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Robert M Inner circle 2482 Posts 
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Does anyone know what the odds are of predicting a number rolled on a single die? Is it 1 in 6?
What are the odds of predicting a number rolled on a single die two times in a row? Three times in a row? Four times in a row? Five times in a row? Thanks! Robert |
M. H. Goodman Regular user Dublin, Republic of Ireland 169 Posts
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The odds of predicting a number rolled on a single die are indeed 1 in 6. If the die is rolled twice, the odds of predicting the correct number on both rolls is 1 in 36 (i.e. 6 x 6). For three rolls, the odds will be 1 in 216 (i.e. 6 x 6 x 6). For N rolls, the odds will be 1 in 6 to the power of N.
Coinucopia available now at http://coinucopia.blogspot.com.
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Robert M Inner circle 2482 Posts
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Thank you. That's what I thought, but I wanted to verify it. Appreciate it.
Robert |
Scott Cram Inner circle 2678 Posts
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One minor pet peeve: The odds of correctly predicting a number rolled on a single die are 5 to 1. The probability is 1 in 6.
Easy Mnemonic: "Odds" and "To" both have an O as their only vowel, so you state odds as "X to Y". "Probability" and "In" both have the letter I, so you state probabilities as being "X in Y". Here in Vegas, I've seen too many magicians try to appear as a gambling expert, only to blow their cover by stating that the odds are "X in Y", or that the probability of something is "X to Y". Semi-related note: The other thing that gives the game away is things like stating that odds of 5 to 1 are the same as a probability of 1 in 5. Nope - odds of 5 to 1 are equal to a probability of 1 in 6. |
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R.S. Regular user CT one day I'll have 188 Posts
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Good info - thanks Scott!
Ron :)
"It is error only, and not truth, that shrinks from inquiry." Thomas Paine
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M. H. Goodman Regular user Dublin, Republic of Ireland 169 Posts
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Good point, Scott. Thanks.
Coinucopia available now at http://coinucopia.blogspot.com.
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stanalger Special user St. Louis, MO 998 Posts
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Quote:
On 2008-10-05 01:08, Scott Cram wrote: Scott, The odds in favor of correctly predicting a number rolled on a single die are 1 to 5. The odds against correctly predicting a number rolled on a single die are 5 to 1. Are you saying "odds of" corresponds to the more familiar "odds against" terminology? I don't think that's right. I would think "odds of" would correspond to "odds in favor of." Stan |
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M. H. Goodman Regular user Dublin, Republic of Ireland 169 Posts
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Odds are normally expressed with the larger number first, so the odds of correctly predicting a number rolled on a single die are 5 to 1 against.
Coinucopia available now at http://coinucopia.blogspot.com.
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Nir Dahan Inner circle Munich, Germany 1390 Posts
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Quote:
On 2008-10-05 17:51, stanalger wrote: don't mess with stan  |
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stanalger Special user St. Louis, MO 998 Posts
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I don't know.
M. H. thinks Scott simply left off the word "against." However, MathWorld seems to agree with Scott: http://mathworld.wolfram.com/Odds.html The MathWorld piece seems to me to have been sloppily written. "The odds of winning are..." But I'm not a gambler, so maybe I just don't understand gambler's argot. What does Scott think? |
S2000magician Inner circle Yorba Linda, CA 3465 Posts
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Quote:
On 2008-10-05 19:37, M. H. Goodman wrote: Odds are normally expressed as odds against a particular event; in that case, the larger number will come first exactly when the probability of the event under question is less than 50%. An event having a probability of 75% - getting a head when tossing two fair coins, for example - would have odds of 1:3 against. Quote:
On 2008-10-06 10:07, stanalger wrote: As a mathematician I'd say that Mathworld's terminology is sloppy. The phrase "the odds of" should mean "the odds in favor of". |
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LobowolfXXX Inner circle La Famiglia 1196 Posts
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All of which is mostly semantic, but is important to keep distinct when doing things like trying to calculate the probability (or odds) on multiple events. For instance, for independent events, you multiply the probability of each event; the probability of rolling a 6 twice in a row is 1/6 * 1/6, or 1/36. If you sloppily conflate odds and probability, you may think that because the odds on each event are 5-1, the odds on the combination are 25-1.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
JasonEngland V.I.P. Las Vegas, NV 1729 Posts
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Scott,
To take your pet peeve a step further, I always made this distinction, though I realize it isn't something universally agreed upon. Sticking with our dice example: The odds are 5:1 against rolling a given number. The chances are 1 in 6 (or 1 "out of" 6). The probability of rolling a given number is 0.16666666667 What say you? Jason
Eternal damnation awaits anyone who questions God's unconditional love. --Bill Hicks
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tommy Eternal Order Devil's Island 16543 Posts
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Or a 16.666666667% chance.
If there is a single truth about Magic, it is that nothing on earth so efficiently evades it.
Tommy |
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Posted: Oct 4, 2008 09:03 pm 
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