And you thought algebra was useless!
In your original scenario you win 100x, where x = 3, five percent of the time. Ninety-five percent of the time, you lose 100. So:
EV = (100x * .05) – (100 * .95) = 15 – 95 = -80
(Thankfully, this corresponds to The Chaperone’s numbers. Whew!)
To find out what value of x you need for a breakeven game, you set EV = 0, and then solve for x. So:
0 = (100x * .05) – (100 * .95)
Simplifying:
0 = 5x – 95
Adding 95 to both sides:
95 = 5x
Dividing both sides by 5:
19 = x
This makes sense because the 1 time out of 20 (5%) that you win gives you 1900, which balances the 19 times out of 20 that you lose 100.