Discuss Skunked Again here

[MatthewV]

Link to Puzzle

[Aalk4308]

Some initial thoughts:

1. All of the cards are red (either hearts or diamonds). Skunks #1 and #5 both have 2d and 3h, but otherwise the skunks do not share any cards.
   
2. We are not told the set of rules by which the skunks move. I guess the point of the puzzle is to determine what the rules are so that Betty can have a winning betting strategy. Some possibilites:
   
   
   
   • If a skunk's card is chosen, it moves a fixed distance
     
   • If a skunk's card is chosen, it moves a distance based on the card's rank or suit
     
   • For each card a skunk holds matching the chosen card's suit or rank, it moves some distance.
     
   • For each card a skunk holds that matches neither the rank or suit of the chosen card, it moves some distance.
     
   
   The story says that when a card is drawn, each skunk moves a certain distance and then stops. This might mean that all skunks move at least x units after each draw, regardless of the card. The rules might also have skunks to move backwards as well as forwards.
   
3. We are not told if the cards are replaced into the deck after being drawn.
   

[dave10000]

[Tahnan]

Dave is of course right. Nevertheless, I think we can infer, based on the word "skunk" and the fact that the track is 121 units long, exactly what mechanism is being used to move the skunks forward. (Hint: it ain't poker.)

[Tahnan]

--though actually, in a sense,

[Tony Gardner]

I know what game you mean Tahnan (easily found with Google), but I don't know how to play the game. If anyone around here does, that would probably greatly simplify the task at hand.

[OcularGold]

I havent done any of the math yet, but I would put my money on 4.

this should help.

[mathgrant]

I would never have figured out the rule without the knowledge that 121 spaces is significant, and that it's based on a game.

Nevertheless, I suck at CRIBBAGE, so I certainly shan't analyze it.
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[Ctorj]

[Tahnan]

So here's my analysis. Setting aside questions of suit,

[dave10000]

[Tahnan]

[Jedo the Jedi]

I would put my money on skunk 3 because regardless of the card drawn, it will always move forward at least 8, assuming the cribbage scenario. It's chances are greatly increased when one of those cards is duplicated. I believe that that hand produces the highest possible payoff in cribbage. Of course, if skunk 4 got lucky with the fives, it would win quite easily. Yeah, what Tahnan said with the statistics.

As for the bit about Skinny Dakota running the races, I don't really put much stock in that changing things. True, there will most likely be a twist of some sort, but not so much that it changes the fact that this is modeled after cribbage. I think that cribbage itself is rather obscure, so that could be part of his money-making plot.
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Paragon Tally: 18 mafia, 3 SKs (1 twice), 1 cultist, numerous chat scum...and counting.

[fadeblue]

I also don't think the 15 to 2 odds are significant except as another hint towards cribbage (where you peg 2 points for making the total 15 on the play, or a group of cards that total 15 in your hand for the show).

[dave10000]

Another thought -- Why are we to assume that the race director is holding up a card randomly chosen from a *full* deck? Isn't it at least as logical -- if not more logical -- that the card would be chosen from a deck in which the cards appearing on the skunks had been removed? (Otherwise the scoring card could be a duplicate of one of the hand cards, which I believe is not possible in cribbage.) If the deck used is such a "reduced" deck (which, again, seems *at least* as likely as using a full deck), doesn't that change the result?

[Aalk4308]

[dave10000]

I still don't see the answer even assuming that the cribbage angle is correct. It is simply not the case that the skunk with the highest average per turn is necessarily the most likely to win the race. For example, a skunk that moved 120 spaces for any ace or the Jack of Hearts, but zero for all other cards, would take on average around 17 cards to cross the finish line, and thus on average would be beaten by each of the other skunks, even though our new skunk had an average move of more than 11 spaces per card, better than any of the skunks currently in the race.

Moreover, even if a skunk might be better head-to-head than any of the others, that does not mean he has a good chance of winning in the field of all other skunks. Consider a hold'em poker hand of 7-7, which is a favorite to beat any of the following in a 1-on-1 match: A-8, K-9, Q-T. But it has almost no chance of winning if ALL of those hands are against it at the same time. Similarly, showing that Skunk 4 has the greatest average move-per-card does not establish that it is the Skunk with the greatest chance of winning the race. More work needs to be done.

Consider, for example, a skunk running against 4 other skunks each of which moved 1 space more per card than that skunk *except* that one of their highest scores was changed to a zero -- with this happening for a different card for each skunk. For example:

Skunk 14 = 14 14 14 14 14 14 . . .

other skunks =

0 15 15 15 15 15 . . .
15 0 15 15 15 15 . . .
15 15 0 15 15 15 . . .
15 15 15 0 15 15 . . .

Skunk 14 would have a better spaces-per-average than any of the other skunks, but would have a lesser chance of winning than any of the other skunks. It could not win any race unless an A, 2, 3, *and* 4 came up in the first 9 cards. The situation in the original puzzle is not so drastic, and it may well be that there the skunk with the greatest number of spaces per card *is* the best one to bet on, but this shows that one cannot simply say "most spaces per card" and end the analysis.


SIMULATION TIME

For those interested in what a simulation shows, here are the results:

1= 0.0%
2 = 4.1%
3 = 42.2%
4 = 44.1%
5 = 9.6%

Given that Betty has a less than 50% chance of winning at all, I don't see how the cribbage answer is consistent with the puzzle language that "After pondering at the board for a few minutes, Betty was positive she was about to make a small fortune . . ." Unless we are supposed to disregard Betty's "positiveness" as a mere statement of her mindset that did not reflect reality -- but if that's true, then there's no way we could hope to answer the question correctly, since she might have bet on *any* skunk having a positive (but wrong) mindset. Certainly her positive mindset was wrong (by about 56%) with respect to Skunk 4.

[dave10000]

Follow-up:

To make the point in my previous post more specific, suppose that we change Skunk 5 from:


16 8 8 16 6 4 8 8 6 12 12 12 12 -- 9.846

TO

8 8 12 12 12 4 8 8 6 16 16 12 12 -- 10.307


Then Skunk 4 still has the best "spaces per move" number, BUT the simulation shows:

1 = 0%
2 = 4.0%
3 = 42.5%
4 = 41.1%
5 = 12.4%

Basically, the slight improvement of Skunk 5 took away from Skunk 4 rather than Skunk 3 (intentionally so). So now, Skunk 3 has the best chance of winning in this field.

But this field looks awfully similar to the previous field, and Skunk 4 still has the best "spaces per move" score. The question is, then, how did Betty know merely from looking at the scores that Skunk 4 was the one to bet on in the previous scenario. It could not have been from looking at the "spaces per move" alone. Did she run a simulation? Is that what we are supposed to assume? The original puzzle says that she was ready to bet "[a]fter watching for a few more minutes . . . ," which does not sound like she had time for, or that she in fact ran, a simulation.

Hopefully the official answer will shed light on some of these issues.

[Jedo the Jedi]

Dang it, Dave! Your post was too long and I forgot my idea about the puzzle. Something you said made me have an epiphany and by the time I went and looked at the puzzle, I had forgotten it! I'll have to come back to this I guess.
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Paragon Tally: 18 mafia, 3 SKs (1 twice), 1 cultist, numerous chat scum...and counting.

[ralphmerridew]

[Tahnan]

[dave10000]

[Zeke Hoskin]

There is something fishy in the game description. Fifteen-two odds on each of five racers? Put a hundred on each. The winner earns seven hundred and fifty, plus that hundred back, net payoff three hundred and fifty. The only way Skinny can win is if the race never ends

[bobandyo]

Keep in mind - that in this race as in real cribbage, its the 1st racer to reach 121 that wins. It does not require a complete turn to transpire and all skunks to move their allotted share of moves.

In all liklihood this will be a close race as it comes down to the finish line. Skinny could control the winner by determining which skunk pegs 1st on the final card.

[Guest]

[Arkive]

Well, the 15-2 odds is clearly either misleading, or the rules to the race itself are. The rules don't specify whether the skunks move in turns, or in unison, so if more then one skunk has a high enough score to cross the finish line on that go, the race would end in a tie. Since the rules state that, "The first skunk to complete the track wins the race", then regardless of who you bet on, even if it was all of them, you could theoretically lose money. Now I don't know what the odds of one skunk clearly winning is, but someone's previous numbers do show that the average points/turn is fairly close so I would guess there is a good chance that Skinny would win money overall. The only problem I have is that the puzzle gives the impression that from what she observed, she clearly thought one of the skunks would win based on his cards, so I'm not sure if my theory holds any water then.

[Holywhippet]

Rules on five card Cribbage can be found here:

http://www.pagat.com/adders/cribbage.html

These analysis seems correct, but as people have said, it doesn't seem to offer much of a guarantee. Skunks 3 and 4 don't have that much between them under the rules suggested so I wouldn't feel either of them to be a certainty. Since Betty is putting everything into one bet there must be some other set of rules being used.

For that matter, there's also the question of what "completing" the track means. If the track is circular with 121 units, a skunk might need to visit every single unit before they win - even though that means several laps.

The other odd thing is that the track is 121 units long. Five card cribbage is first to 61 points.

Let me try a poker analysis with the hand rankings (found here: http://www.pagat.com/vying/pokerrank.html) being used to determine distance. Assuming pair is one movement and royal flush is 9:

Card
A 2 3 4 5 6 7 8 9 10 J Q K
S 1 1 1 1 1 4 0 0 0 0 0 0 0 0
K 2 0 0 4 1 1 1 1 4 0 0 0 0 0
U 3 0 0 0 4 1 1 1 1 4 0 0 0 0
N 4 1 1 1 1 1 1 1 1 1 1 3 2 2
K 5 2 6 6 2 2 2 2 2 2 2 2 2 2

Under these conditions, skunk 5 is going to rocket to the finish line.

BTW, if I'm wrong, I wonder why the cards on the skunks are only diamonds or hearts - not clubs or spades?

[Arkive]

Holywhippit:

5 card cribbage is considered the older style game, with 6 card replacing it as the more common variation (at least in terms of 2 players). Also, while some of the older boards may have 60 holes, it's usually two laps around the board for a score of 121 or higher to win the game. However, your poker logic might be along the lines of what she was thinking, which would explain why she was so confident that a skunk (in this case, #5) would win the race.

[Guest]

[bobandyo]

6-card cribbage is the 2-player game. 5-card cribbage is the 4-person game (at least as I play it) and I always play to 121.

[Lucky Wizard]

It probably doesn't really matter whether it's five-card or six-card -- according to http://en.wikipedia.org/wiki/Cribbage , either way you still end up with 4 cards plus the turn-up card at the end.

Not that I have any idea on the puzzle other than what's been suggested.

[MatthewV]

Cribbage with three people is played by dealing each person five cards and one to the crib; all players add just one card.

[LoudmouthLee]

15 to 2 could just be a cribbage hint, eh?
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-LmL

I'm sorry. I have no desire to talk to you.

[dave10000]

[Guest]

If indeed the poker analysis presents such a clear winner and the cribbage analysis offers no real advantage at all, then I would assume this is the best solution offered thus far. Any chance the owner of this puzzle could give us a yay or nay?...or least offer a friendly hint otherwise?

[warpdragon]

I think the fact that that there are only two suits may lead to the idea that the deck is not a standard deck.

Wikipedia says the disambiguation of skunk is equivalent to a total victory or a shutout. http://en.wikipedia.org/wiki/Skunk_%28disambiguation%29 This may imply that if looked at hard enough there is a clear cut winner.

[L'lanmal]

[ralphmerridew]

Holywhippet: Your post will look better if you put the table within CODE tags.

[Holywhippet]

[Thok]

Random thought-maybe only part of the cribbage game is implemented? In particular, if you only do the cut, hand 4 has an extremely dominant advantage (scores 1 point on any red card, every other skunk needs a jack to get points).