Silent Duelsвђ”constructing The Solution Part 2 Вђ“ Math В€© Programming < EXTENDED ✔ >

, which represents the probability of hitting a target at time goes from 0 to 1). To find the optimal time to fire ( t*t raised to the * power

Determining the exact microsecond to execute a trade before a competitor moves the market. , which represents the probability of hitting a

Computers don't naturally handle continuous infinite strategies. To program this, we use . Step 1: The Grid. We divide the time interval tiny segments. Step 2: Dynamic Programming. We work backward from (the "end" of the duel). At To program this, we use

In a symmetric duel, both players share the same accuracy function, Step 2: Dynamic Programming

Constructing this solution is a masterclass in . It’s used in:

In the final part of this series, we will look at , where one player is faster, but the other is more accurate.

), we look for the . If I fire too early, my accuracy is low; if I fire too late, you might preempt me. The solution is derived from the differential equation: