CORDIAL MINUET ENSEMBLE

I was sceptical at first, but after trying the new design, I do think
something like this could be interesting.

Having it so similar to poker is a bit boring, though, and it's a shame to
lose the cabalistic connotations. I also just find 9*4 an aesthetically
displeasing decomposition of 36. I wonder if there couldn't be a neater design
waiting to be discovered.

Here's one idea. 36 is 9 choose 2, so it's the number of lines on an enneacle
(which appears to be the etymologically correct term for the analogue of a
pentacle with 9 vertices). I don't know if this coincidence has been remarked
on in existing daemonological texts... but there's nothing wrong with
inventing new daemonology!

So in place of the numbers 1 to 36, each square could be a single line between
two of nine points equally spaced around a circle.

Then once you've picked three, you draw the three lines on a single enneacle,
and see what pattern results. Rarer and more aesthetically pleasing results
are worth more. So maybe a triangle would be worth most, followed by having 3
connected lines forming a path which isn't a triangle, followed by a path of
length two. Having two or three lines of the same length could also be worth
something, and ties could be broken by looking at the lengths of the lines
involved. With appropriate graphical indications of why a pattern is worth
something, I think a system like this could be learnable.

One thing maybe worth mentioning: the problem I have with deep stacks is risk
aversion. I'm quite sure that if I ever ended up in $10 game, and my opponent
went all-in, I would fold even if I were sure the odds were in my favour. It's
just too much to gamble.

+z for experimenting with higher antes.

Anyway, thanks for fixing the bug with low framerates. It works nicely at 7.5 fps now.

OK. If there's no abstract representation of the UI state you can check for
equality between frames, I guess it's too late to insert one now. Supporting
low frame rates is good enough.

There's an obvious optimisation you could make for the assist graphs, though,
to deal with drawing so many sprites each time - blit the graphs from a buffer
which is redrawn only when they change.

zed:
> It could give me the necessary shove to try to hack something up, time
> permitting.

It didn't.

If you got a reward of more than 1-3 coins for being the last in, I'd expect to
see people trying to bore their opponents into leaving by refusing to bet
anything and leaving it until the last moment to move.

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!

> I've heard from someone else who came the the same conclusion as you
> regarding the infeasibility of applying minimax to the betless game as a
> single move.  There was some reference to a linear programming algorithm for
> computing such things that had a specific running time given the number of
> possible strategies, but I can't find it now.

That was probably me, by email, a couple of months ago.

The algorithm is roughly cubic in n where n is the number of strategies for
each player.

> Can you post a link that explains "recursively dominated?"  My searches
> aren't turning up much on that topic.

I don't know a standard reference, but searches gave me this:
http://www.umass.edu/preferen/Game Theory Evolving/GTE Public/GTE Eliminating Dominated Strategies.pdf
which gives the basic definitions and has a nice 3x3 example where elimination
collapses it to 1x1. There's a zero-sum example in the exercises (f).

jasonrohrer:
> But it is NOT optimal in terms of how much you could win against various
> different strategies.  If your opponent is not playing the Nash eq, you'd
> better switch strategies, because by playing the Nash eq, you've stuck
> yourself with no net winnings and rewarded your opponent with more winnings
> than they deserve.  Let's say their strategy is as simple as "always pick
> column 1 for me and 2 for you."  If you're sticking with your Nash eq
> strategy, you will win 50% of the rounds.  Your opponent's strategy is just
> as good as your Nash eq strategy in terms of the outcome.

That's only correct if the oppenent is not playing a recursively dominated
strategy (being one which is dominated once you ignore recursively dominated
strategies). The equilibrium strategy wins against such strategies more than
half the time. As far as I know, it's infeasible to actually do the
computations for this game, so I don't know how common domination is. But I
would be surprised if humans didn't regularly play recursively dominated
strategies.

I just tried this out. I like the column picking; being able to immediately
tap out my choices once I've made them is quite satisfying.

I see what you mean about typing bets being problematic, and adding 1 or 10 at
a time seems to work nicely.

I'm not sure about 'x' for folding, just because it isn't easily discoverable.
I tested before reading your post carefully, so was trying 'f' and 'F' and Esc
and BkSp and such for folding; 'x' didn't occur to me at all.

Bonus points, of course, for making the keys configurable! Personally I'd
prefer dvorak vi keys for bet increments, but that's unlikely to be a popular
choice.

One last thing: it felt natural to me to use left and right to choose a column
to reveal, in the final stages. Maybe left and right could always move the
currently active slider between viable columns?