Also it does not agree with our double-verified exact answer by script; yours is an overestimate - 8.19, 1058791184067875423835403125849552452564239501953125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/129277986730885202106151856642773382549665465071825090615034369359178917814747670780594211447306244001059786961886915926297133393516168977984471526892507817 to be exact.
We're not saying floor of expected, we're saying expected of floor. That is, if you have raised the probability of success to 33% but your 100 turns are used up, the 33% is wasted and the win does not count. Expectation is fractional but whatever is inside must be floored.