## Wave Surfing Explained

I’ve recently reignited my interest in Robocode but this time armed with everything I’ve learned since September.

For the uninitiated, Robocode is an educational programming game, originally written with Java in mind, where players code up algorithms to guide virtual tanks in destroying each other. It’s a unique challenge, combining fields like programming, statistics, linear algebra, and game theory all into one.

Originally intended for students, the game was quickly picked up by experienced programmers and is now rather competitive. Many players use sophisticated algorithms in order to dodge enemy bullets and make sure their own find their mark.

Anyway, let me continue to explain wave surfing- but first I need to explain segmentation.

**Segmentation**

Since in Robocode neither bot can see any of the bullets, developers have to find ways to track their enemy through alternative means. Segmentation is a targeting technique that involves finding which firing angles are most likely to hit the target by dividing the continuous range of firing angles into discrete bins, and finding which bins are most popular. To implement segmentation, one needs to track each bullet with “waves”.

A wave is basically analogous to a ripple in a pond after tossing a stone into the water. We track the bullets until the “wave” hits our opponent. At that point, we can determine what the correct firing angle was at the time of firing, and subsequently increment the value in the bin which contains the correct firing angle. We then proceed to fire at the center of the most popular bin whenever we get the chance.

A primitive approach of segmentation might only segment by firing angle. However more sophisticated approaches first segment by distance, and then angle. (And even more sophisticated approaches segment by even more dimensions.) However, these improvements come at a cost of slowing down the rate of learning, but the accuracy gain is typically well worth the price.

Optimal segmentation (I think anyway) ought to reduce the number of bins down to the minimum needed to hit every possible position of the opponent. For example, an opponent at point blank range would only require one bin, since all firing angles within the escape angle would be guaranteed to hit the target. As the distance increases however, more and more bins become necessary (I believe at an exponential rate). By reducing the number of bins in this fashion, we increase learning speed, and reduce memory costs.

**Wave Surfing**

Wave Surfing is an evasive technique first developed and implemented by ABC in mid-2004. To put it succinctly, wave surfing is anti-segmentation. Every time the enemy fires a shot, we create a wave, and see whether or he not the bullet hit when the wave reaches our bot, and subsequently increment our own bin. In this way, we know what our opponent believes to be the most popular firing angle, and therefore make sure to avoid it, producing a near uniform distribution at all ranges.

**Why this is optimal**

Refer back to my earlier post on the game theoretical solution to Rock-Paper-Scissors. Basically, to do anything else is to tip our opponent off to a flaw in our strategy. If you know for example that your opponent will play Rock 2/3 of the time and Paper 1/3 of the time, your optimal strategy becomes to keep playing Paper.

**Implementation Issues**

A literal implementation of the above is still susceptible to intelligent algorithms. For example, at the start of a game or Rock-Paper-Scissors, if your opponent first plays Scissors, it would be illogical to assume that because your opponent has so far only played Scissors, it would be logical to assume he would do so again. This illustrates the problem of determining when the opponent is playing sub-optimally with an unequal probability distribution. Thankfully, statistics provides an answer. Using statistical methods to determine statistically significant variance will lead to a solution- typically, with low amount of data, statisticians say nothing can be concluded, and when more data, more confidence can be placed on inferences. A simple implementation of confidence intervals ought to be sufficient.

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