Discuss 'Two-Finger' Dakota here

[Caveman]

When is the solution going to be posted?

[boyenigma]

The best strategy assuming the other person always holds out a random number is to always show only one finger. That way skinnys expected gain is 1/4*(1.5)(Assuming other person shows both fingers randomly) whereas if the other players gain is only 1/4*(1).

But again this would rest on the fact that the other person does not realise this and plays on. The moment he does realise this, the game would become symmetric(both rational players) and theres no fun in playing it!!!

[troy]

Way tooooooo easy

[poo]

Way tooo easy

[asmussen]

The problem with assuming that the other player will always hold out a random number of fingers, and guess a random number, is that you CAN'T assume that. When you calculate the best strategy for the game, you have to assume that the other player will also employ the best strategy available to him. Only games that make some sort of rules differentiation between the two players can result in the existence of a strategy that will mathematically give you an advantage over the other player. For example, in chess both players are treated identically by the rules, except for the fact that white gets to move first, which gives white an advantage. If no such differentiation exists, what you end up with is a break even scenario for both players, provided both players are skilled at the game, because if there exists a 'best strategy', you have to assume that your opponent will also be employing it, which means that the best strategy is also a break even strategy. The only way to win is if your opponent does not understand the game, which is often the case in real life situations. For the purposes of puzzles like this, however, you should assume that the opponent will be making the best possible moves that are available to him, because that is the only way to determine if there is an available strategy that will guarantee long term victory.

Shawn Asmussen

[Speeder]

Although in principle I would agree with Mr Asmussen i.e. that in such a game as this one might expect an equal chance of each player winning, but I still reckon it's possible to con some kids out of cash, even playing noughts and crosses if they'd never played before, because until they realised the strategy they would lose a certain amount of times.

Speeder.

[asmussen]

In the real world that's definately true. You can con all sort of people out all sorts of things because they don't understand what's going on. But for a brain teaser such as this one, you have to assume that the opponents will play the optimal strategy available. If you can make any assumption about your opponent's play that you wish, you could simply say that you are assuming that your opponent will always show 2 fingers, and guess 1 finger. Therefore your optimal strategy will be to always show 2 fingers and guess 2 fingers. That's no less valid of an assumption than an assumption that your opponent will always play perfectly randomly and never employ any kind of strategy whatsoever. Frankly, I think that this puzzle has probably been hashed over as much as it is useful to do, and I wish that they would just post the solution that they had in mind and put up a new puzzle. This one has been up for a very long time now.

Shawn Asmussen

[kormeister]

Skinny dakota plans to always hold 2 fingers and always have "2" for his guess. He wins half-a-chip per turn on the average.

[ajhaub0]

It's very simple. No matter which finger you show always guess 2 for him. You will win 75% of the time when someone wins on the 3 or the 4. He will win 75% of the time there is a 2 or a 3 payout. Eventually, you will come out ahead. Just keep your fingers at a random 1 or a 2 and always guess 2. That is until he catches on and starts guessing 2 all of the time...then it is a wash.

[ajhaub0]

And just how frequently do the answers get posted....I've been on this site all of 5 minutes now. I'm new here. let me know.

Thanks

[Icarus]

So here’s my take on it – Normally I would go with the first answer that seems to make the most sense, mathematically, and then not give it too much of a second thought. And it seems most people believe holding out 1 finger guessing 2, and then later alternate once you’ve been figured out gives Skinny the highest return when he wins. But that strategy doesn’t guarantee he will win. So since this puzzle has been up here for such a long time…I’ll offer another view.

At first it would seem to make sense that the strategy Skinny has come up with is to hold out 1 finger and guess 2 – of course mathematically that maximizes his return when he finally does win. But as with all puzzles, wouldn’t the equally clever opponent know that is what Skinny would do ? Therefore, why wouldn’t the opponent only stick out 1 finger and guess 1 ? And then of course why wouldn’t Skinny know the equally clever opponent would think that – so now Skinny will hold out 2 and guess 1 – but then the clever opponent would anticipate that, and hold out 2 and guess 2, and etc. etc. etc…. I don’t see the “guarantee” that Skinny will win. I see it as luck of the draw. So where’s the consistency ?

The nature of any puzzle should be there isn’t a con involved – so naturally we have to assume there is no cheating involved (Skinny holds out 1 finger on one hand, 2 on the other, changes his finger’s as he puts his hand forward, etc). Also, you are led to assume the other participants fully understand the nature of the game and the rules. But the way this puzzle is specifically worded – it leads me to believe those aren’t the proper conclusions to draw for this puzzle. Maybe Skinny’s strategy is to seek out individuals who do not fully understand the game - kids. The puzzle even states that is what Skinny is doing - “Skinny goes on to explain that he's found a strategy whereby he is pulling a very nice. As Skinny walks off to con more kids out of their lunch money, you begin wonder what his strategy is.”

So I guess when the solution is finally posted, we’ll then finally know what the intended solution was.

[asmussen]

Hmmm... The 'seeking out kids' thing as his strategy is an interesting idea. However, it does also say in the puzzle, that you wisely decline to play him, the wording of which seems to imply to me that Skinny is supposed to have a winning strategy even if you should happen to understand the game. However, I can't see how this could possibly be true. Given the nature of the game, if two people have an equally good understanding of the game I don't see any conceivable way that one could have an advantage over the other short of cheating.

Shawn Asmussen

[daleliop]

He can hold out his middle finger, 1 finger, in every game he plays - depending on what his opponent has, it can either represent 1 finger or just swearing, forfeiting the game.

[Navigator]

I don't mean to sound rude, but the GL has sort of broken its own rule. It says on the puzzle page, "there is at least one unsolved puzzle at all times." But right now there is no unsolved puzzle.

You should really do one of the following:
1)post a new puzzle, or
2)remove the solution to Two-Finger Dakota, or,
3)remove the text on the puzzle page that says "there is at least one unsolved puzzle..."

Again, I don't mean to be rude and I'm not angry or anything. The GL is a great site. I realize that Dan and the people who run this site are busy, and they probably have many other commitments in their life other than the GL. And I realize that it's not easy to write puzzles. But you really should fix this; it kind of shows bad integrity, and it looks weird, especially to someone visiting the site for the first time.

[IrishJoe]

Looks weird to someone who was gone for over a year, also, but there's so much to catch up on that I'm not missing the next puzzle... yet.

Did anyone figure out the "numerically optimal strategy" used in the script on http://www.frontier.net/~grifftoe/morra.html ???

I haven't had any trouble defeating it, but haven't tried a properly structured strategy - I just used "call 1 show 2" and switched it with "call 2 show 2" periodically, but it seems as though the script is doing "call 1 show 2, call 1 show 2, call 2 show 1 ..." in a cycle.


I played some more and there is a pattern, but I haven't gotten it yet. It seemed to switch to alternating for a while, then went back to the same cycle it had evidenced earlier. I never saw it 'call 1 show 1', nor did I see it 'call 2 show 2'.
Always (s far as I saw) it was 'call 1 show 2' or 'call 2 show 1'.


[This message has been edited by IrishJoe (edited 04-20-2004 03:17 AM).]