To the person I've been playing today/yesterday...

AnoHito · 2014-12-18 19:44:52

...please stop calling my all in's on the first turn. I have only been doing it at times when I knew I had a better chance of winning based on the board layout at the end of the first pick. But you still insisted on calling me even despite this, and I'm honestly starting to feel bad... Just so you know, betting in the first round is very dangerous. When you do it so often I can force you to risk everything in a situation where you have the disadvantage, or force you to fold. In general you need to play Cordial Minuet conservatively or you can easily find yourself committed to a match where the odds are against you.

Edit: By the way, you know what would be really great? A chat feature so you can talk to the person you are playing. It doesn't need to in any way identify them, just allow you to communicate with them if you choose to.

Last edited by AnoHito (2014-12-18 19:47:52)

jere · 2014-12-18 20:26:10

In general you need to play Cordial Minuet conservatively or you can easily find yourself committed to a match where the odds are against you.

In the same paragraph as talking about you all-inning on the first turn.

I agree with the sentiment though. I used to get really annoyed by people that would bet 5 on every round or all-in more often than not. I've learned that it's exploitable behavior.

AnoHito · 2014-12-18 20:46:07

jere wrote:

In general you need to play Cordial Minuet conservatively or you can easily find yourself committed to a match where the odds are against you.
In the same paragraph as talking about you all-inning on the first turn.

Ah, yes, I see your point. But in my case, I already know the odds are in my favor, and getting another player to match my all in when I have a stronger position basically guarantees I will win more money over the long run than I lose. Even more so if I can exploit their picking strategy in the second/third rounds. It's the same trap set by casinos. Even if you are able to win some of the time, the longer you play the more you will lose. Calling my all ins so much when your position is weaker than mine is like giving me free money.

Last edited by AnoHito (2014-12-18 20:46:24)

jere · 2014-12-18 21:35:53

I've thought about exactly what you're saying. If I get the 36, why not all in because I've definitely got a better first round pick than my opponent.

It's an interesting thought, but there's one issue to consider: if you bet high (especially all in) when you get get that high number, you're telegraphing information to your opponent and their later picks could be much more informed than yours. The ~6 point advantage you have in the first round can be squandered easily in the rounds that follow.

AnoHito · 2014-12-18 21:55:31

Because I still play with a strategy biased toward giving the other player their worst column in the first round, I usually know what they picked too, so it cancels the advantage out. But I can see where that would be a problem otherwise. And I only go all in if the other player raises first, so I know they either picked what I think they picked or they are bluffing.

Last edited by AnoHito (2014-12-18 21:56:00)

jasonrohrer · 2014-12-18 23:11:52

Going all-in in a situation where you have a known edge (like you have a 36 in turn 1, or AA in poker) is actually not optimal in some senses.

Yes, in terms of the isolated case, the more you bet in a positive edge situation, the more you will win on average in those situations. Betting more increased your expected payoff.

BUT, if you take that to the limit, you arrive at "I will win the most, on average, if I bet everything I have." Because an edge is not a guarantee, you WILL lose often enough in those positive edge situations. That means if you play this way, you will experience ruin very quickly. Yes, you "maximize your expectation," but that's not an optimal thing to do over a series of bets where you actually want to survive financially.

http://en.wikipedia.org/wiki/Kelly_criterion

This criterion is used by pro blackjack players, poker players, horse racing people, and even hedge funds.

There's an AMAZING book about the history of this criterion called "Fortune's Formula." That book was one of the inspirations for Cordial Minuet.

(This ties into the "bankroll management" stuff that was discussed earlier. Also, when we're talking about Kelly-optimal betting, we could be talking about fractions of the entire bankroll or fractions of this given table buy-in.)

jasonrohrer · 2014-12-18 23:13:01

Oh, and separate from the math, there's the notion that if you DO have a turn-1 edge, you don't want to go all-in and scare the opponent into folding, generally. You'd want to soft-play it and get as much money from them as possible.

AnoHito · 2014-12-19 11:11:33

jasonrohrer wrote:

Oh, and separate from the math, there's the notion that if you DO have a turn-1 edge, you don't want to go all-in and scare the opponent into folding, generally. You'd want to soft-play it and get as much money from them as possible.

True, but if the other player never folds...

Anyway, the reason why going all in is such a good idea in situation where you know you have an edge and you know the other player will call is that it creates certainty. You have created a situation, where the longer you play, the more you will win. This would not necessarily be true if you didn't go all in, because uncertainty would give the other player room to manipulate your decision making by bluffing later in the game or by folding to limit their losses. Even if the edge you have is small, over the long term you can't lose. Don't believe me? Here is a simple ruby program that proves it:

stake = 10.00
edge = 0.00
1000000.times do
if rand > 0.50 - edge #rand returns a random number between 0.0 and 1.0
stake += 1.00
else
stake -= 1.00
end
end
puts stake

You'll note that when you run the program with no statistical edge, the results are all over the place. You can win a large amount of money, or lose a large amount, or just about break even. But try changing the edge to 0.01 (1%) and see what happens. No matter how many times you run the program, you will always win. It's possible you may go negative at some points, but the longer you play, the less likely it is you will end up behind. After playing a million games, the chances of being behind are almost a statistical impossibility. It's true you might be able to make more money by playing with a more elaborate betting strategy, but honestly, why take the risk? Any other betting strategy you could use would make you more susceptible to manipulation, and if the other player's betting strategy was as good as yours it wouldn't give you an advantage either way.

Last edited by AnoHito (2014-12-19 11:16:04)

jere · 2014-12-19 13:58:49

Don't believe me?

We believe you. A weighted coin wins on average. Of course.

Here's the part you're missing:

stake = 10.00
edge = 0.01
1000000.times do
if rand > 0.50 - edge #rand returns a random number between 0.0 and 1.0
stake += 1.00
else
stake -= 1.00
end
if stake <= 0
puts "BUSTED"
break
end
end
puts stake

If you exhaust your bankroll, you don't get to keep playing.

The above program, in fact, fails most of the time. Even if you lower the number of bets to ~1000.

AnoHito · 2014-12-19 15:34:13

Again, true, but it's sort of beside the point. You can always just buy in again if your initial stake dries up. As long as you can keep finding people who will go all in when it's not in their best interest, eventually you will win all your money back. Also, the 1% advantage I used as an example isn't realistic. Usually it ends up being something like 5-10% depending on how reliably I can predict the row the other player has picked. With even a 5% edge, it takes a much lower initial stake to make going bust statistically impossible.

jere · 2014-12-19 20:11:15

jasonrohrer · 2014-12-19 23:01:33

Love that Rounders GIF, Jere!

A good example here is a game where you have a 1/1M chance of winning a billion dollars, you can play a game once a day for $1.

The EV of a single play of this game is $999 (bet $1, and win $1000 on average). But intuitively, no one would play this game. The positive EV there is "off" somehow, intuitively. And it's off in reality, because if you play the game every day for the rest of your life, you probably won't win, and you'll be out thousands of dollars.

Suppose you were allowed to play multiple times in one day, and you had $100K, your life savings. You have an "edge" here... would you go all-in and play the game 100K times? You'd expect to walk away with $99M by doing this.

This is a variation of this paradox:

http://en.wikipedia.org/wiki/St._Petersburg_paradox

Bernoulli solved this paradox by realizing you should maximize the geometric mean, not the EV. The geometric mean is the same as the Kelly Criterion.

ALL IN means that there will be at least one 0 term in your geometric mean if you don't have 100% chance of winning, pulling the whole thing to 0. Essentially, "do this long enough, and you will eventually be broke."

What you are saying is that you are playing for a fraction of your bankroll anyway, and that's true. By viewing one table in isolation, because it will end after one all-in win (or loss) for you, and there are no re-buys at that table, the same "long term" reasoning doesn't apply.

But if you think you have an edge going INTO a table, and you don't want to eventually go broke, you should not put your whole bankroll into that one table. See the Rounders GIF.

AnoHito · 2014-12-19 23:35:08

The premise that you are describing does not apply to this situation though. If you bet 100% of your entire bankroll every time, it is inevitable you would go bust eventually. And likewise, if you bet a fixed percent of your bankroll every time, you will also eventually go bust. You could easily make some simple modifications to my script to demonstrate this. But if you commit to betting the same amount every time, you can create a situation where going bust is statistically impossible. Allowing players to set the stake for a table allows them to exploit this. As long as you keep betting a fixed amount, over time the percentage of your bankroll that you're risking will decrease, lowering your odds of busting. And in practice can gradually increase the amount you bet, as long as the average increase percent is less than that of your statistical edge. Of course, the less you increase it the less risk you expose yourself it, but you will eventually be able to raise it a fair amount without ever putting yourself in serious danger of busting.

jere · 2014-12-20 01:32:02

I think you've got things backwards. Betting a fixed percentage of your bankroll guarantees you won't go bust (though you could approach 0). It's Asminthe's bankrollment managment stuff: always do 5% of your bankroll as stakes.

Betting a fixed amount is likely to bankrupt you. This is very clearly demonstrated by the modified script I posted earlier.

The whole "you can always buy in again" thing is silly. Sure, if you have infinite money, gambling is no problem. But nobody does. And if your bankroll is a lot smaller than what you can comfortably afford, you're throwing away money.

AnoHito · 2014-12-20 03:09:43

Ah, okay, yes I see what you mean now. I should have actually tested what I was saying in my code before opening my mouth. :X So yes, is it in general better to bet a percent of your stake. But assuming you can engineer things so the odds of going bust are low enough, betting a fixed amount over time yields a much more consistent return. Meaning that you could for example do this:

stake = 10.00
edge = 0.05
10000.times do

if rand > 0.50 - edge #rand returns a random number between 0.0 and 1.0
stake += (stake > 10.0 ? 1.0 : stake * 0.1 )
else
stake -= (stake > 10.0 ? 1.0 : stake * 0.1 )
end

end
puts stake

This yields both a stable return and eliminates the chance of busting. But on average you would do much, much better by just betting a percent of your stake, even if on some occasions you might do worse. I'm sure their is a balance to be struck there somewhere.

But in the end, this only tells you what you should put on the table for a given match. I'm still convinced going all in during the first betting round is a good idea for the following reasons:

1. The other player may decide to fold. Paradoxically, there is a point where your level of commitment to a round would make it less damaging to call the all in then to fold, but knowing what that is exactly would be difficult. I think jere was onto this when I played him earlier.

2. You can't be beaten by bluffing. If your goal in Cordial Minuet is to create certainty, bluffing is your greatest enemy. If you force the other player to go all in, they will never get the chance to bluff.

3. The human factor. When going all in with a statistical advantage, the certainty that the odds are in your favor would promote clear thinking in the picking rounds, while the uncertainty the other player would feel from knowing the odds were against them might cause them to second guess themselves and make poor decisions. From what I have observed, the second picking round is by far the most critical, and is last the time you would want to be questioning your own judgment.

4. The tribute. The more money you can move in a single round, the less you will lose the the tribute on average. I played many matches where more was lost to the tribute than either player won, and forcing all ins seems like the best solution.

5. Time is money. Coridial Minuet tends to be played conservatively by many players. This is bad if you're trying to make as much money possible in as little possible time, because you can easily find yourself in a long and drawn out game that doesn't go anywhere. Forcing all ins gets money moving quickly, because the other player will quickly realize they have to call you in order to play. Or they could just leave, which is also okay, because if they weren't willing to bet large amounts they weren't worth your time in the first place.

6. You may succeed in pressuring the other player from ever raising in the first round. This is actually ideal, because if they raise in the second round, you have even more accurate information to determine whether you should go all in. And it gets even better in the third round. Unless they are willing to bluff sometimes, which you can exploit, it turns the game into "pick numbers to win a chip".

These are just reasons I could think of off the top of my head. Even if going all in is in theory a suboptimal strategy in theory, the structure of Cordial Minuet makes it a better idea that it would initially appear. I'm not convinced there is actually any betting strategy that could overcome the above advantages.

jasonrohrer · 2014-12-20 05:54:35

Well, if you're only doing this when you have the advantage (and never bluff), then the other player should always fold in response, which means you win 1 chip in situations where you have a clear advantage.

It seems like betting one chip at that point, which if your opponent has a decent first round, they will clearly match, would be better. Or, "betting whatever the market will bear."

Or the Poker classic of betting nothing and simply matching what they bet along the way, with a small raise at the very end. Maybe intentionally giving them good numbers on turn 3.

It's like, if you have AA in Holdem Poker... you have a 70% chance of winning at a 6-person table (something like that). But if you go all in, all you're likely to win is a few blinds. Better to set a trap, right?

AnoHito · 2014-12-20 13:00:44

jasonrohrer wrote:

Well, if you're only doing this when you have the advantage (and never bluff), then the other player should always fold in response, which means you win 1 chip in situations where you have a clear advantage.

The trick is to only do it after they raise first. That way it forces the other player to fold away their chips, or call at a disadvantage. And if you do it enough, it pressures the other player to not raise early in the game, which is what you really want. Then as the frequency and amount of their raising lowers, you can incorporate strategies such as matching when you only know you probably have the better position, or even bluffing some of the time. It depends on what the other player is doing, and it's more of an art than a science. But the only potential risk is if you scare the other player into never raising, and in this case you can just leave the match without losing anything.

Incidentally, I think poker is a bad game to compare to Cordial Minuet in this particular case. In poker (at least Texas Hold 'em style poker), every round has the power to increase the uncertainty that you will win. For example, in a two person table, say you are dealt pocket aces, bet half your stake before the flop, and the other player calls you. At this point you know for certain that your position is as least as strong as the other player's. But what happens if the flop has a pair of twos? You know you've still probably won, but if the other players raises you all in, would you call? You know they are probably bluffing, but then why would they bluff in a situation where they know they'd be finished if you called. Do you think it's likely they had a two in the first place when they called such a high raise before the flop? Is it possible they even had pocket deuces? You went from a situation where you knew you were winning for certain, to a situation where you don't even know you have probably won anymore.

In Cordial Minuet, this would never happen. Every round in Cordial Minuet gives you more information about whether you have won than the previous round. But that applies to the other player as well. This means that the longer the game goes on, the worse it is to be the first person to bet. By betting, you are either telecasting the strength of your position to the other player, or if you're bluffing you're taking a huge risk that the other player could exploit. This is why in Cordial Minuet, I strongly believe the first person to bet is always at a disadvantage. The only problem is, if you never bet first, the other player can pressure you into folding too much. Going all in is the solution, because as long as the other player raises enough at times when they aren't sure they're in the lead, the will have to call you or you will be able to buy the pot too often for them to keep their lead. Their only choice to counteract what you are doing, is to never raise first (which is the strategy you are using, meaning no one ever raises), or to lower the amount they bet early in the game (which allows you to call them at significantly less risk). It's pretty much win win.

In my experience, going all in in Cordial Minuet has consistently worked better than slowly betting up the pot. When you try to slowly bet up the pot in a game where every round just tells you more about whether you've won, you're playing a dangerous game. Cordial Minuet just gives you so much information about whether you have won by the end of the second round. If you telegraph the strength of your position in any way, the other player will probably just fold. And being able to know when it's safe to bluff in the second round requires you to have a very good read of the board layout and what the most likely potential outcomes are. Miss one little detail that the other player saw, and it could be very costly. When two experienced players play Cordial Minuet, they tend to scare each other away from taking big risks, and they end up fighting over increasingly small margins. This is why I initially quit playing the game. It's not fun when the reward for beating a strong player is so much less than a weak player. But going all in so much solves the problem completely. Either a lot of money gets moved around, or no one gets to play. It made the game interesting for me again, and so far the strategy has paid off financially as well. I went from below $7 to above $11 in a very short time. I've since switched to $0.01 to refine my strategy further before completely committing to it, but so far I think it's a winner.

ukuko · 2014-12-22 10:20:31

AnoHito wrote:

The trick is to only do it after they raise first.

This was the key piece of information missing from your first post!

jasonrohrer · 2014-12-22 17:11:59

You're right about the differences between CM and poker in terms of the possibility of mounting uncertainty in Poker. Well, not exactly... in poker, certainty can mount too. The point is, in Poker, additional cards can change everything, whereas in CM, additional numbers are additive to your score.

I've now lost the term for this... it has something to do with partial ordering, but that's not all. Essentially, in CM:

If X < Y and C < D, then X + C < Y + D.

This is NOT true in Poker, where X could be 22, Y could be AA, C could be 2, and D could be K.

Essentially, as more cards come out, the partial ordering is not preserved.

Math people: what's this property called?

I'm not totally happy that CM doesn't have this element. I've thought about ways to add this element (like, giving a bonus for 3 odd or even numbers, or 3 numbers under 10, etc.), but some of that stuff (sets) feels too much like existing games.

jasonrohrer · 2014-12-22 17:52:01

So... maybe the property I'm looking for is "partial order where the add-a-card function is non-monotone".

If F(h) = h + 2 (add the two card), then even though
22 < AA

we have:
F(22) > F(AA)

In other words:
(222 > AA2)

Is that the best way to describe this? Has this "non-monotonic" property of Holdem been formally recognized anywhere? I can't find anything about this.

jere · 2014-12-23 00:04:25

Relevant to this thread, since this appears to be what Ano is currently doing: http://en.wikipedia.org/wiki/Martingale … _system%29

And it's a miraculous way to play if you have infinite moneys.

jere · 2014-12-23 00:31:53

And congrats by the way. I'm awful at coin flips.

Wait. Scratch that.

Last edited by jere (2014-12-23 03:59:54)

jere · 2014-12-23 12:26:44

Ah. I take all that back! It was a case of mistaken identity.

CORDIAL MINUET ENSEMBLE

#1 2014-12-18 19:44:52

To the person I've been playing today/yesterday...

#2 2014-12-18 20:26:10

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#3 2014-12-18 20:46:07

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#4 2014-12-18 21:35:53

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#23 2014-12-23 12:26:44

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