CORDIAL MINUET ENSEMBLE

I would guess from the users graph that a lot of people only played for a day or two and haven't been on much since then; i.e. that the spikes in the graph are largely due to new batches of users. The graph does drop to 0 or 1 players/hour for much of the day and I've also had the experience of waiting for hours due to my unusual time zone. Not sure whether the scale is one + per player for both graphs, but I assume so.

I'm guessing that this article is responsible for the spike in new users over the last day or two.

Too bad that the tribute percent stated in the first paragraph is no longer right.

I agree, it's quite difficult to take note of the choices the opponent made and I've never really managed it, though I expect that the best players do. It's even more difficult because rows on the board get progressively darker and eventually blacked out - e.g. for artificial reasons, which does also concern me. Maybe the paint strokes could be made a little more transparent? Funny that turning up the brightness of your monitor is an advantage (just like in TCD). Also, it would be very nice if you could stop and look at the board at the end rather than it disappearing quickly. I think that playing with paper and pencil to keep notes would be quite helpful and I might start doing that. The game showing symbols to track order in which columns/rows were picked is another option.

It's stronger than that. If you play to a Nash equilibrium and your opponent doesn't, then by definition (since they aren't playing their optimal strategy) you will do better than if they did (because it's zero-sum), eg, making a profit in CM. It would be interesting to know on what scale the profit rate against other strategies would be in CM.

Provided that a game is one with perfect recall (the players remember their previous moves, true here) you can also exactly solve games in extensive (game tree) form directly without converting to normal form (payoff matrix), which causes the exponential blowup that you describe. See for example:
Koller, Megiddo, & von Stengel. (1996). Efficient Computation of Equilibria for Extensive Two-Person Games
This translates into a linear programming problem linear in the game tree size. There's various other papers on ways to do this. I found one in particular that looks like it could be practical for the betless version of CM because it (sort of) prunes the game tree. If I understand correctly, they successfully ran it on games with up to 10^11 game tree nodes, and can run in half a minute if the tree is pruned to a few thousand nodes.
Bosansky, Branislav, et al. (2013) "Double-oracle algorithm for computing an exact nash equilibrium in zero-sum extensive-form games."

Cordial Minuet with betting is definitely infeasible to solve, and not just because there's a huge number of different possible bet amounts. But this is all moot anyway, because if you were to write a bot to play against humans you'd want to use approximate solutions instead, and opponent modelling at least for the betting.

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Noone has mentioned yet that adding betting to the game changes how you should pick columns, for several reasons. These include that the game can end early, and that it's not just score that matters at the end, but also the amount of information you have (and not just information revealed through the column reveal and early bets). I suspect that a bot that computes an optimal (for the restricted game) column picking strategy by ignoring betting, and then separately an optimal strategy for betting, would be highly suboptimal because information is very valuable.

Here's one data point: a day or two ago I played the most unbelievably predictable player I've ever seen. I could pick the first row they gave me 90% of the time, and also knew how they picked the 2nd turn rows (hint: the same way a lot of other people seem to). Despite this enormous advantage, I was losing badly, because they were so much better at betting than me. Now, I admit, I must be horrible at betting. But wait, I checked the scoreboards to see who this was. This player ranked at the top.

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If you want to brush up on game theory, I can recommend this, as I just read some parts of it myself. Easy to read and lots of examples:
http://www.math.ucla.edu/~tom/Game_Theory/mat.pdf

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The endgame of CM is very interesting; I agree that it's a lot like the Monty Hall problem. But until Monty Hall, I don't think we can work out the optimal strategy without computer assistance or a lot of maths, because it's another complication on top of the endgame betting, which is itself very complicated (Ferguson and Ferguson (2007) "The Endgame in Poker" looks interesting).

It was me again. Partway through I actually had an insight not into your strategy but into the game itself, which is why you went from winning to losing. In fact I switched from trying to determine your strategy to just assuming that you hadn't had the same realisation. Obviously I can't tell you what it is However you played so conservatively that I gave up on extracting much from you and just tried to get you to concede one coin at a time. I definitely could have done far better there.

BTW, we played 57 rounds in that second game!

I couldn't parse this sentence, so I can't confirm that I was doing whatever you mean. Later I switched to something definitely completely different.

(Haven't read the rest of this thread; bedtime)

Well, I think that 5 coins would be too high. Plus, I haven't seen any other players play as conservatively as you, so I suggested wait-and-see what develops.

I noticed you often play a slow beginning if you had a good number, preferring to let the other raise, and only matching. Bet amounts were quite indicative of numbers held, and you didn't bluff with large amounts.

After playing a bunch of games today, I feel that the amount taken through the tribute is probably lower than you wanted. In my own games it seems to total to 3-4 times less than before. The new system only takes a larger tribute than the old system if the pot is between 6 and 8 coins. In many other cases it takes less than before. Obviously 6-8 coins is an extremely narrow band, so it's inevitable that you much less than before.

I find that the more experience I get, the less I look at the graph on the right. I never consult it on the first move. I think it's not as useful as it could be, as for example you can't see what your expected (average) score is. Actually I find it much easier to look at the grid and figure out rough what the average of each column is, etc, than to look at the graph. In addition, you can compare different columns against each other in more detail. For example I look for a pair of columns such that if I get a high number in mine then I know that the opponent didn't get the high number in theirs (same row). The graph can't tell you that sort of thing.

IMO the main importance of the graph is to tell you what your range of possible scores is, as seen by the other player. Increasingly important the closer you get to the endgame.

Cordial Minuet is written in C++ because it builds on the codebase Jason has used for all his previous projects. Game development is like that: the majority of your code can't be reused, but repeatedly adapting and improving some parts lets you greatly speed up development and code quality. However I assume it's his intention to make it easy for other people to write clients; the protocol is well documented.

I went and read a poker glossary for half an hour and feel much better now. I have to admit, a lot of these terms translate directly and it obviously makes sense to use existing terminology that poker players will understand, but agree that borrowing terms like "blind" isn't a good idea.

Actually, I had a question about this. What if I want to donate a small amount (say $1) to a friend (whether by email or codename)? Use case: friend doesn't have a debit/credit card or doesn't trust the game enough to pull out their debit card. Use case 2: Someone wants to give away 10 accounts with a $0.50 balance without all the money going to the credit card company. But both cases require being able to create an account without depositing money in it.

Completely agreed.

I've found it pretty easy to find games today. I think I saw 3 open games at one point. This is probably due due to checking the users graph and turning up when it's active. And there seems to be a certain someone who's been hanging around all day. Plus even if there are no games open, it seems like some people (myself included) irrationally sometimes would rather wait for someone else to open a game rather than doing it themselves.

As for reading skill, I think that every game I played today was against the same person today. I could recognise them from their actions even before confirming by checking the scoreboard. They probably knew it was me too. Eventually I started to learn their strategies but before that I was losing quite consistently.

Although as I said I have little poker experience, opponent modelling seems far more interesting and important in this game than poker, because you get so much more information, especially on the first turn (whereas during the later ones you don't know what the opponent's choices were). This is wonderful, though it often feels like betting is still more important than selecting columns.

I'm curious: you don't have a single recording of a tie game? Or doesn't it happen all the time?