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Author Topic: New probability of winning graphs for 2p games  (Read 15455 times)

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rrenaud

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New probability of winning graphs for 2p games
« on: September 24, 2011, 03:15:02 am »
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Are they so bad that they should just be removed? 
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AJD

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Re: New probability of winning graphs for 2p games
« Reply #1 on: September 24, 2011, 03:19:01 am »
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What exactly do they represent?
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rrenaud

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Re: New probability of winning graphs for 2p games
« Reply #2 on: September 24, 2011, 03:23:47 am »
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I trained a linear logistic regression model on the data that tries to predict the probabilities of winning given game state.  It uses a fairly simple set of features I choose.  The features are mostly the current score, players deck composition, the action balance of their decks, etc.  The model barely has any card interaction effects (no card by card features), so it's definitely a big over simplification of the game.
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DStu

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Re: New probability of winning graphs for 2p games
« Reply #3 on: September 24, 2011, 03:28:43 am »
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Are they so bad that they should just be removed?

Just looked at one, but I would clearly say: Let them in.
a) They are completely at the bottum, so they don't disturb
b) If they are really so bad, maybe you get some feedback where they are the worst, which could let you improve them if you are interested in, which I think you are...
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DStu

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Re: New probability of winning graphs for 2p games
« Reply #4 on: September 24, 2011, 04:17:47 am »
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Edit: For example, do you have any idea what it thought by this oszillation at the end here:
http://councilroom.com/game?game_id=game-20110922-130953-e192036f.html

I bought nothing suspiscous in turn 15-16, two selfreplacing action (Alchemist), a Treasure (Bank) and a terminal (Torturer) and he goes like mad. Piles are far from ending, Victories also, my opponent didn't buy anything at all. Yes, I lost my Alchemist stack (think I could have avoided that), but I don't see your model testing on anything that can see that, if I read your code correctly.

Anyway, it seems like it sees it, kind of intersting...
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rrenaud

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Re: New probability of winning graphs for 2p games
« Reply #5 on: September 24, 2011, 11:05:04 am »
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Maybe that's an outpost bug?  Maybe it thinks your outpost turn is your opponent's turn?
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Euphemism

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Re: New probability of winning graphs for 2p games
« Reply #6 on: September 24, 2011, 11:35:52 am »
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Win prob graph is mysteriously absent under Chrome, but present under Opera. Also, rather than a scale of 0 to 2, if it's configurable, maybe you could make it a scale of 0 to 100%? With at least the 50% interval marked (I thought it would be fine to see the 50% whenever the two lines cross, but it doesn't actually work like that... seems like only one player's % gets updated at a time)
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WanderingWinder

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Re: New probability of winning graphs for 2p games
« Reply #7 on: September 24, 2011, 12:58:06 pm »
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On Firefox, I can see a spot for the graph, but it's just a blank white space.
Love the concept, even if it is pretty flawed at first. I'd keep it there.

DStu

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Re: New probability of winning graphs for 2p games
« Reply #8 on: September 24, 2011, 01:07:01 pm »
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On Firefox, I can see a spot for the graph, but it's just a blank white space.
Love the concept, even if it is pretty flawed at first. I'd keep it there.
I'm on FF, too (6.0.2), and it works for me.
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WanderingWinder

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Re: New probability of winning graphs for 2p games
« Reply #9 on: September 24, 2011, 01:15:09 pm »
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On Firefox, I can see a spot for the graph, but it's just a blank white space.
Love the concept, even if it is pretty flawed at first. I'd keep it there.
I'm on FF, too (6.0.2), and it works for me.

I'm also on 6.0.2
This is weird.
Can you see the graph here: http://councilroom.com/game?game_id=game-20110923-214239-b793cbf8.html for instance?
I wonder what the reason is for the difference...


Edit: Also I can see the money and VP graphs, just not this new one.

DStu

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Re: New probability of winning graphs for 2p games
« Reply #10 on: September 24, 2011, 01:32:10 pm »
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Can see the graphs. I am on Linux here, but that shouldn't make difference for the browser.  No addons installed for the Browser...
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rrenaud

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Re: New probability of winning graphs for 2p games
« Reply #11 on: September 24, 2011, 01:37:24 pm »
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Euphemism, I try to tell the graphing library that the y axis should only go up to 1, but maybe that fails sometimes?

WW, I see the win probability graph on that page.  Can you try a hard browser refresh?
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WanderingWinder

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Re: New probability of winning graphs for 2p games
« Reply #12 on: September 24, 2011, 01:43:52 pm »
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Can see it now, and now I'm gonna try to start looking through my games to see what level of 'understanding' this thing has.

jonts26

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Re: New probability of winning graphs for 2p games
« Reply #13 on: September 25, 2011, 02:34:50 pm »
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I think this is a great idea, but I'm a little confused at the implementation. For starters, the two lines don't always add up to 1. It seems to me that at any point, if I have a 60% chance of winning, my opponent should have a 40% chance (assuming 2P). Also at the end of the game, the winning player doesn't always have 1, while the losing player has 0. Once the game is over, the win probability should be 1 for someone.

This reminds me somewhat of the WPA graphs you get in baseball. See here for an example. http://www.fangraphs.com/wins.aspx?date=2011-09-24&team=Mets&dh=1&season=2011

These are generated based on the current game state (inning, score, runners on base, outs) and probabilistic models.

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Buggz

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Re: New probability of winning graphs for 2p games
« Reply #14 on: September 25, 2011, 05:56:02 pm »
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if I have a 60% chance of winning, my opponent should have a 40% chance (assuming 2P).
Unless there a chance of a tie. But, in order to follow the rules of "both players rejoice in their shared victory" the sum should be over 1.
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rspeer

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Re: New probability of winning graphs for 2p games
« Reply #15 on: September 25, 2011, 06:06:20 pm »
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Sharing victory doesn't mean you get all of it any more than sharing a cookie does. Otherwise you could maximize victory by agreeing with your opponent beforehand to score 27 points.

My guess at why the lines might not add up to 1 would be that my chance of winning at the start of my turn isn't necessarily the same as my chance of winning at the start of your turn.
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jonts26

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Re: New probability of winning graphs for 2p games
« Reply #16 on: September 25, 2011, 06:31:15 pm »
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Right, but the start of my turn and the start of your turn are two different game states. Our odds of winning will change and should be updated for each of us at the beginning of each of our turns.

I would also see a tie as we each get .5 of a win at the end of the game. Still needs to sum to 1.
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WanderingWinder

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Re: New probability of winning graphs for 2p games
« Reply #17 on: September 25, 2011, 06:46:13 pm »
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2 issues. One is that I think the numbers on the graph like 5 mean the probability of you winning (plus half the probability of you tying) after your turn 5. And for your opponent, the same after THEIR turn 5. So you probably want like half-turn increments instead of the slightly disjoint thing we have, but that might be a bit hard to program in. Further, I think there's either a slight bug or a rounding issue, because I think the reason a probability of 2 is popping up sometimes is because in those cases, the evaluator thinks someone's probability has gone over 1. At least that seems to be the case in the instances I remember.

Finally, I'd like to wonder why it doesn't jump to 1/0 when the game has ended. Probably I'm interpreting stuff wrong.

rrenaud

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Re: New probability of winning graphs for 2p games
« Reply #18 on: September 25, 2011, 07:56:05 pm »
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The model doesn't say the probability of winning at the game end is either 0 or 1 because it underfits the data. It uses this:

http://en.wikipedia.org/wiki/Logistic_regression

which finds weights on features I selected.  The features are all independent, it's not even smart enough to say, if (game_over && p1.score > p2.score), because it only has per feature weights, it doesn't do any feature combination.  Can I con a stats guy reading this into building better models? :P

The reason why the probabalities don't add to one is because it only puts the refreshes the probability of winning once per turn per player.  I should probably fix that.

Does the probability ever exceed 1?  I think the graphing library I am using has a bug, or I am using it wrong, but I don't think I ever tell the library to graph a number > 1.
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WanderingWinder

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Re: New probability of winning graphs for 2p games
« Reply #19 on: September 25, 2011, 11:33:24 pm »
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Perhaps also if it hits exactly one. All the games I'm finding that have the 2 bug have the issue that the probability at least gets very close to 1; it's possible that every one I see actually has over half the possible VPs being gained before game end - a quick check and I don't see anything to contradict that, except the presence of VP chip cards in a game where only I'd bought them and had a 6-1 province lead, big curse lead, and a few VP chips to boot, where your model might either not understand that or round it to 1, as honestly my win probability there WAS 1, assuming I wasn't a total idiot.

Buggz

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Re: New probability of winning graphs for 2p games
« Reply #20 on: September 26, 2011, 04:18:14 am »
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Sharing victory doesn't mean you get all of it any more than sharing a cookie does.
It would be the exact opposite because you share a metaphysical thing: the victory.

Here's (another) comparison to poker. WSOP shows you the chances of winning a hand at showdown both pre- and postflop for each participating player. They chose to include ties into each players chances because a split pot still gives the players chips, and thus you can see percentages such as "Player A: 95%, Player B: 92%". You'd think those numbers are useless, but they actually tell you the chances of the player winning some chips at all, not necessarily the whole shebang.

Whether or not a graph includes ties into the chances of winning or not is imho just a matter of preference and doesn't change anything one way or another. It should be clear what the numbers mean though.
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DStu

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Re: New probability of winning graphs for 2p games
« Reply #21 on: September 26, 2011, 06:06:02 am »
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Sharing victory doesn't mean you get all of it any more than sharing a cookie does.
It would be the exact opposite because you share a metaphysical thing: the victory.

But as the Music Industry teached us, that's at least as bad as sharing real things...
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ehunt

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Re: New probability of winning graphs for 2p games
« Reply #22 on: September 30, 2011, 01:02:13 pm »
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Possession seems to confuse this graph a little?

http://councilroom.com/game?game_id=game-20110814-103840-7887199d.html

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rrenaud

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Re: New probability of winning graphs for 2p games
« Reply #23 on: September 30, 2011, 01:11:31 pm »
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Possesion and outpost both.

Argh, special cases! :(
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ehunt

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Re: New probability of winning graphs for 2p games
« Reply #24 on: September 30, 2011, 03:34:14 pm »
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I think there may also be a gardens bug? Here, on the graph, my probability of winning is something like a tenth of my opponent's probability of winning, even at the very end after my gardens become worth provinces (the game at that point is clinched for me):
http://councilroom.com/game?game_id=game-20110516-094825-df525d77.html

(I like this feature a lot by the way! I've looked up all the games in memory where I've had a lucky comeback. It's funny how they're easier to remember than the games in which my opponent has had one.)

By the way, one thing that might be helpful is more points on the y-axis.
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