charged move
First TM
50% Chance to get wanted CM
50% Chance to get not wanted CM
Second TM
50% Chance to get wanted CM
50% Chance to get original CM
Conclusion: To get a wanted CM out of three, you should have 2 Charged TMs.
Over all you get follwing propabilities:
50% to get wanted CM with 1st Machine
25% to get wanted CM with 2nd Machine
25% to get original CM with 2nd Machine - 2 Machines wasted.
The [ To get a wanted CM out of three, you should have 2 Charged TMs ]
Is an ''a priori expected value'', infact you can only use ONE TM at time, so if you fail the first one , then you still got a 50% chance to get what you want.
So the overall 2/3 chance is a not precise prediction.
Still I might stock 2 charged TM to try get C on one of my SE Tyranitar...(who had Fire Blast, I already used a TM onto him!).
Yeah assuming a 50:50 probability between the 2 other charge moves then it's a geometric distribution with a probability of success 0.5. So the expected number of TMs needed is 1/0.5 = 2 .
One thing to note is if your mon has a legacy move set then the probabilities are changed. If your mon has a legacy quick move then you aren't guaranteed to get the quick move you want.
