- A 50% risk of losing without causing any damage
- A 50% chance of taking out at least 1 unit
- A 25% chance of taking out at least 2 units
- A 1/8 chance of taking out at least 3 units
- A 1/16 chance of taking out at least 4 units
- A 1/32 chance of anihilating the enemy (without casualties)
I fear your calculation is wrong because your assumptions are wrong.
You assume that this is like a mathematial experiment in which the lone trooper fights against only one trooper of the enemy army at the same time, so one after the other. If he survived against trooper one, he will fight against trooper two, and if he survived that fight again, he will fight against trooper three, and so on.....and then you calculated the probability of the lone trooper to win this game.
But the "reality of war" is different. In reality the lone trooper has to fight against all five enemy trooper AT THE SAME TIME. The moment he can fire one single shot at one of the enemy troopers he is hit by five shots of the enemy. His chance to win this fight is about 0%. His chance to take out only ONE enemy trooper is also about 0%. Let's assume that a trooper dies when he is hit by five shots. Then the lone trooper wouldn't survive even the first "round of fire". And even if he dies after 10 shots he would die before he could even endanger one of the enemy units.....
Therefore a "reality-based" or even "RTS-based" autocalculation of a "1 trooper vs 5 troopers" battle had to lead to a 100% chance to lose the battle and a very, very, very tiny chance to even kill one single enemy unit.
