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[painted_cow]

Does anyone know how the 3 player games are rankend?

Lets assume I win a 3 player game. Councilroom says that I win vs Player 2 and Player 3 (I am Player 1). Do I really get 2 wins out of it?

Lets assume I lose a 3 player game. Councilroom says that lose vs Player 2 (highest amount of points) and draw with Player 3 (I am Player 1 again). So I lose to one player and get a draw with the other? Or will the Isotropic server only count my loss to Player 2 in this case?

How are draws treated in general? When I draw to a low level player I will lose some points?!

[rrenaud]

Win points == total winners / total players.  I've forgotten how I account for partial wins on the record, but win points are a better measure than win/loss/ties anyway.

On isotropic, from reading dougz's trueskill code, the order matters for multiplayer games.  It's better to finish 2nd than 4th.  Because of the complicated nature of trueskill, finishing 2nd in a 4 player game is not the same as losing a 2p game against the winner, and winning two 2p games against the 3rd and 4th players.

If you tie with a lower rated player, you can lose points.

[painted_cow]

thx for this information. Its quite important to know, that getting second is better than third. Interesting, that you better get the last province, even if you cant win with it, but getting second place for sure.

So basically if I have a higher average win points in 3-player than in 2-player this would be better for me (in terms of getting points...). Or are these number not comparable to each other?

Sorry for this detailed questions 

[rrenaud]

I haven't thought much about trying to climb the isotropic ladder by playing 3p games rather than 2p games. 

For skilled players, avg win points will tend to be higher for 3p than for 2p (the max for 3p is 3, max for 2p is 2), so that alone should not make you think you are better when playing 3p than 2p.

From a game design rather than statistics sense, I dislike encouraging players to take a guaranteed 2nd rather than a possible first.  If I designed the isotropic rating system, I'd make 2nd == last for multiplayer games.

[painted_cow]

For skilled players, avg win points will tend to be higher for 3p than for 2p (the max for 3p is 3, max for 2p is 2), so that alone should not make you think you are better when playing 3p than 2p.

I also thought, that these numbers cant be compared. At least the automatch 3-player games are not that bad imo, even for ladder issues. Why do only a really small number of the good players play 3p?

Before today I always aimed to getting first place in a 3-player-game, even when it was very unlikely instead taking a second place.

[rod-]

For skilled players, avg win points will tend to be higher for 3p than for 2p (the max for 3p is 3, max for 2p is 2), so that alone should not make you think you are better when playing 3p than 2p.

From a game design rather than statistics sense, I dislike encouraging players to take a guaranteed 2nd rather than a possible first.  If I designed the isotropic rating system, I'd make 2nd == last for multiplayer games.

Avg win points for a given win % will be greater, but avg win % for a given skill in 2p shouldn't be equal to avg win % in 3p.  I contest your claim.  If you lose 40% of your games in 2p, why wouldn't you lose 64% of your games in 3p? (Lose to 2p * lose 3p).  (I'll admit that my personal statistics do NOT bear my point out, but i'm fairly sure that 25 of the 45 3player games on my record are against a grand total of 0 levels summed across my opponents - the people that play 3p are in general quite low-ranked)

From a game design standpoint, i much prefer people being incentivized to claim 2nd place rather than fight for 1st, as often in 3p, a player has a 'kingmaker' decision where he can take 3rd (but still have some marginal 'hope' of 1st) by not claiming the last province or take 2nd by taking it, and the choice he makes influences who ends up in 1st.  Being able to predict his choice ("he'll take 2nd because it's better for him") makes it much easier to buy the penultimate province, resting fairly easily on the knowledge that the next player will take it if possible.

[rrenaud]

The clearest heuristic reasoning I can give is due to the saturation effects (like the 2 max vs 3 max) that I gave above.

Consider the limit case where a superstar wins 99% of games against average players in 2p games.  Each average individual has a 1 in 100 chance of winning the lottery or hitting the hail mary to win. You might expect him to win 98% or something like that of his 3p games (he just needs to dodge 2 independent, rare events instead of 1), and so his 2p and 3p win rate would be something like 1.98 and 2.94 respectively.

The behavior stays at lesser skill differentials, but obviously to a lesser degree. I suggest you run/tweak this small program until you believe me, or can come up with a similarly small program that shows that I am wrong. 

Code: [Select]

#!/usr/bin/python

import random

GOOD_P_MAX = 120
AVG_P_MAX = 100

def sim(strength_list):
  outcomes = [random.random() * s for s in strength_list]
  winner = max(outcomes)
  # ignore ties, will basically never happen with random floats anyway.
  return outcomes.index(winner)

def sim_many(strength_list, N):
  ret = [0 for i in strength_list]
  for i in xrange(N):
    ret[sim(strength_list)] += len(strength_list)
  for ind, v in enumerate(ret):
    ret[ind] = v / float(N)
  return ret

print sim_many([GOOD_P_MAX, AVG_P_MAX], 100000)
print sim_many([GOOD_P_MAX, AVG_P_MAX, AVG_P_MAX], 100000)
# sanity check that order doesn't matter
print sim_many([AVG_P_MAX, AVG_P_MAX, GOOD_P_MAX], 100000)

output:

[1.1701600000000001, 0.82984000000000002]
[1.3330200000000001, 0.83103000000000005, 0.83594999999999997]
[0.83675999999999995, 0.83099999999999996, 1.3322400000000001]

[rspeer]

I haven't thought much about trying to climb the isotropic ladder by playing 3p games rather than 2p games. 

In terms of mean skill, there shouldn't be any reason for it to come out different, unless you're actually better or worse at 3p.

But what it does do is it decreases your variance twice as fast (per game) by comparing you to twice as many people. So if you play a 3p game faster than two 2p games, your level goes up a bit faster because it's catching up with your skill faster. (This has diminishing returns, of course, as you play more.)