Re: UPDATE #3
 

Here is a simple solution. If an alliance has 2 or more no shows they will be penalized 10 points for each no show over 1. That gets rid of the 0-0 tie.

Re: UPDATE #3
 

Hardly. You have based this assumption on a fundamentally unsound application of game theory.

Using some VERY basic assumptions: If an alliance fields no robots, nobody can win. If an alliance fields more robots than the opposing alliance, the alliance with more robots will win. If both alliances field the same number of robots, nobody wins.

BLUE ALLIANCE
3 2 1 0
RED 3 Robots (0,0) (1,0) (1,0) (0,0)
ALLIANCE 2 Robots (0,1) (0,0) (1,0) (0,0)
1 Robot (0,1) (0,1) (0,0) (0,0)
0 Robots (0,0) (0,0) (0,0) (0,0)


From a pure strategy point, both alliances will go with 3 robots, as that is the dominant strategy - that is for every scenario, 3 robots has a greater or equal outcome to any other strategy.


Now the biggest assumption is that if both alliances play the same number, no body wins. So we'll factor in X as the probability of Blue Alliance winning with equal numbers of bots (allowing for X < 0 if Blue will 'probably' lose, but X<=1,X>=-1). Let's also assume that a loss does more than not harm a team, but negatively affects it.
This gives us:

BLUE ALLIANCE
3 2 1 0
RED 3 Robots (-X,X) (1,-1) (1,-1) (0,0)
ALLIANCE 2 Robots (-1,1) (-X,X) (1,-1) (0,0)
1 Robot (-1,1) (-1,1) (-X,X) (0,0)
0 Robots (0,0) (0,0) (0,0) (0,0)

Thus, at the very least Blue's dominant strategy is 3 if X>=0, and Red's dominant strategy is 3 if X<=0, so one team will play 3 regardless.

Let's go one step further (without working out all of the mixed-strategy equilibriums that is). Let's assume that any team that fields no robot LOSES a match where the other team fields any robots(consider any sporting event, a complete no show results in a forfeit victory for the team that is there). Even if that is not a judged outcome (that is, if the judges declare no show = tie), scouting teams will be disappointed by not being able to see robots in action, and that will likely negatively affect their decisions, hurting the chances of a no show team getting picked for a final alliance.

So we are given:

BLUE ALLIANCE
3 2 1 0
RED 3 Robots (-X,X) (1,-1) (1,-1) (1,-1)
ALLIANCE 2 Robots (-1,1) (-X,X) (1,-1) (1,-1)
1 Robot (-1,1) (-1,1) (-X,X) (1,-1)
0 Robots (-1,1) (-1,1) (-1,1) (-1,-1)

This shows that both alliances will ALWAYS play 3 robots if possible.

Re: UPDATE #3
 

I think you could argue this assumption.

Re: UPDATE #3
 

Which is why I specifically said

While it is certainly possible for 2 robots to beat 3, in an average playing field, with randomly assigned team mates, the 3 robot team usually has a significant advantage over a 2 robot team.

Re: UPDATE #3
 

Any alliance that allows a 0 score for the other team would be at fault themselves. It is too easy to score a few for the other alliance just to preserve your advantage in the following matches. In the end play to have fun and watch how other robots work:)

Re: UPDATE #3
 

If both sides play "optimally", the alliance with 2 robots will always win, since two trailers cannot hold as many game pieces as 3.

(I'm just playing devil's advocate; I know that this won't be a practical limitation on scoring) :D

Re: UPDATE #3
 

I don't think so, while the 2 bot alliance will have more targets, they can only focus on one at a time. While the other alliance will have another bot to "pick" and "bully" with.

Re: UPDATE #3
 

Unfortunately they will have a hard time with that, because if the other side is also playing optimally they can better control the ball supply (there may be more room for balls in trailers, but the 2 robot alliance will not be able to get as many balls to score with).

Re: UPDATE #3
 

If there are more than 2 match scores in any regional in which an alliance fields 2 or more robots and attains a (pre-penalty) score of 0, I'll eat my hat. And yours, too.

Re: UPDATE #3
 

I'm gonna buy one of those big 10 gallon hats, just so you have a hard time of it. :)

Re: UPDATE #3
 

It seems reasonable, so I am assuming it will be the case, that it turns out that the trailer is left on the field for a no-show robot. It doesn't happen often, but it does happen, so my team has been discussing strategies for dealing with a no-show alliance partner. We think that the best course it to put the no-show at the outpost because of the outpost PS finite ball supply and then to "rescue" it in autonomous mode by sweeping it away from the outpost with our robot, for which we plan to have such autonomous modes.