This method weights and adds up the probability curves for each wave, resulting in a single probability curve. The effective risk of all potential positions is calculated as follows:
P = P1 + P2 / 2^w + P3 / 3^w + P4 / 4^w + ... + Pn / n^w, where n is the total number of waves, and w is the weighting (higher w gives less importance to the risk of farther-off waves).
Usually there are only two, or at most three waves present at any one time. So this method has very little effect in general. However, it does make a noticible difference in weaving, and avoiding "trap shots."
I'm still tweaking the weighting and probability calculations, but once I have something concrete I'll post scores and source code.
Hope this is at least an interesting idea.
I think most surfers do something like this. In fact I think Dookious is somewhat unique in only considering the two closest waves. CassiusClay/Butterfly weights the danger according to the time to impact and and bullet power (Bullets arriving sooner are more dangerous as are bullets with high power.) -- PEZ
This idea reminds me of WaveSurfing/PathFinding. I should add that Dookious does something a little different than most, he actually uses PrecisePrediction on the evaluation of the second wave; so he actually takes the minimum of three 2nd-wave positions for each one of the movement options. That's part of the reason he only considers two - the other being that it seems a tad pointless to me to consider more. It just doesn't seem right to me (speaking in terms of CassiusClay's style surfing algorithm) to consider the same spot for the first and second waves, since you will definitely have time to move from there before wave 2 hits. And since most use a formula like (1/distance_squared), the third wave's relative influence would be pretty close to zero.
But, in the end, it turns out it's a lot more important to get everything bug-free, no matter what surfing algorithm you use. (You know, I actually think Dooki's weird algorithm might have an unintended side effect that helps against high level guns, but it's just a hunch. If the second level considers every spot in its whole range and takes the lowest, it decreases performance, even though it seems correct to me!)
Of course! You mean I only predict the closest wave and then check that GF on all the others? I haven't given that a thought even so you're probably right. I'll start working on this ASAP. Thanks! -- PEZ
Well, the same (x,y) spot is a different GF on each wave, but I meant that you have plenty of time to move the spot itself before wave 2 hits, also. -- Voidious
In X2 I'm surfing the first for 3 different decisions (reverse, stop, ahead), then I surf the second one with the 3 different decisions from each of 3 positions I got from the first wave. And so on for all the bullets in the air, that's partly why X2 is slow. I have 3 positions for the first wave, 9 for the 2nd, 81 for the 3rd ... -- Florent
Holy cow, Florent! That's cool. Do you have any weighting for the waves that are further away, or do you just try and choose the best path overall? Even with PrecisePrediction over multiple waves, I've still found it very advantageous to weight the first wave more, but I'm interested to hear what you've found. -- Voidious
I guess I should have been more clear about my algorithm. I'm not just adding up the probabilities for the same position on every wave, I add the minimum reachable probability for future waves using modified prediction code from the WaveSurfing tutorial. --Speal
I also use the minimum danger path and each wave is weighted according to its time to arrival. -- Florent
I´m doing the same in Krabby2 like Florent does, but only for two waves and only reverse and ahead (6 positions). I wonder how CC could be that good with that simple implementation :) --Krabb