Ah, yes, it appears it did. Sorry, I just kind skimmed through the video because it was rather long. Incidentally, one method I thought of to help keep your distribution random, is to glance at the value in the seconds position of the match timer before you input a throw to determine which one to use. Assuming you are using the probabilities for Wolf's throws in the video's example, that would mean if you see the second position is 0-2 you'd do the back throw, if 3-6 you'd do neutral, and if 7-9 you'd do forward. Although for the best possible distribution using this method you should also rotate which numbers correspond to which throws.

Haha! That made me smile, because I thought the exact same thing. Ever since I calculated these probabilities I've been wondering how to act randomly without falling into the trap of trying to fill a distribution (as you correctly mentioned in your last post).

My thought was to look at the seconds timer, exactly as you described. Although even then I thought I might end up being too predictable, as if it's the last few seconds on the clock then I would end up doing the same thing every time. So then my thought was to rotate the numbers->throw mappings based on stage... but even that might be too predicable! People are really good at picking up patterns. What I really need is the real life superpower ability to just pause time, compute the nash equilibrium of every scenario, and then roll a die to pick the randomly weighted option

We appear to have very similar thought processes

Could just mash the joystick in all directions and spam on P+G. That'd be random!

That's true, and that's actually an excellent way to be random with equal weights. That's what I try to do when I or my opponent are low on life and any direction would kill them (like in standing neck clutch).

But how to act in a weighted random strategy? That's where the suggestion of using the clock fits in.

Mmmmm. Very nice info here. Thanks for typing that up.

Makes me think a bit of one of Sirlin's old articles.

Yes i have

At the time i was trying to point out that the guessing game is "complete" for every character since all the options available are known to both players in advance.

AFAIK it's one the hypotheses one has to make in order to appreciate Zass's approach.

can we see the nash equilibrium
for aois chougarmi chain throw

You should be able to follow the instructions in the video and work it out for yourself. I know diddle-squat about maths and I was able just to plug-in the numbers for Eileen and and Kage and see what's what.

This info is cool props for digging deep but IMO...Breaking throw directions comes down to Habit, Flow and Ring postioning in FS. In Vanilla you can basically eliminate the 2 strongest directions depending on certain characters so you can protect yourself well against Habit,Flow and Ring Positioning.

Habit, flow and ring positioning are pretty big things to consider but as a general idea, considering this concept is pretty good if you're trying to analyze your own throwing style. Most people say that this game is more dealing with the player than the character and understanding how this works can allow you to understand why something occurred the way it is when you're playing against someone.

Is it possible for this to take into account setups after a throw successfully executes? The time left to you before they rise is pretty critical for what you're able to do to keep the pressure on. For some characters it's the whole point of doing a particular throw to begin with.

That's an excellent point, Emx, and yes, a more accurate nash calculation would take this into account.

The way one would do this would be to calculate the nash value of each setup. Similarly, to calculate the nash value of striking vs throwing, one would want to factor in not just the damage a strike does, but the frame advantage on hit/block.

In essence, the problem becomes translating frame advantage to damage. In other words, how much damage is being +5 frames worth? For high numbers, we can do this. For example, if I'm at +20 frames, one could argue that the value of +20 frames is the damage of the biggest combo I can land at +20. But at +5, nothing is guaranteed. How do we find the value of being at +5? Well to do that, we'd have to draw a nash matrix of every possible attack, and every possible response -- and see what damage comes out of all of those. But not all of those combinations would lead to damage. Some would lead to another situation where you are at -3 on block (for example). So then to calculate the value of -3 frames, we have to again consider every possible response... the problem quickly becomes one of comparing every move in the game to every other move in the game.

With such data, one should be able to calculate the nash value for the entire game! This would be interesting, as one could then predict with theoretically perfect play the value of character matchups.

Going back to more practical matters, if a good player could list all the setups after each throw for a given character, I could try my hand at calculating a nash value that takes into account those setups. I confess however, that since most setups involve strikes, it will be very hard to do this without ending up having to calculate everything as described above.

As a final thought, one way to approximate the values of being +5 frames would be to list the damage values of +10 and above. At +10 we have the nash values from throw setups, at +12 we have the damage of p+k, and at higher values we can take the guaranteed best combo. We could plot those as a graph and interpolate (best guess) what the damage values for lower frames would look like from that data. That would seem like a reasonable approximation.

So I'd need a table like

+12: XXX guaranteed damage
+13: YYY guaranteed damage
+14: ZZZ guaranteed damage
....


Anyone up for listing out that data? That would be a step towards finding the approximate value of the setups you describe.

It'd be interesting to see an A.I. do this. I'd be curious to see how strong it would be, since, theoretically, it wouldn't have anything exploit (such as always doing rising low sweeps or whatever) and would being playing in a statistically superior manner, but would not be adjusting to the opponent's inputs or 'learning'. And then, the next step would be to create a system that allowed the A.I. to update the weightings for every attack and defence based on the opponent's actions (such as giving a higher weighting to a particular throw direction every time the opponent uses it, for example), so that it is dynamically applying the 'correct' weightings to every situation based on how the opponent plays. It would likely lead to being able to set-up the A.I. to be almost guaranteed to take a certain action (by doing things that repeatedly force it to increase the weighting on a certain action) and then capitalise, but that would come at the expense of doing the same thing over and over and having the A.I. use the correct response several times over. Would be an interesting exercise and I'd like to observe it fight against the standard A.I. as well as against players with varying degrees of skill.

Genzen, that's a very astute observation. Just because a strategy is Nash equilibrium doesn't mean it's what would win a tournament. As you point out, a Nash strategy can't be exploited, but it also isn't smart enough to capitalize on opponent's mistakes.

A good read on this subject is the 1999 first rock-paper-scissors (RPS) programming competition. The nash equilibrium strategy in RPS is quite simple: select randomly.

With that said, a robot playing random (nash equilibrium) would not be even close to winning a contest. A fascinating read here:

http://webdocs.cs.ualberta.ca/~darse/rsb-results1.html

Very related to your point, Genzen, is the following section:

They make the case here that the optimal strategy (nash equilibrium) is not the "best", for the reasons you correctly point out. An opportunistic strategy, that can learn and take advantage of opponent's weaknesses, could be stronger. Of course, any such strategy would necessarily deviate from nash equilibrium and thus be vulnerable itself to more advanced strategies.

PS: the winning RPS bot, "Icoaine powder", is explained by the author in this fascinating page: http://ofb.net/~egnor/iocaine.html . A must read for any AI enthusiast.