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[rrenaud]

This feature is due almost entirely to http://councilroom.com/player?player=tlstyer.  He came from the internet came and gave me a nice implementation of an idle idea I had a year ago.  Yay open source!

This tries to answer question, I am going for an X/Y combo, what order should I buy the cards?  It contains two heatmaps of how often players in a particular X/Y part of the combo win. One for the final game state (what should my deck look like when this is over), and one for all intermediate game states (how should I get it there).

http://councilroom.com/optimal_card_ratios?card_x=Ambassador&card_y=Silver (everyone's favorite question)
http://councilroom.com/optimal_card_ratios?card_x=Tunnel&card_y=Warehouse
http://councilroom.com/optimal_card_ratios?card_x=Gardens&card_y=Workshop
http://councilroom.com/optimal_card_ratios?card_x=Potion&card_y=Alchemist

[DStu]

So "Progressive" is: 'Win Rate conditioned on X/Y has been intermediate game state [edit: and conditioned on X and Y being in the supply]'?

edit: For the row/line with zero X/Y probably you also want to condition on X and Y being in the supply, otherwise you would also consider the games where they aren't...

[rrenaud]

Yup, that's exactly the definition of progressive.  It's a little weird if the same card is bought and trashed in the same turn, but funny issues like that aside, you've got it.

[Davio]

Great feature.

I always thought the second Potion was redundant.

The way I read the Progressive table is: You start at 0/0, you can go up or left right and both will have an impact on your end game win ratio.
If you look at Workshop/Gardens, you can see it's better (and logical) to go up (gain Workshops) first and go right (get Gardens) at about 8.

[DStu]

I know it's already in the output, but how about plotting a path from 0/0 to the maximum winrate along the states with best winrate?

[Qvist]

Great feature.

I always thought the second Potion was redundant.

The way I read the Progressive table is: You start at 0/0, you can go up or left and both will have an impact on your end game win ratio.
If you look at Workshop/Gardens, you can see it's better (and logical) to go up (gain Workshops) first and go right (get Gardens) at about 8.

I second "Great feature".
But I still have some problems with drawing conclusions. Taking the Workshop/Gardens example. It seems best to get as many Workshops as you can get first.
But in the end you want as many Gardens as you can get. But here it seems best with only one Workshop (both Progressive and Final). How does that fit?

Other interesting graphs:
http://councilroom.com/optimal_card_ratios?card_x=Duke&card_y=Duchy
I would conclude to switch to Duke with 5 Duchies at the earliest.

And for the Gardens vs. Silk Road discussion:
http://councilroom.com/optimal_card_ratios?card_x=Silk+Road&card_y=Gardens
I would conclude: No matter what you choose (Gardens or Silk Road), just stick to it. Get all of one first, than get all of the other ones.

[DStu]

But I still have some problems with drawing conclusions. Taking the Workshop/Gardens example. It seems best to get as many Workshops as you can get first.
But in the end you want as many Gardens as you can get. But here it seems best with only one Workshop (both Progressive and Final). How does that fit?

http://xkcd.com/552/

What is happening most likely is: In most cases where you get as many Workshops as you can get, you are not contested on the Workshops. So your opponent most likely goes for some other strategy, which most likely will lose to Workshop/Gardens. Actually, Geronimoo's sim goes to 8 WS if the opponent does not play Gardens.
So in the samples that get many Workshops have an opponent that play suboptimal, in which cases the optimal play for you is to get as many WS as possible. But this are only a few games, you see somewhat 200 games out of 60.000. In most cases, you don't have an suboptimal opponent, which alone will lower you winchance. In these cases, you don't want as many Workshops, but need to get the Gardens quickly.
So the problem is that, depending on you opponent, there are 2 different strategies how to play WS/Gardens, which disturbes the whole data.

[DStu]

More feature-request:
Can we have a uniform color-scale over all graphs? At teh moment it seems to adjust itself to maximum-minimum value. Or what do other people think?

[Qvist]

But I still have some problems with drawing conclusions. Taking the Workshop/Gardens example. It seems best to get as many Workshops as you can get first.
But in the end you want as many Gardens as you can get. But here it seems best with only one Workshop (both Progressive and Final). How does that fit?

http://xkcd.com/552/

What is happening most likely is: In most cases where you get as many Workshops as you can get, you are not contested on the Workshops. So your opponent most likely goes for some other strategy, which most likely will lose to Workshop/Gardens. Actually, Geronimoo's sim goes to 8 WS if the opponent does not play Gardens.
So in the samples that get many Workshops have an opponent that play suboptimal, in which cases the optimal play for you is to get as many WS as possible. But this are only a few games, you see somewhat 200 games out of 60.000. In most cases, you don't have an suboptimal opponent, which alone will lower you winchance. In these cases, you don't want as many Workshops, but need to get the Gardens quickly.
So the problem is that, depending on you opponent, there are 2 different strategies how to play WS/Gardens, which disturbes the whole data.

That sounds plausible. Thanks for that.

[Geronimoo]

This is great fun, but I wouldn't draw conclusions from these things: people play far from optimal and there are too few games.
You can find (close to) optimal play for a lot of these combos with the simulator.

[rrenaud]

I am not sure the "get 5 duchies before first duke" idea is bad.  Consider if you are playing against a Province player, you will be contested for the Duchies, but not for the Dukes.  I am sure I could find decent players recommending it if I searched enough.

Of course, this does suffer from being unconditioned on opponent's strategies.  There could be two very different paths depending on the opponent's strategy, and what you see is a probability weighted mix over all opponent's strategies.  So really you might want to go in one direction vs one kind of opponent, and a totally different direction vs another, and you'll see some muddled incoherent mixture that does well in the this output.

The no second potion thing MUST be wrong!  I usually like getting the second potion in Alchemist games.

Of course, I don't recommend just blindly trusting the data, but it could be useful to think about.  Also, optimal play is sufficient but not necessary for the stats to tell the right thing.  You need that the players play equally badly conditioned on their state.  Then there is no bias since the skill problems cancel.  I think this condition will be violated for things like Ambassador (I'd bet on a randomly picked player who went 2 Ambassadors vs a completely random player), but should usually help the data from not being too off.

[DStu]

I am not sure the "get 5 duchies before first duke" idea is bad.  Consider if you are playing against a Province player, you will be contested for the Duchies, but not for the Dukes.  I am sure I could find decent players recommending it if I searched enough.

Of course it's a good idea. In a mirror, if you split Duchies 5/3, you have almost won. When you go for the Duke once you have 4 Duchies you give your opponent the chance of splitting them 4/4, so you are just one Duke in front, so maybe they also split 4/4, and the game decides on the Estates. You only have a one-turn advantage at this point to get a tie after Duchy/Dukes.
If you split 5/3 and your opponent gets the Duke, even if you split the Dukes 3/5, you have 30 vps against 24. You still have a one-turn advantage for this goal (you need 3 Dukes, they 4), but you are also 6 points in front. As there is no danger of someone getting a province at this state of the game, you just get two Estates and the game is yours.
Someone getting a Province earlier of course changes this, but in that case you should get more than 8 Duchies+Dukes in total.

[WanderingWinder]

I am not sure the "get 5 duchies before first duke" idea is bad.  Consider if you are playing against a Province player, you will be contested for the Duchies, but not for the Dukes.  I am sure I could find decent players recommending it if I searched enough.

Of course it's a good idea. In a mirror, if you split Duchies 5/3, you have almost won. When you go for the Duke once you have 4 Duchies you give your opponent the chance of splitting them 4/4, so you are just one Duke in front, so maybe they also split 4/4, and the game decides on the Estates. You only have a one-turn advantage at this point to get a tie after Duchy/Dukes.
If you split 5/3 and your opponent gets the Duke, even if you split the Dukes 3/5, you have 30 vps against 24. You still have a one-turn advantage for this goal (you need 3 Dukes, they 4), but you are also 6 points in front. As there is no danger of someone getting a province at this state of the game, you just get two Estates and the game is yours.
Someone getting a Province earlier of course changes this, but in that case you should get more than 8 Duchies+Dukes in total.

In fact, it should almost certainly be MORE than 5 if you're going duchy/duke. If you're fighting a provincing player, you basically need at LEAST 6 duchies, more preferably 7.
This changes with more players.

[Atto]

Interesting feature. Thanks for that.

Compare this:
Village/Smithy - Fazit: Buy approx. 3 Smithies, don't buy Villages. (Which is well known to be correct.)
Village/Torturer - Fazit: Buy 2 or 3 Torturers, then alternate between Village and Torturer. (Which is imho a quite good rule of thumb.)

[rrenaud]

I was thinking about this a bit.

Is there some algorithmic way of finding "interesting" combination graphs?

This one is uninteresting.  The diagonal is bad.  http://councilroom.com/optimal_card_ratios?card_x=Smithy&card_y=Envoy

This one is also uninteresting.  Just want moar Hunting Parties.
http://councilroom.com/optimal_card_ratios?card_x=Horn+of+Plenty&card_y=Hunting+Party

This is somewhat more interesting, the diagonal looks good.
http://councilroom.com/optimal_card_ratios?card_x=Jack+of+All+Trades&card_y=Silver

[DStu]

would it make sense to include the Prices?

[rrenaud]

What do you mean, include the prices?

[DStu]

What do you mean, include the prices?

Followers et. al. are not in the optimal card ratios at the moment (or at least I don't see them). So they would make a quite small 2x2 chart, but nevertheless the winchance given the order you buy them might be interesting.

[Thisisnotasmile]

Prizes.

[DStu]

Prizes.

thx.