cornish sam 923 Posted July 10, 2019 ATG, be careful with your language there, permutations and combinations are a different kettle of fish when it comes to probability... If we are talking combinations then it will most likely change the probability. Share this post Link to post Share on other sites
Indy 3,232 Posted July 10, 2019 (edited) 1 hour ago, cornish sam said: ATG, be careful with your language there, permutations and combinations are a different kettle of fish when it comes to probability... If we are talking combinations then it will most likely change the probability. Exactly right! OK let’s put this to bed....... If you roll one dice with 21 sides you have a 1 in 21 combination. If you have three and specify that each one has a unique designation as per say a 1 to 21 numbered combination lock on a brief case or pad lock then indeed it’s 1 in 9261 combinations. If you roll all three dice together without designating individual dice like you do in normal dice games than it’s about number combinations outcomes in each roll, (like my explanation above using two six sided dice there are only 21 number combinations).! Which for three the same is 1 in 9261 combinations but any two dice the same and one dice different it’s 9261/3 = 3087/1, all three dice to have different numbers would have other number combination is actually 9261/6 = 1543 / 1. So the likelihood of rolling three different numbers are about 6 times more likely than rolling all the same numbers on three 21 sided dice. So it’s not as straight forward as people posted and that’s why we’ve had a five page debate. Edited July 10, 2019 by Indy Share this post Link to post Share on other sites
Duncan Edwards 2,190 Posted July 10, 2019 Except it is that simple because we are talking about rolling a solitary, fair die three times. So it’s (21x21x21)/1. Admittedly, it’s a long while since I did any Maths, but that’s the answer I’d have given. Share this post Link to post Share on other sites
All the Germans 1,070 Posted July 10, 2019 2 hours ago, Indy said: OK let’s put this to bed....... We did that already. The correct answer to the question asked is on the first page. Share this post Link to post Share on other sites
Thirsty Lizard 3,085 Posted July 10, 2019 Oh I do like this thread.............. Okay, on to something a little more challenging for those that are up for it. Honest Thirsty Lizard, your friendly local bookie, offers you the following wager. I will give you odds of 11/10 of you getting at least one 6 if you roll the same dice three times. The dice is a standard six sided one and it is fair and not weighted in any way. Should you accept the bet? 'Yes' or 'No' answers accepted but you only get top marks if you explain your decision and give the relevant working. Share this post Link to post Share on other sites
cornish sam 923 Posted July 10, 2019 (edited) The obvious answer (and so probably the wrong one) would be yes (unless I'm reading the odds the wrong way round) because three chance to roll a single number is 1/6+1/6+1/6=3/6=1/2. So for every £20 you put in you should get £21 back (2 £10 bets, win one lose one as it's a 50:50 chance)... However, that's pure probability, it doesn't take any of the variables that would contribute towards likelihood into consideration. In theory though if you double your bet every loss then eventually you would end up in a very small profit if you cut and run as soon as you win... Edited July 10, 2019 by cornish sam Small point, is the singular of dice not die or has that changed? Share this post Link to post Share on other sites
Thirsty Lizard 3,085 Posted July 10, 2019 15 minutes ago, cornish sam said: The obvious answer (and so probably the wrong one) would be yes (unless I'm reading the odds the wrong way round) because three chance to roll a single number is 1/6+1/6+1/6=3/6=1/2. So for every £20 you put in you should get £21 back (2 £10 bets, win one lose one as it's a 50:50 chance)... However, that's pure probability, it doesn't take any of the variables that would contribute towards likelihood into consideration. In theory though if you double your bet every loss then eventually you would end up in a very small profit if you cut and run as soon as you win... 🙂🙂 The obvious answer (and maybe the wrong one). Your calculation is definitely wrong though. You're right that the chance to roll a single number is 1/6, but you're wrong in how you calculate the chance of rolling that number once in three throws though. The maximum probability that you can have of something happening is 1 (i.e. it's a 100% chance or a total certainty). Think if I had asked 'could you roll a 6 at least once in 7 throws?'. By your calculation method you would add 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 which would give you 7/6 or 1.16 which is a probability greater than 1. But if you think about it, it would be perfectly possible to roll a dice seven times and not throw a 6. Share this post Link to post Share on other sites
Duncan Edwards 2,190 Posted July 10, 2019 Ok, my best guess is that you should not take the bet because the odds offered are not better than the actual odds of achieving a 6. I might be barking up the wrong tree, but, the odds on each die of not rolling a 6 are 5/6. So, with three rolls that’s 125/216 or around 58%. That means there is a 42% chance of achieving a 6 whereas odds of 11/10 suggest a 48% chance. I think. I’ve been in the pub with Morty for three hours so... Share this post Link to post Share on other sites
Thirsty Lizard 3,085 Posted July 10, 2019 5 minutes ago, Duncan Edwards said: Ok, my best guess is that you should not take the bet because the odds offered are not better than the actual odds of achieving a 6. I might be barking up the wrong tree, but, the odds on each die of not rolling a 6 are 5/6. So, with three rolls that’s 125/216 or around 58%. That means there is a 42% chance of achieving a 6 whereas odds of 11/10 suggest a 48% chance. I think. I’ve been in the pub with Morty for three hours so... 🙂 All correct - You're a smart fella Mr Edwards - as such you're barred from placing any bets at Honest Thirsty Lizard bookmakers as we don't like punters who know what they're doing. 1 Share this post Link to post Share on other sites