

Subject:
Chances of Throwing Six Sixes in ONE Throw
Category: Miscellaneous Asked by: oraccompdavega List Price: $6.00 
Posted:
15 Jun 2006 08:49 PDT
Expires: 15 Jul 2006 08:49 PDT Question ID: 738413 
I need the statistics/figures for the probability of throwing (x) number of sixes with six dice. So, because that's as clear as mud, how about, how many throws would I need, using SIX dice, to get 4 sixes, 5 sixes and 6 sixes? Still doesn't sound right. OK, if it's 50p a throw of six dice, what should the prize values be for getting 4,5 or 6 sixes with one throw? Oh, and I need to know by Saturday lunchtime! Cheers, oraccomp (Dave) 

Subject:
Re: Chances of Throwing Six Sixes in ONE Throw
Answered By: eiffelga on 15 Jun 2006 11:35 PDT Rated: 
Hi oraccompdavega, Assuming you toss six fair dice, there are six to the sixth possible outcomes, i.e., 6 x 6 x 6 x 6 x 6 x 6, or 46,656. Of these, only one outcome is all sixes, so the chance of that occuring is one in 46,656. There are 30 possible ways of throwing five sixes (because there are six different dice which might be "non6", and the "non6" die could show 1, 2, 3, 4 or 5), so the chance of throwing exactly five sixes is 30 in 46,656. There are 375 possible ways of throwing four sixes (because there are 15 possible pairs of dice which might be "non6", and the "non6" dice pairs could show any of the 25 combinations of 1, 2, 3, 4 or 5), so the chance of throwing exactly four sixes is 375 in 46,656. If it's 50 pence per throw, the notional "prize pot" if every possible combination is thrown (all 46,656 of them) would be £23,328. You could divide that into three separate "prize pots" of £7776. During 46,656 throws, you would expect one throw of six sixes  you can give them £7776. You would expect 30 throws of five sixes  you can pay them each onethirtieth of £7776, i.e. £259.20. You would expect 375 throws of four sixes  you can pay them each one375th of £7776, i.e. £20.73 and sixtenths of a penny. If this is a fundraising event, you will probably be making much smaller payouts to provide a profit margin and to help cover the uncertainty of random events. And if there's big money involved, do doublecheck these calculations before running the competition. The relevant math is here: "Bernoulli Trials" http://www.ds.unifi.it/VL/VL_EN/bernoulli/bernoulli1.html Finally, remember that there's a one in 46,656 chance that the very first toss will result in six sixes, so you will need a sizeable float. However, you won't be paying out too often  fewer than one in a hundred tosses is expected to win something. Regards, eiffelga Google Search Strategy: combinatorial dice ://www.google.com/search?q=combinatorial+dice combinatorial bernoulli trials ://www.google.com/search?q=combinatorial+bernoulli+trials 
oraccompdavega
rated this answer:
and gave an additional tip of:
$5.00
Well guys, I'll rate it FIVE stars for the answer as you did your best! However, it was useless! We had the event and in 450 throws, we only had 14 x 2's, and 3 x 3's. Then as we packed up (chaos theory steps in) a kid chucked them on the floor and got 5 x 6's up! No stats or maths could have demonstrated that! So thank's very much to ALL, (except the guy who's piggybacking his chance of dying!), until my next question. 

Subject:
Re: Chances of Throwing Six Sixes in ONE Throw
From: tillga on 15 Jun 2006 09:41 PDT 
As your question is not very clear I post this as a comment. The probability of getting a certain number is: 1/6 for a single dice 1/6*1/6 for two, thus 1/6^n for n dices. It´s impossible to say how many throws you will need to get 4,5 or 6 sixes with one throw, all you can say is the mathematical probability of such a result. tillga 
Subject:
Re: Chances of Throwing Six Sixes in ONE Throw
From: wtallen4ga on 15 Jun 2006 09:44 PDT 
There are six to the sixth power possible ways to throw six sixsided dice. That's 46,656 possible throws, of which 666666 is one possibility, so the odds are 46,6551 against. 
Subject:
Re: Chances of Throwing Six Sixes in ONE Throw
From: redfoxjumpsga on 16 Jun 2006 00:06 PDT 
There are people of great athletic skill who can throw dice in such a way as to greatly improve their odds of a certain number. There are also dice that have been shaved and weighted and have extra sixes added. And people who can switch the altered dice into a game. You might want to buy an experience pit boss a drink and get some advice on how to do the game without inviting the cheats. 
Subject:
Re: Chances of Throwing Six Sixes in ONE Throw
From: transam82ga on 23 Jun 2006 16:14 PDT 
Hi guys. I have a reaaaaally simple question. What is the probability that ill die tomorrow? It certainly isnt 0% and certainly not 100%. So what value is it? 
Subject:
Re: Chances of Throwing Six Sixes in ONE Throw
From: eiffelga on 30 Jun 2006 02:56 PDT 
Hi oraccompdavega, Thanks for your interesting comments and kind tip. I had been wondering how the event had turned out. It was interesting to hear about the outcome, fortunate as it was for the competitor and unfortunate as it was for the fundraisers. If the outcomes were certain, we wouldn't need to call this field "statistics". But in the long run, in events designed to exploit statistical outcomes, the "house" should always win... Regards, eiffelga 
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