CORDIAL MINUET ENSEMBLE

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#51 2015-03-06 19:01:46

jasonrohrer
Administrator
Registered: 2014-11-20
Posts: 799

Re: Eliminating all random elements

Additional clarification of the UIGEA provided by the Treasury and Fed:

Therefore, even if chance is not the predominant factor in the outcome of a game, but was still a significant factor, the game could still be deemed to be a "game subject to chance" under a plain reading of the Act.

See page 19 here:

http://www.scribd.com/doc/7916861/UIGEA … g-11-12-08


It's pretty clear that the layout of the board that may favor one player is not a significant factor in the outcome of the game.  On a given round, the layout of the board is not going to tilt the game in the favor of a beginner over an expert.

In Poker, the beginner could get dealt AA and flop AA4.  Thus, chance is a significant factor in Poker.

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#52 2015-03-07 04:06:26

frank
Member
Registered: 2015-03-06
Posts: 2

Re: Eliminating all random elements

Dan_Dan84 wrote:
frank wrote:

(I haven't tried the game yet because I'm a tad fearful of putting my CC info into a portable app. Sorry if my suggestion doesn't actually make sense for it.)

This thread might help put you at ease:

http://cordialminuet.com/incrementensem … .php?id=51

Yes, thanks, Dan. That was an interesting read, to boot.

@jason: Yeah, it is a little overly complex; I was only thinking about the legal question (and maybe a little bit about shoehorning in auctions, because they are cool).

My reading of the legal quotes I've seen in this thread is that, yes, the procedure

1) Pay stake
2) Flip coin to play first
3) Play Hex to win the pot

*would* constitute a game subject to chance. The procedure sounds very much like gambling, since step 3 degenerates to "first player wins" (or should, based on the strategy-stealing argument you mention, anyway).

This procedure is analogous to what happens in your game, right? You pay before you see the random handicap you've been given. It's not the asymmetry that is the problem per se, but that the players have paid in before seeing it.

jasonrohrer wrote:

It's pretty clear that the layout of the board that may favor one player is not a significant factor in the outcome of the game.  On a given round, the layout of the board is not going to tilt the game in the favor of a beginner over an expert.

You could permit this randomness into your game, yeah, but then you'd have to fight the prosecutor's claim that it is a "significant" factor. It may be pretty clearly not, but who knows how that can be shown to a judge's satisfaction. You have to show that it's like flipping a coin to play white in chess. If you think you can do it, then I guess you're on pretty secure footing against the line of legal attack we're talking about in this thread.

The board-twice-in-a-row thing could also do the trick, as you say, so long as the second round is always reached and is arguably just as valuable no matter what happened in the first round. Again, an argument is required. I think rearranging the sequence of events so that players can't be construed as paying for a chance (i.e., something determined by "Nature") at a favorable handicap would put you on unassailable footing, but it might entail compromising your vision for the game...

Anyway, thanks for inviting me to try the game! I've just played my first match and look forward to trying it out some more.

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#53 2015-03-07 04:26:16

jasonrohrer
Administrator
Registered: 2014-11-20
Posts: 799

Re: Eliminating all random elements

Well, the reason that Hex is an interesting example is that we can prove White wins without actually being able to say how.  I.e., the players are on the same footing in practice, with the more skilled player winning more often.  All we know is that the extra move White gets to play can only help, not hurt, White in a game like Hex.  That's a simplified presentation of the strategy-stealing argument.

So, in theory, the coin flip would make the game subject to chance, if both players knew the perfect strategy that we know exists.  In that case, whoever played first would use that perfect strategy and win.

In practice, because the perfect strategy is unknown, the coin flip does not make the game subject to chance.

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#54 2015-03-07 19:23:53

context fabric
Member
Registered: 2015-02-21
Posts: 23

Re: Eliminating all random elements

Even a board with a poor statistical advantage can win if played correctly, because the skill of CM is to accurately predict what your opponent will play for themselves and you.

The only argument for the game to have any aspect of chance is, given two players of significantly high skill levels, does the favour of the board determine the victor?
I believe the answer is no because I believe CM is and ideal skill based game (comparable to chess, go shogi), and there is no cap on the amount of skill one could have.

Post pick-2 forced win scenarios do exist in CM, these aren’t invisible to the opposing player if they can deduce the possible outcomes (of the game) and know the odds of you having one (of the forced wins).

Now Im curious, In boards containing post turn-2 forced win scenarios are the potential games resulting in these (% of 720) equal for both players? (does one player have a higher chance of getting a forced win?)

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#55 2015-03-09 20:23:08

jasonrohrer
Administrator
Registered: 2014-11-20
Posts: 799

Re: Eliminating all random elements

No, I'm pretty sure there are boards that offer forced wins to one player and not the other.  But you can use turn 1 and 2 picks to NOT let yourself get painted into that corner.

It's interesting to think about how there's no skill cap in CM as compared to perfect information games.

In those game, a perfect strategy exists, and after you master that, you can get no better.  Hypothetically, of course, because for most games beyond tic-tac-toe, the perfect strategy is unknown.

Here, even if you discover and play the Nash equilibrium strategy (and one does exist), you still are not maximizing the amount you win against a non-equilibrium player, so you can STILL get better.  It seems like the dance in donkeyspace can recurse into infinite layers of complexity, as you develop a strategy to exploit the strategy that is supposed to exploit the strategy that your opponent thinks you are using, etc.

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#56 2015-03-12 00:41:15

storeroom leaflet
Member
Registered: 2015-02-19
Posts: 45

Re: Eliminating all random elements

jasonrohrer wrote:

It's interesting to think about how there's no skill cap in CM as compared to perfect information games.
In those game, a perfect strategy exists, and after you master that, you can get no better.  Hypothetically, of course, because for most games beyond tic-tac-toe, the perfect strategy is unknown.
Here, even if you discover and play the Nash equilibrium strategy (and one does exist), you still are not maximizing the amount you win against a non-equilibrium player, so you can STILL get better.  It seems like the dance in donkeyspace can recurse into infinite layers of complexity, as you develop a strategy to exploit the strategy that is supposed to exploit the strategy that your opponent thinks you are using, etc.

This picture isn't qutie accurate. Even in a perfect information game a player can still sometimes improve on their equilibrium strategy against a poor player. For example, you pick an equilibrium strategy for checkers. A poor player memorises the main line of your strategy and can get a draw every time, until you change your strategy (maybe even to a non-equilibrium one) where they won't know what they are doing and lose. I'd argue that the reason that poker players for example, focus much more on explouiting weak play than chess, checkers or go players (and these players do look at playing sub-optimally to exploit weak opponents, Emmanuel Lasker was famous for making "psychological moves", and there are opening traps etc.), is the increased granularity of the result. Even in go results are scored generally as win-loss, and there's no benefit to winning by more points, whereas in poker you are given a monetary reward which can be much smaller or larger. As a result a chess player has no need to play differently against a weak player as a win is still a win, might as well assume they're going to see that 10-move winning combination, even though they usually can't see two moves ahead. In poker if you assume your opponent is going to play well then you won't win as much money from them. So in perfect information games there is still room for getting better at exploiting weaker players by playing off equilibrium strategies, just like imperfect information games.

i think the difference between perfect and imperfect information games in this ballpark is that in imperfect information games equilibrium strategies are typically mixed strategies. Games with mixed equilibria do have interesting properties which arguably adds a level of skilll not found in other games. For instance, there's actually no particular strategy against which mixing has any benefit at all (every pure strategy has a calculable EV against any given strategy, so against that strategy just pick any of the pure strategies which maximise your EV against that strategy, no need to mix them). When you mix then it must be because you think your opponent will guess your strategy and counter it, but of course if you can predict what strategy she will guess you have then you can just counter her counter etc. Mixing only makes sense if you think they can model your thought process [including your model of their thought process!] better than you can model them. So picking the equilibrium strategy is sort of acknowledging you can't win the modelling war (in poker they call it a "levelling" war). This modelling war is an element of skill not captured by the nash equilibrium, and cannot be present in perfect information games where both players know an equilibrium strategy.

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#57 2015-03-12 18:11:10

jasonrohrer
Administrator
Registered: 2014-11-20
Posts: 799

Re: Eliminating all random elements

Well, it sorta seems like any game where you can reliably force a draw is inherently broken for the purpose of this discussion.  So, let's use Hex as the example here.

If you are playing the optimal strategy as player 1, you can do no better than to play that strategy.  There's nothing about a weak opponent that is worth exploiting.  A win is a win.

I agree that non-binary win states are part of the picture here.

But with the tribute, two Nash Eq CM players will both lose money.  The only way to win money is to draw your opponent out into sub-optimal play through sub-optimal play.

Well, I guess it's the same as Checkers, then, were the opt-vs-opt states is a draw, and the only way to win is to play sub-optimally and draw your opponent out into sub-optimal play.  In Checkers, you'd be hoping that they would be trying to exploit you for better than a draw, and thus play sub-optimally, and thereby open themselves up to exploitation.

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#58 2015-03-29 00:15:41

storeroom leaflet
Member
Registered: 2015-02-19
Posts: 45

Re: Eliminating all random elements

jasonrohrer wrote:

Well, it sorta seems like any game where you can reliably force a draw is inherently broken for the purpose of this discussion.  So, let's use Hex as the example here.

Why is a forced draw broken but a forced win not broken? What if we calleda draw in chess a "small win for black" instead of a draw? Does the presence or absence of a forced draw somehow affect the skill cap?

jasonrohrer wrote:

If you are playing the optimal strategy as player 1, you can do no better than to play that strategy.  There's nothing about a weak opponent that is worth exploiting.  A win is a win.

That's true but I think that's peculiar to hex rather than indicative of perfect information games in general. For example consider just being the second player in hex, knowing the equilibrium play won't help you because EVERY strategy is in equilibrium for the second player, however there is still room for the second player to do better than just playing random moves (if they are not playing against an ideal opponent.

jasonrohrer wrote:

Well, I guess it's the same as Checkers, then, were the opt-vs-opt states is a draw, and the only way to win is to play sub-optimally and draw your opponent out into sub-optimal play.  In Checkers, you'd be hoping that they would be trying to exploit you for better than a draw, and thus play sub-optimally, and thereby open themselves up to exploitation.

It's not quite the same. Call a strategy co-optimal if no equilibrium strategy "beats" it. In a game with mixed equilibria any pure strategy which is mixed between in an equilibrium strategy is co-optimal. These are the sub-optimal strategies you'd want to play to entice an equilibrium player to dance in donkeyspace, as if they don't they don't get any benefit from your "mistakes". In a game like checkers the co-optimal (but non-equilibrium) strategies still exist but look very different, they are strategies which only go wrong once the opponent has already gone wrong. As a result they can't be used to draw an opponent out into donkeyspace, because unless they go out there voluntarily they'll never know you're playing co-opimtally rather than optimally, and once they do make such a mistake you are best off playing optimally from then on.

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#59 2015-03-30 17:41:20

jasonrohrer
Administrator
Registered: 2014-11-20
Posts: 799

Re: Eliminating all random elements

I'm proud to be making games that are played by people who are clearly way smarter than me.

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#60 2017-07-22 10:08:36

ShirleyArnold
Member
Registered: 2017-07-22
Posts: 1

Re: Eliminating all random elements

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