May 13 RussCon Report:

There were 10 of us, and we played 9 games. The April 29 Devil (JonathanB) didn't make it and so forfeited the dining table rights. This led to the normally ghettoized RoboRally actually being played on the dining table! We carefully made a more reasonable map:

+---------+---------+---------+ | 3| |2 | | | | | | | | | | 1| |4 | +---------+---------+---------+

The flags were not in hard to reach places, so we didn't take forever to finish! Woohoo. We used the pit and teleport filled Chasm map in the center, which turned out to be rather fun and make for some rapid movement when the cards permitted. There also turned out to be quite a few conveyor belts off the edge which came into play. Unusually, Jay and William were both completely eliminated during exactly the same turn! (But Jay died 2 phases before William, giving William a better rank...) This also led to a first-time anomaly: after survivors Tim & I finished RoboRally, 2 other games continued on the floor while the dining table sat unused. A curious scheduling quirk.

It was also fun to play Titan the Arena again. A very curious little game. Since you can often calculate exactly what people's final scores will be during the final round, it can lead to some heavy diplomacy and kingmaking! And any secret bets that remained secret to the final round add a fun element of bluffing.

Wizards is a trick-based card game I'd never seen before which Brady brought. I didn't play and know nothing about it, except their score sheet reveals that Dawn seriously kicked their asses.

We were graced with the unexpected presence of Randy this week, a new face to many of you, but an old time gamer and Go player who'd forsaken the True Path of gaming these past couple years out of a misplaced sense of priorities and finishing a PhD or some such nonsense. It is good to see Randy back in action!

William brought a cool windup Nunzilla toy -- thanks! "Say your prayers! Nunzilla comes, breathing fiery sparks as she walks!" If only she were smaller, I'd have used her as my RoboRally robot... She was useful as an informal Agonization Phase ender: "Ok, we're winding up Nunzilla -- you have until she finishes walking and sparking to do your turn!"

In other news: correspondents report that Scott of Chicago was recently married. Congratulations, but you should have come to Austin for a fun-filled honeymoon of boardgaming!

And Tim got himself a car -- cool beans!

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Evening's results:

Your humble host won RoboRally, Titan the Arena, and Entdecker.

William won Settlers and Titan the Arena.

JP won the amazingly popular Euphrates and Manhattan (by just 1 point!).

Dawn won the incredibly popular Euphrates and Wizards.

Rank ratings: 0.7273 RussW (4) 0.5000 JP (4) 0.3333 Tim (1) 0.2308 William (5) 0.1667 Dawn (4) -0.1538 James (5) -0.3333 Marty (4) -0.5556 Randy (3) -0.6000 Jay (2) -1.0000 Brady (2) Win ratings: 0.7419 RussW (4) 0.5000 Dawn (4) 0.5000 JP (4) 0.2800 William (5) -1.0000 Tim (1) -1.0000 James (5) -1.0000 Marty (4) -1.0000 Randy (3) -1.0000 Jay (2) -1.0000 Brady (2)

(Number in parentheses = # games played.)

And so the partial ordering combining these 2 ratings is:

RussW 9 7 / \ / \ / JP 6 5 Dawn 4 4 / \ \ Tim 3 3 William 3 3 \ | / \ | / James -1 1 Marty -3 -1 Randy -5 -3 Jay -7 -5 Brady -9 -7

The first numbers in the partial ordering are

(#opponents you're > than - #opponents > than you),

as in previous weeks. The second numbers are

(#levels you're above - #levels above you),

and are discussed further below.

This leads to total ordering:

RussW, JP, Dawn, Tim=William, James, Marty, Randy, Jay, Brady.

Thus it turns out that I am the Devil! Woohoo! Next week I rule the dining table. It's about time.

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Distilling the data to a total ordering: the plot thickens!

Earlier reports with the partial ordering have mused about whether # opponents or # levels is a more meaningful measure of performance. In most cases they work out to the same total ordering, but not always. I've previously just been showing the #opponents measure. The second numbers in the above graphic are

(#levels below you - #levels above you).

E.g. JP has 6 levels below him and 1 above him. Dawn has 5 levels below her and 1 above her. James has 4 levels below him and 3 above him (always count the maximal length path in both directions).

The #opponents measure seems obviously meaningful -- if I'm > more people and have fewer people > me, that's clearly good.

But the #levels measure also seems meaningful. If I'm > 2 people who are equal or incomparable (i.e. 1 level), that somehow seems a little less impressive than being > 2 people, one of whom is > the other (i.e. 2 levels), because the latter means I'm 2 strength levels up instead of 1 strength level. Consider the following hypothetical partial ordering:

T 8 4 / \ / \ N 3 1 K 2 2 /|\ \ / | \ \ / | \ L 0 0 X Y Z-1-1 / \ | / M -2 -2 \ | / / B -8 -4

(where X, Y, Z are all -1 -1, i.e. they are each > 1 opponent (B) and have 2 opponents > them (N & T), and likewise for levels.)

Note that N > 4 opponents (X, Y, Z, B) and N > 2 levels. K > 3 opponents (L, M, B) and K > 3 levels. (Both N & K have 1 opponent and 1 level above them.)

Now note that if we use #opponents for our partial order we get:

T N K L X=Y=Z M B

But if we use #levels for our partial order we get:

T K N L X=Y=Z M B.

I.e., K and N have different final positions depending on whether we measure #opponents or #levels!

Just looking at that partial ordering, it's not obvious whether it seems N or K performed better: N beat more opponents than K, but K beat a stronger opponent (L) and so K is at a higher level than N. Both seem worthy.

How to resolve this dispute between 2 different measures which both seem to have some intuitive validity? Iterate the procedure! Just as we consider the partial ordering from the win and rank ratings, we can now consider the partial ordering from the #levels and #opponents ratings! I.e., partially order people by the pairs formed by (#opponents, #levels) vectors. This gives:

M / \ N K \ / L X=Y=Z M B

And now both #levels and #opponents end up the same for N & K, and we end up with

M N=K L X=Y=Z M B.

Thus N & K of the original diagram end up being considered equally good, which feels reasonable to me. What do you think?

I hypothesize that iterating this process on a finite partial ordering (using #opponents and #levels) is guaranteed to eventually terminate with a total ordering. Now that Randy has a math PhD, I leave it as an exercise for him to prove this conjecture or construct a counterexample.

Bring your proof on April 20!

Aloha,

Russ