Flipping off Skinny

[Gomez]

One day, you are sitting in a bar with Skinny Dakota when he takes out a coin and proposes a wager. After getting over the shock of discovering that Skinny was a betting man you decide to check out the game. "The rules" Skinny says "are simple". "You are to choose a combination of 3 possible results of a coin toss, either HHH, or TTT, or THT, or HHT etcetera, so long as there are three. I will then do likewise. Then I'll start flipping. The first person to have their combination comes up is the winner. As a gesture of goodwill, and to prove that I'm not the hustling little weasel you're always making me out to be, I'll let you choose your combination first. Ok? Is ten bucks a good bet?"

You prepare to make the first choice. You think for a little, wondering which combination would most likely come up. After examining the coin to make sure it wasn't weighted or double headed you realise that one particular strategy would benefit you immensely. What is it?

[This message has been edited by Gomez (edited 02-05-2002 01:47 PM).]

[HyToFry]

So that's how you do it.

[ctrlaltdel]

rules of strategy:
1 make skinny dakota get a coin worth $10
2 convince him you will do the flipping
3 chose any combination
4 make skinny dakota look away
5 cash the prize

[ctrlaltdel]

on a second thought i would use one of the following:

tth, htt, thh or hht - this is because choosing ttt or hhh is clearly silly, and likewise chosing either tht or hth would be risky as it is not likey the coin will keep alternating between the two

or else just make him drunk....

[Lepton]

If I pick HTH, Skinny will pick either HHT or THT, so that the last two of his combination line up with my first two.

I think this gives him a slim advantage.

What if I offered him the "priviledge" of picking first?

[Marvin]

Do you have to give the choices in order (i.e. HHT is different to THH)? If so, then there are eight equally likely outcomes so it doesn't really matter which one you choose.
If the order doesn't matter and you're just choosing, say, 3 heads, or 2 tails and a head, then either choose 2T1H or 2H1T because there are more possible combinations that match these patterns than the other outcomes (3 heads or 3 tails). Whichever of these two you choose, Skinny will probably choose the other.

[This message has been edited by Marvin (edited 02-05-2002 03:15 PM).]

[Ghost Post]

I agree with Lepton, except

Let Skinny pick first, and when you choose change the last of his choices. This increases your odds of winning to 50%

Qn

On second thoughts, no it doesn't. Unless there's a trick your odds of winning are already 50%. I'll just go back to agreeing with Lepton ... I think that way may be slightly better.

[This message has been edited by quidnunc (edited 02-05-2002 03:27 PM).]

[Icarus]

Walk away - haven't you people been paying attention ?

Nothing Skinny does puts the favor on your side. Any bet you take with Skinny is in his favor.

[HyToFry]

fix bump.

the next time a thread like this crashes... all you have to do is open up the reply screen for another thread in the same forum, change the &topic=??????.cgi part in the subject line to the number of the crashed thread, and reply.

And you don't even have to be a mod to do this.

[Chuck]

If it's so easy to fix, why not have UBB fix threads when they crash?

[ralphmerridew]

I remember on another Skinny Dakota post, somebody made a comment that the problem was very easy once you stripped out all the irrelevant information. In that case, the reduced problem was "Skinny Dakota offers you a bet. <SNIP> Should you accept?". The answer obviously is NO.

In this case, I think the correct answer is to punch him in the face. You won't get any money, but he won't be expecting that.

[mathgrant]

That was my version of Monty Hall with weighted probabilities on the doors!

[Lepton]

For example, I pick HHT and Skinny picks THH.

Assuming that HHT doesn't come out as the first 3 flips, there is a 1 in 2 chance that T will precede my HHT.

My math is probably flawed, but I see this as him having an 11 in 16 chance of winning, while I get the sloppy seconds (5 in 16).

[Laramie]

Lepton is basically correct. No matter what you pick, Skinny can then choose a dominant strategy. It isn't all that intuitive, but the possible choices are not transitive.

[ralphmerridew]

mathgrant, on that problem, IIRC, Skinny would choose one of the doors with a given probability; the player would name one of them; Skinny would reveal one of the doors to reveal a goat; the player could then choose one of the doors.

At the time, I asked if the trap was that nothing in the rules forbade Skinny from opening the door the player chose, which would lower the player's odds, but you never bothered to acknowledge my question. Was that the trap you had in mind?

(Was that the thread where the "Hey, you didn't say I couldn't drop a bowling ball on your foot!" came from?)

[mathgrant]

Re bowling ball: I think so.

[Gomez]

Lepton has it. The strategy you should employ is to defer the first choice to Skinny. That way you will always be able to choose a combo that's more likely to come up than his.

For example, assume you pick HHH. Skinny would then pick THH. Unless HHH were the first 3 results of the first 3 coin flips Skinny cannot help but win. In fact his odds would be 7/8 to win (or thereabouts). I shan't bother with the math for the other results but whatever you pick Skinny will always have an advantage of at least 66%.

[Chuck]

Offer to bet someone else that you'll beat Skinny and ask for 3 to 1 odds. Anyone who knows Skinny would figure his chances of winning would be higher than that.

[Lepton]

~saves this idea for GL Convention 2002~