CORDIAL MINUET ENSEMBLE

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#26 2014-11-30 23:55:12

AnoHito
Member
Registered: 2014-11-24
Posts: 116

Re: More Thoughts on Cordial Minuet/The Problem With Tributes

I said it should be taken at the end, but you might have missed my edit. Well, the thing is, taking the tribute at the end leads to a low tribute when a game goes back and forth and little money exchanges hands, and a higher tribute when a player busts. If things didn't work this way, close games would keep costing each player more and more money the longer they lasted, so it would never be to your advantage to play a close match. If you sensed that the other player had a strategy that wasn't obviously worse than yours, you should just leave the match right away or you would probably lose money. At least that's my take on it. When the game is eventually released, my strategy would be to take advantage of the newer players who didn't know what they were doing for as long as I could, and then quit playing when the new players eventually dried up because it would be too difficult to make money against more skilled players. Keep in mind that in most games, the higher the level of play, the smaller the difference in skill tends to be between two players. If that difference is not great enough for at least one player to make money in Cordial Minuet, then both players end up losing money. This is why it's very important that even games (even long ones) don't cost too much money.

Asminthe wrote:

Just saw your edit. While taking the tribute at the end would resolve the problem of forcing the game to last until someone busts, I don't know how it is an improvement over the current system, especially considering the tribute percentage would probably have to be increased in order to maintain the same profit for the house.

Economics 101: The correct price to charge for something is the price the most people are willing to pay. Using myself as a sample size of one, I would not continue to play for very long given the current tribute system. With my style of play I would tend to lose money once the unskilled players dried up, and I don't want to be put in the position of using a less conservative (worse) betting system in order to have a chance at making money.

Last edited by AnoHito (2014-12-01 00:01:39)

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#27 2014-12-01 00:34:13

zed
Member
Registered: 2014-11-25
Posts: 25

Re: More Thoughts on Cordial Minuet/The Problem With Tributes

Asminthe:
> I'm curious why you think that betting actions are cheap and unsatisfying.

Obviously this is subjective, and rather to the side of the discussion here.
I should probably say "differently satisfying" rather than "unsatisfying";
betting games are interesting too, but they have a very different feel from
"pure" simultaneous move games. As for what it is I mean by "pure"... nothing
well-defined, I imagine, but I guess it's essentially a matter of this:
picking a number based on estimations of probabilities feels too directly like
calculation. Of course all simultaneous move games come down in the end to
estimating probabilities, and when played properly to calculating probability
distributions. But I find games in which the reasonable available moves on any
turn are well-differentiated, and not too large in number, to be satisfying in
a way betting games aren't. Sadly I know very few examples of such games, and
none I'm really happy with.

As for "cheap" - I just mean that if you take a game with hidden information,
and add a betting to it, it suddenly becomes massively richer.

I don't at all mean to put CM down here - it's a very neat and
canonical-feeling betting game, and the world needed it too!

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#28 2014-12-01 00:41:15

zed
Member
Registered: 2014-11-25
Posts: 25

Re: More Thoughts on Cordial Minuet/The Problem With Tributes

jasonrohrer:
> As for simultaneous decision games that are intractable to solve, I think
> space of possible strategies is exponential in the number of rows/columns.
> So... wouldn't 8x8 or 10x10 do the trick there?

I expect so! But I doubt it would be much fun as a game - even an 8x8 matrix
is just too much information to process. I expect.

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#29 2014-12-01 03:16:21

Asminthe
Member
Registered: 2014-11-21
Posts: 44

Re: More Thoughts on Cordial Minuet/The Problem With Tributes

AnoHito wrote:

Economics 101: The correct price to charge for something is the price the most people are willing to pay. Using myself as a sample size of one, I would not continue to play for very long given the current tribute system. With my style of play I would tend to lose money once the unskilled players dried up, and I don't want to be put in the position of using a less conservative (worse) betting system in order to have a chance at making money.

Even with no tribute at all, if you're only good enough at the game to beat the most unskilled players (or insist on using a strategy that can only work on them) but end up in a situation where you are playing skilled players instead, you are going to lose money.  I don't know how you think the game could be structured such that even people who refuse to play better than their opponents make money.

All the tribute does is mean your edge has to be roughly 2% higher over your opponent than it would otherwise need to be for you to make a profit over the long term, and in my experience that is easily accomplished in this game. You keep imagining scenarios where everyone is playing this game so close to perfectly that even the tiniest additional obstacle makes any opponent insurmountable, and that is a laughably inaccurate representation of the current state of the player base.

Edit: Another thing to keep in mind is that if, after a long session, one player has 80 coins left and the other player has 105, the tribute didn't take 20 coins from the first player, the other player did, and he's winning the game by enough to potentially be making a decent profit over the long run.

Last edited by Asminthe (2014-12-01 03:20:13)

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#30 2014-12-01 18:31:30

jasonrohrer
Administrator
Registered: 2014-11-20
Posts: 801

Re: More Thoughts on Cordial Minuet/The Problem With Tributes

jasonrohrer wrote:

To rephrase it, in the turn-based, full-information version (where p2 sees p1's picks before picking), do any boards exist that are not an automatic win for player 2 using a per-pick greedy strategy?  Is the turn-based, full information version trivial to solve for every board as a win for p2?  Or can you force p2 to explore the game tree?  Is p2 guaranteed to win if p2 explores the game tree, or can P1 force a win on certain boards?

Okay, I wrote some code to answer this question.

First, if your opponent is playing a known minmax gametree search strategy, then a simple greedy, per-move choice beats them on 100/100 test boards.

However, there exists a strategy that beats a per-move omniscient greedy strategy for certain boards.  In my tests, it's about 3% of boards where we can force a win against a per-turn greedy opponent even if the opponent knows what we are picking (even if they are running our algorithm and picking the per-turn greedy choice against our picks).

Here is a sample board where this is true:

      0   1   2   3   4   5 
------------------------------
0 |  14  22  12  24  30   9 
------------------------------
1 |   5  32  15  36   6  17 
------------------------------
2 |   3  27  33  29  18   1 
------------------------------
3 |  26   4  23   2  25  31 
------------------------------
4 |  35  16   8   7  11  34 
------------------------------
5 |  28  10  20  13  21  19 
------------------------------

Here are the player moves:

Player moves:  R    C
               ------
               0    5
               4    0
               2    4
               5    2
               1    1
               3    3

Read that move table as the first line picking a square for the R player, and the second line picking a square for the C player.  Assume the C player is knows what R is going to pick (can simulate R's strategy).  Note that the C player makes a greedy choice each turn.

On turn 1, C gives the R player a 9 and takes 35 for itself.

On turn 2, C gives the R player 18 and takes 20 for itself.

BUT, on turn 3, C is stuck taking a way-lower score (32 vs 2 or 36 vs 4).

Essentially, it is possible to paint the greedy player into a corner on certain boards.  Note that, on boards where such a move sequence exists, there is exactly one move sequence (out of 720) that does it.


However, the R player still loses here if the omniscient C player simply runs minmax against it.  Minmax vs. Minmax, where C can simulate R's choice before picking, makes R lose by at least 25 points on this board.



To summarize:

A)  If your opponent is playing any deterministic (pure) strategy that you can simulate on your end, a simple greedy choice per-turn will win on 97% of boards.

B)  If your opponent is playing any deterministic (pure) strategy that you can simulate on your end, a pure strategy exists that will beat that strategy on 100% of boards.

I've measured (B) empirically but not proven it.  If is true, then there is no pure Nash equilibrium for this game.

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