Edit: these figures are for Van Saar!!
Disclaimer 1: The XP rate used in the following calculations are probably a bit low due to me not having played in a while. The bottom line remains unchanged, though - on average you need 9 advances before you get Inventor.
Let's do the maths on a typical gang, leader, two heavies, five gangers and one juve (not taking into account gang members bought after inital roster). Let's say that all gang members get an average of 6 exp per game. I don't think that's far off (3,5 exp average on diceroll + 1/2 kill per game. The leader gets and average of 10 per game due to the "winning gang leader" XP.
The chance of getting a new techno skill per advance is 33,33% (
source). First roll on techno has a 16,66% chance of getting Inventor. Second roll has a 33%% chance of getting techno. Third roll has a 50% chance. This is due to getting to pick any skill if you roll one you already have.
Disclaimer 2: I'm not a math teacher! Please feel free to correct me if I'm wrong! And I know that probability and "probability" ain't exactly the same thing.
Juves (starts with 4 xp):
* XP after 10 games: 64.
* Number of advances: 8
* Number of techno advances after 10 games rounded down/(actual): 2/(2,66)
* Probability of getting inventor after 10 games rounded down/(actual): 50%/(83,33%)
* Number of games needed on average to get inventor: 13 (81+ XP/9 advances)
Gangers (start with 24):
* XP after 10 games: 84
* Number of advances: 5
* Number of techno advances after 10 games rounded down/(actual): 1/(1,66)
* Probability of getting inventor after 10 games rounded down/(actual): 16,66%/(38,88%)
* Number of games needed on average to get inventor: 23
Heavies (start with 64):
* Xp after 10 games: 124
* Number of advances: 3
* Number of techno advances after 10 games rounded down/(actual): 1/(1)
* Probability of getting inventor after 10 games rounded down/(actual): 16,66%/(16,66%)
* Number of games needed on average to get inventor: 37
Leaders (start with 64):
* XP after 10 games: 164
* Number of advances: 5
* Probability of techno advances after 10 games rounded down/(actual): 1/(1,66)
* Probability of getting inventor after 10 games rounded down/(actual): 16,66%/38,88%
* Number of games needed on average to get inventor: 22
Total probability getting Inventor after ten games (actual):
Juve (1x): 83,33%
Gangers (5x): 194,4%
Heavies (2x): 77,76%
Leader (1x): 38,88%
Total total: 394,37%
Ten games having selected Techno at every oportunity should yield you nearly four inventors using this gang.
Disclaimer 3: These numbers are so high I'm assuming that I fucked up the calculation in one or more ways.