Mathematical Riddle

In the spirit of sharing the pain and suffering, I figured I’d make an entry dedicated to the kind of stuff I currently spend my days doing. Well: apart from giving you gruesome details of my current state of health or finding new, inventive, ways to scratch my ass.

Yes, brace yourself, for today is about Mathematics. Physics may come in another post later this week.

Probabilities

Since, I’m confident none of you, the nerdiest included, really want to hear about quadratic integration and advanced set theory (basing this guess on the fact that I would myself be much happier not knowing anything of their existence), I’ll talk about the only mathematical field remotely interesting to the common: Probabilities.

Unfortunately, probabilities are a very minor part of my curriculum, in what is probably my personal gods’ way of telling me: “see that finger? well that’s all you get, so stick it wherever you see fit and don’t hope for anything better”.

Mathematics, past early college level are fairly useless. The farther away, the more completely, utterly, devoid of potential real-life applications they get. And I don’t mean merely for those who later go on working full-time as stunt doubles in the San Fernando valley: even advanced engineering hardly ever requires mathematical tools that go beyond a first or second year university program, the rest is all for the mere glory of it. That leaves you with research and teaching as the two only career somewhat approaching full use of the curriculum.

Since no institution sane in their mind would ever let me anywhere close to a research lab (least of all: pay me to do so), while the degree of contempt I hold for my fellow humans happens to peak around the age group that frequents universities, it is safe to assume that I won’t ever be needing most of the stuff I am currently expected to master.

Lost in this ocean of tediousness, the barren islands of semi-useful fun that are Probabilities and Game Theory are the most paradisiac coasts you’ll ever lay an eye on. They let you actually glimpse into real uses for some of the wildly abstract mathematical constructs you’ve been using for years… That’s pretty unheard of for a student of Mathematics…

Even if the gist of it is: you would have to be a complete moron to ever lay a chip in a Vegas casino and, in the long run, we are all dead. If you squint really hard, you could nearly imagine that hypothetical situation where an idealized version of yourself, self-assured and composed, would step forward amidst the panic-stricken crowd of your fellow plane-crash passengers, and proclaim loudly: “We may as well save ourself the jump in these shark-infested waters: our chances of survival regardless are below 1% with a 97.48% probability factor. I would know: I am a mathematician.”

A Riddle

Probabilities have such good potential for layman’s entertainment that oftentimes they are the gateway for all the metaphysical bridges mathematicians like to throw around their discipline.

The ubiquitous Pascal’s wager (although often presented in an erroneous oversimplified way) is the common example. But, imho, any probabilist riddle that contradict common sense in a sufficiently striking fashion, does as much, if not more, to titillate the mind in similar ways.

And to illustrate my point, preferably without getting into the finer details of Kolmogorov axiomatic, here is an easy riddle for y’all. No prize for this one (if you want a bottle of fine Japanese spirit, ’tis over there), just the bottomless admiration of my cat (she really digs the nerdy types) and a deep feeling of self-accomplishment.

Here goes:

Does one stand better chances of: 1) getting at least one ace with 6 throws of a die, or 2) getting at least two aces with 12 throws?

(reformulated to enhance clarity)

It’s a dirt easy one. I’ve removed all historical context to prevent immediate Googling. Of course, extra points go to whoever can justify their answer.

Check back tomorrow for the answer and some background.

7 comments

  1. Sorry back to the question at hand – isn’t an Ace in a pack of cards and not on a die? I assumed that you were talking about a 6 or a 1…. or whatever you define as the Ace?

    However, from my poor math, I would say that option 2 is more likely than option 1.

    My reasoning (probably flawed).
    Chance of Ace 1/6 per throw. (Six sides to a die)
    6 throws is 1/6 *6 = 1
    12 throws is 1/6*12 = 2

    Or crap here is where this reasoning falls over.. ah well I look forward to the results

  2. “ace” can be used for both cards and dices, I think… either way, I replaced ‘six’ in the original formulation by ‘one’/’ace’, as I thought it may add to clarity (between number of dices, score of each dice) and it doesn’t make no difference (each side being as likely as any other one to appear).
    Answer will come later today when I got a sec.

  3. Tracey: Remember in the second experiment he wants two sixes, not just one. And you know your probability is shaky when you’re not in the [0 — 1.0] range.

    Dave: The reason that I’m not justifying my math is that I don’t want my sloppy guesswork to be archived by Google forever :p And can’t bother to relearn stats to make a proper calculation.

    Anyway, probability guess for #1= 1; guess for #2 = 1/3. Both are probably way off the mark (esp. for #1, given that a probability of 1 says you’ll get the wanted result come hell or high water), but there you go.

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