The probability of killing a troll in one hit is 0 (the troll's victory condition) only if the difference between the titan's attack and the troll's defense is no more than 3 (40 = 30 * 1.33), meaning the hero's defense with the troll must be at least 7 higher than the hero's attack with the titan. Here's the thing.
In this case, the troll will win when controlled by a human player, by retaliating against the titan's attacks and skipping their own turns. Or, if the titan skips its turns, the troll will attack it at the end of the round, receiving a retaliatory strike but immediately recovering. And if the titan tries to run away, the troll will still manage to catch up, finding moments when the titan can't escape the attack, and eventually win.

The cart isn't playing a significant role here. If the difference between attack and defense is 3 or less, the troll will win anyway. If it's more, then over a large number of turns, during which the troll attacks the titan, the titan will likely, at least once, deal more than 40 damage.
You can test this on my experimental map.