WildCard Posted July 22, 2016 Report Share Posted July 22, 2016 100 dice simply means 100 chances of hitting a 1 in 6 outcome. The odds are still 1 in 6 for any one of those 100 dice to land on a 3. Probability and odds are not the same things, mathematically speaking. How are they not? Quote Link to comment Share on other sites More sharing options...
Thorny Posted July 22, 2016 Report Share Posted July 22, 2016 100 dice simply means 100 chances of hitting a 1 in 6 outcome. The odds are still 1 in 6 for any one of those 100 dice to land on a 3. Probability and odds are not the same things, mathematically speaking. Yes, the odds of any SINGLE ONE of the dice hitting doesn't change. But the collective chances of at least ONE hitting, when you have 100, is a near certainty. The odds of one individual isn't being argued here. The point is that with multiple chances, the likelihood of reaching the desired outcome goes up. Multiple chances = more likely to hit. More picks, more likelihood one pans out. This is simple math. The equation I posted is the correct mathematical equation for one of four 25% outcomes reaching the desired conclusion. Quote Link to comment Share on other sites More sharing options...
WildCard Posted July 22, 2016 Report Share Posted July 22, 2016 Yes, the odds of any SINGLE ONE of the dice hitting doesn't change. But the collective chances of at least ONE hitting, when you have 100, is a near certainty. The odds of one individual isn't being argued here. The point is that with multiple chances, the likelihood of reaching the desired outcome goes up. Multiple chances = more likely to hit. More picks, more likelihood one pans out. This is simple math. The equation I posted is the correct mathematical equation for one of four 25% outcomes reaching the desired conclusion. You are correct. Quote Link to comment Share on other sites More sharing options...
K-9 Posted July 22, 2016 Report Share Posted July 22, 2016 How are they not? In a word, context. Yes, the odds of any SINGLE ONE of the dice hitting doesn't change. But the collective chances of at least ONE hitting, when you have 100, is a near certainty. The odds of one individual isn't being argued here. The point is that with multiple chances, the likelihood of reaching the desired outcome goes up. Multiple chances = more likely to hit. More picks, more likelihood one pans out. This is simple math. The equation I posted is the correct mathematical equation for one of four 25% outcomes reaching the desired conclusion. I don't disagree with the math. I am just clarifying that odds don't change, only probability. Quote Link to comment Share on other sites More sharing options...
WildCard Posted July 22, 2016 Report Share Posted July 22, 2016 Semantics ;) Quote Link to comment Share on other sites More sharing options...
K-9 Posted July 22, 2016 Report Share Posted July 22, 2016 Semantics ;) No, context. Quote Link to comment Share on other sites More sharing options...
WildCard Posted July 22, 2016 Report Share Posted July 22, 2016 No, context.No, semantics! Quote Link to comment Share on other sites More sharing options...
North Buffalo Posted July 22, 2016 Report Share Posted July 22, 2016 Sigh slow hockey day.. Quote Link to comment Share on other sites More sharing options...
K-9 Posted July 22, 2016 Report Share Posted July 22, 2016 No, semantics! OK, you win. Which is far more important than any actual understanding, anyway. Quote Link to comment Share on other sites More sharing options...
WildCard Posted July 22, 2016 Report Share Posted July 22, 2016 OK, you win. Which is far more important than any actual understanding, anyway.Yeah, the winky face and ! mark really didn't convey joking? Tough crowd. Quote Link to comment Share on other sites More sharing options...
kas23 Posted July 22, 2016 Report Share Posted July 22, 2016 You are correct. X2 Quote Link to comment Share on other sites More sharing options...
K-9 Posted July 22, 2016 Report Share Posted July 22, 2016 Yeah, the winky face and ! mark really didn't convey joking? Tough crowd. What, you didn't get my joke, either? Quote Link to comment Share on other sites More sharing options...
WildCard Posted July 22, 2016 Report Share Posted July 22, 2016 What, you didn't get my joke, either?Guess not Quote Link to comment Share on other sites More sharing options...
K-9 Posted July 22, 2016 Report Share Posted July 22, 2016 Guess not I'll be sure to incorporate more winky faces and exclamation points in the future. In the meantime: :beer: Quote Link to comment Share on other sites More sharing options...
WildCard Posted July 22, 2016 Report Share Posted July 22, 2016 I'll be sure to incorporate more winky faces and exclamation points in the future. In the meantime: :beer: Tone on the internet is a hard thing to figure out :lol: Annndd I'm off work, so :beer: indeed Quote Link to comment Share on other sites More sharing options...
Thorny Posted July 22, 2016 Report Share Posted July 22, 2016 In a word, context. I don't disagree with the math. I am just clarifying that odds don't change, only probability. No, the odds of each INDIVIDUAL dice rolling the desired outcome don't change. The odds, however, of reaching the desired outcome, do go up, depending on how many events are included in the equation. The collective odds. Individual vs. Collective Anyways, apart from the language here, we are all in agreement. Dog days of summer, indeed. Quote Link to comment Share on other sites More sharing options...
K-9 Posted July 23, 2016 Report Share Posted July 23, 2016 No, the odds of each INDIVIDUAL dice rolling the desired outcome don't change. The odds, however, of reaching the desired outcome, do go up, depending on how many events are included in the equation. The collective odds. Individual vs. Collective Anyways, apart from the language here, we are all in agreement. Dog days of summer, indeed. From Dr. Math himself: Let me clarify the difference between probability and odds. Theprobability of an event is defined as: (Chances for) P(x) = --------------- (Total chances) So, for example, the probability of drawing an ace in a single deck of 52 cards is 4/52 = 1/13 (or about 0.077 = 7.7%). Odds, on the other hand, are given as: (Chances for) : (Chances against) Incidentally, odds of 1:1 would be read as "one TO one", not "one OUT OF one." (The words "out of" seem to imply total chances, which is probability, not odds.) Since (Total chances) = (Chances for) + (Chances against), we can calculate (Chances against) = (Total chances) - (Chances for). The odds of drawing an ace in a deck of cards is 4:(52-4) = 4:48 = 1:12. Notice the difference in the second value; probability uses (Total chances), but odds use (Chances against). This is why the probability (if considered as a ratio) and the odds are different. What can I say, I'm a stickler for detail. Hockey season can't get here fast enough. GO SABRES!!! Quote Link to comment Share on other sites More sharing options...
pi2000 Posted July 23, 2016 Report Share Posted July 23, 2016 (edited) On a standard die the general formula for rolling at least one 6 in n rolls is 1 - (5/6)^n. 5/6 meaning 5 of the 6 sides are not a 6. So let's say each 3rd rounder is a 12 sided die, meaning a 3rd pick has an 8.3% of becoming a serviceable NHL player. If you roll a "12" that player becomes an NHL'er, and we have 4 3rd round picks, or "rolls". The probability of landing 1 NHL player out of those 4 picks is.... 1 - (11/12)^4 = 29.4% For 3 picks (rolls) 1 - (11/12)^3 = 22.9% For 12 rolls: 65℅ If you had all 30 picks: 92.6℅ Edited July 23, 2016 by pi2000 Quote Link to comment Share on other sites More sharing options...
Thorny Posted July 23, 2016 Report Share Posted July 23, 2016 (edited) On a standard die the general formula for rolling at least one 6 in n rolls is 1 - (5/6)^n. 5/6 meaning 5 of the 6 sides are not a 6. So let's say each 3rd rounder is a 12 sided die, meaning 8.3% of 3rd rnd picks are serviceable NHL players. If you roll a "12" that player becomes an NHL'er, and we have 4 3rd round picks, or "rolls". The probability of landing 1 NHL player out of those 4 picks is.... 1 - (11/12)^4 = 29.4% For 3 picks (rolls) 1 - (11/12)^3 = 22.9% Again, I was going with 25% chance a 3rd round pick "makes it". If we have 4, the odds are 68%. Your numbers are correct if the odds of a pick hitting is 8.3%. We are using the same formula. This can move away from Math, now. What we are disagreeing on is the likelihood of a pick hitting, of which we can't be sure. To my mind it was easily worth dealing one pick for Vesey's rights, potential hindsight notwithstanding. Edited July 23, 2016 by Thorny Quote Link to comment Share on other sites More sharing options...
K-9 Posted July 23, 2016 Report Share Posted July 23, 2016 Still no respect for the difference between odds and probability, I see. The purist in me weeps. I'm out. But thanks for the exercise. GO SABRES!!! Quote Link to comment Share on other sites More sharing options...
Thorny Posted July 23, 2016 Report Share Posted July 23, 2016 Still no respect for the spirit of the discussion rather than the minute trivialities, I see. G'day. Quote Link to comment Share on other sites More sharing options...
K-9 Posted July 23, 2016 Report Share Posted July 23, 2016 Still no respect for the spirit of the discussion rather than the minute trivialities, I see. G'day. Spirit of the discussion? You mean the vilification of a 23 year old young man, blessed with hockey talent, that has a chance to exercise his collectively bargained right to become a free agent? Or is it the spirit of the portion of the discussion that condemns GMTM for using a low risk asset for a chance at a high reward? Christ, after wading through the mounds of crap and trolling along those lines, I thought the math discussion was a welcomed distraction. I really don't give a flying phuck whether anyone appreciates the difference between odds and probability. Like I said, it was a welcomed distraction. Carry on. GO SABRES!!! Quote Link to comment Share on other sites More sharing options...
Thorny Posted July 23, 2016 Report Share Posted July 23, 2016 Dude. But what does mine say? Quote Link to comment Share on other sites More sharing options...
pi2000 Posted July 23, 2016 Report Share Posted July 23, 2016 Again, I was going with 25% chance a 3rd round pick "makes it". If we have 4, the odds are 68%. Your numbers are correct if the odds of a pick hitting is 8.3%. We are using the same formula. This can move away from Math, now. What we are disagreeing on is the likelihood of a pick hitting, of which we can't be sure. To my mind it was easily worth dealing one pick for Vesey's rights, potential hindsight notwithstanding. I'd like to think GMTM is better than average at finding talent in the 3rd round, but we just don't know yet. I suppose you could look back at the drafts from 2000-2010, and figure out what the odds are, but you'd also need to have a clear definition of serviceable NHL player. Maybe I'll look into it next week because it's Friday and 96 out, my sister is visiting and I'm sitting by the pool drinking. Quote Link to comment Share on other sites More sharing options...
WildCard Posted July 23, 2016 Report Share Posted July 23, 2016 I HAVE A PALTRY BACHELORS IN MATHEMATICS Quote Link to comment Share on other sites More sharing options...
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