Conundrum....
I ran across what looks like an old plastic film canister that was used to package something call3d "Pocket FARKEL," billed as "a game of guts and luck." The game equipment is pretty simple: six dice, a cup to shake them in, and a score sheet.
I've never played, and I don't really know the rules, but a naive interpretation of the guidelines printed on the score sheet suggests that scores do not necessarily correspond to probabilities. (This is not a judgement, merely an observation.)
For example, there are exactly six ways to roll six dice and have them come up as the same number (e.g., 1,1,1,1,1,1), and according to the score sheet, one gains 3000 points for this accomplishment. On the other hand, there are 6x5x4x3x2x1 = 720 ways to roll six dice and have each show a different number (e.g., 1,3,5,4,6,2), for which one scores 1500 points. (In other words, half as many points for something that's 120 times more likely to happen.)
I spent a little time calculating the number of ways various combinations could happen, and got lost somewhere along the way, particularly when it came to figuring out how many ways six rolled dice can show exactly two pairs (e.g., 1,1,2,2,3,4). The number I kept coming up with was very nearly as large as the number of ways six dice can come up (46,656, if you must know). Perhaps I'll try to find out where I lost my way over the weekend), but it's not as if the whole exercise was futile.
I found it curious that rolling three ones, for example, scored a mere 300 points, while rolling three sixes netted 600 points, despite the fact that both events are equally likely, from the point of view of probability. The point it that we humans are really good at creating our own little reality, though based on the real thing. Furthermore, the line between reality and the interpretation of reality can blur very easily.
Specifically, I am reminded of a conversation I several years ago, in which my interlocutor, in arguing for Intelligent Design, brought up an example of a monkey, banging away at a typewriter, who managed to output a line from a Shakespearean sonnet. I don't quite remember the fine points of the argument—something along the lines of this event proving that the monkey's fingers were being guided in some inexplicable way—but I do recall being asked, "What's the probability of that happening?" And my immediate answer was, "Exactly the same, assuming truly random letter strikes, as that line appearing backward, or of a line appearing from a poem by François Villon, or a line of complete gibberish!"
This probably doesn't make much sense, but allowances must be made for first drafts. It's been a long day.
I've never played, and I don't really know the rules, but a naive interpretation of the guidelines printed on the score sheet suggests that scores do not necessarily correspond to probabilities. (This is not a judgement, merely an observation.)
For example, there are exactly six ways to roll six dice and have them come up as the same number (e.g., 1,1,1,1,1,1), and according to the score sheet, one gains 3000 points for this accomplishment. On the other hand, there are 6x5x4x3x2x1 = 720 ways to roll six dice and have each show a different number (e.g., 1,3,5,4,6,2), for which one scores 1500 points. (In other words, half as many points for something that's 120 times more likely to happen.)
I spent a little time calculating the number of ways various combinations could happen, and got lost somewhere along the way, particularly when it came to figuring out how many ways six rolled dice can show exactly two pairs (e.g., 1,1,2,2,3,4). The number I kept coming up with was very nearly as large as the number of ways six dice can come up (46,656, if you must know). Perhaps I'll try to find out where I lost my way over the weekend), but it's not as if the whole exercise was futile.
I found it curious that rolling three ones, for example, scored a mere 300 points, while rolling three sixes netted 600 points, despite the fact that both events are equally likely, from the point of view of probability. The point it that we humans are really good at creating our own little reality, though based on the real thing. Furthermore, the line between reality and the interpretation of reality can blur very easily.
Specifically, I am reminded of a conversation I several years ago, in which my interlocutor, in arguing for Intelligent Design, brought up an example of a monkey, banging away at a typewriter, who managed to output a line from a Shakespearean sonnet. I don't quite remember the fine points of the argument—something along the lines of this event proving that the monkey's fingers were being guided in some inexplicable way—but I do recall being asked, "What's the probability of that happening?" And my immediate answer was, "Exactly the same, assuming truly random letter strikes, as that line appearing backward, or of a line appearing from a poem by François Villon, or a line of complete gibberish!"
This probably doesn't make much sense, but allowances must be made for first drafts. It's been a long day.