Calculating Standard Deviation for Margin of Victory in a Game of Chance

[Firefight]

I want a simulation ran for this problem:

Assume that the goal in a game is to hit a total of 1000 damage before the other person does.

Now, two people are both competing against each other in this goal to 1000 damage.

Each person has an equal chance to beat each other to this thousand (they both hit at the same time, and if both of them hit >1000 at the same time, a random winner is chosen).

Here's how the damage works:

50% of the time (randomly), the people hit 0 (or miss).
and, 50% of the time the people hit a random number in between 1 and 112.

I want to know the standard deviation of how much the winner beats the other. EG: How often would the person who wins beat his opponent to 1000 by a margin of 30, and how much rarer would it be if he did it by 300, etc.

The more simulations ran, the better. I want a small 95/99% confidence interval. If anyone could do this for me, that'd be great. And I would be forever grateful if anyone of you actually told me the formula to do this w/o having to run the simulation!

 

[lippyka]

To run this simulation, you would need to create a program that randomly generates numbers between 0 and 112 and then tracks the total damage inflicted until one of the players reaches 1000. You would then need to calculate the difference in total damage between the winner and the loser and use that to generate a standard deviation for the margin of victory. Depending on how many simulations you want to run, it may be simpler to create a program that does this or you could use a spreadsheet program such as Excel to track the results manually.