| | | | 
10-27-2009, 01:06 PM
|  | Exalted Member | | Join Date: Oct 2005
Posts: 2,647
| | |
If you could choose between one try of a lucky dice throw at a 60% chance of winning, or two tries of winning something at a 40% winning rate (with the added possibility of winning double if both tries succeed), which would be the option to choose?
I saw a billboard on my way to town this morning that displayed some kind of computer sale with this very action in mind. The question stuck in the back of my head, but I'm having a bit of a bad brain day. It seems there's a really crystal clear solution to this.
| | |
10-27-2009, 01:31 PM
|  | Super Moderator | | Join Date: Mar 2001 Location: The sun, the moon, and the stars.
Posts: 30,316
| | |
One chance at 60%. You stand an above average chance on one throw, as opposed to a below average chance on each of two throws.
__________________
To the Righteous belong the fruits of violent victory. The rest of us will have to settle for warm friends, warm lovers, and a wink from a quietly supportive universe. | | |
10-27-2009, 01:59 PM
|  | Moderator | | Join Date: Sep 2001 Location: Mindlessly floating around.
Posts: 4,262
| | |
Two chances of 40% is better. Even if you don't care about the double win the risk of not winning anything is only 36% with two chances at 40%.
__________________
While others climb the mountains High, beneath the tree I love to lie
And watch the snails go whizzing by, It's foolish but it's fun | | |
10-27-2009, 03:22 PM
| | Exalted Member | | Join Date: Oct 2005
Posts: 2,647
| | |
How do you get to 36% Dottie? It's an odd percentage..
Leaving out the percentages, outcomes for double drawings are false/false, false/true, true/false, true/true. A 1/4th chance of not getting any winnings at all. On the 40% game, wouldn't that mean 1/4th of the 60%? 15%?
| | |
10-27-2009, 04:01 PM
| | Moderator | | Join Date: Sep 2001 Location: Mindlessly floating around.
Posts: 4,262
| |  Quote:
Originally Posted by Tricky  How do you get to 36% Dottie? It's an odd percentage.. | To lose you need to fail two tests at 0.4 which is the same as two tests at 0.6 need to succed: 0.6 * 0.6 = 0.36 Quote:
Originally Posted by Tricky Leaving out the percentages, outcomes for double drawings are false/false, false/true, true/false, true/true. A 1/4th chance of not getting any winnings at all. On the 40% game, wouldn't that mean 1/4th of the 60%? 15%? | Those options are not of equal value, and the last operation is not understood by me at all.
The value of all the options should be as follows:
false/false 0.6*0.6 = 0.36
false/true 0.6*0.4 = 0.24
true/false 0.4*0.6 = 0.24
true/true 0.4*0.4 = 0.16
so, 16% chance of a double and 48% of a singel win.
__________________
While others climb the mountains High, beneath the tree I love to lie
And watch the snails go whizzing by, It's foolish but it's fun
Last edited by Dottie; 10-29-2009 at 04:36 PM.
| | |
10-27-2009, 04:19 PM
| | Exalted Member | | Join Date: Oct 2005
Posts: 2,647
| |
Wow. Somehow I feel I knew this stuff better way back in highschool. Math has never been my strong point, but that doesn't mean it fails to fascinate me. Thank you for explaining this.  | | |
10-27-2009, 04:24 PM
|  | Exalted Member | | Join Date: Aug 2009 Location: Right after that really long cutscene
Posts: 162
| | |
Two at 40%. I hate probability. You either win or lose. It's always 50/50 no matter how statisticians try to gussy it up. Two chances are better than one, therefore take the second bet.
| | |
10-27-2009, 04:39 PM
|  | Exalted Member | | Join Date: Oct 2005 Location: UK
Posts: 1,254
| |
Well; being totally hopeless at figures, and not understanding - or even wishing to understand! - the explanations, I would go with one @ 60% chance of winning. I understand that in normal circumstances every throw of a die is 50/50, but in the given circumstance it's either one at 60% or two at 40% each. The one is above the average, the two are below the average, as Fable said, so you have a slightly better chance with the one 60-percenter, imo. But what do I know? I'm dumb with numbers.  | | |
10-27-2009, 04:41 PM
| | Exalted Member | | Join Date: Oct 2005
Posts: 2,647
| |
Hmm, I should've made this into a poll..  | | |
10-27-2009, 04:45 PM
| | Exalted Member | | Join Date: Aug 2009 Location: Right after that really long cutscene
Posts: 162
| | Quote:
Originally Posted by Tricky Hmm, I should've made this into a poll.. | Then the statisticians will win!
| | |
10-27-2009, 06:15 PM
|  | Exalted Member | | Join Date: Nov 2006 Location: Kernow (Cornwall), UK
Posts: 2,319
| | |
Instinctively I side with Dottie, but can't be assed to work it out, but statistically I believe that two at 40% is the better option.
Of course that's with honest random numbers, start including computer generated pseudo-random numbers and conventional statistics go out the window.
__________________
"Football isn't a matter of life and death ..... It's more important than that." - Bill Shankly
| | |
10-28-2009, 04:06 AM
| | Exalted Member | | Join Date: Oct 2005
Posts: 2,647
| | |
That depends on the computer. Pseudo generated random numbers are a major security leak. My old Pentium 3 had a small temperature measurement tool that measured the thermal vibrations of a small metal element and based its random calculations on that.
| | |
10-28-2009, 09:03 AM
| ![Loki[D.d.G]'s Avatar](http://www.gamebanshee.com/forums/image.php?u=43011&dateline=1241940266) | Exalted Member | | Join Date: Jun 2007 Location: The initial frontier
Posts: 2,462
| | Quote:
Originally Posted by Tricky That depends on the computer. Pseudo generated random numbers are a major security leak. My old Pentium 3 had a small temperature measurement tool that measured the thermal vibrations of a small metal element and based its random calculations on that. | Good point. It'll be pretty interesting to see just how random a random generated computer number is. After all, it is a machine coupled with a software that conforms to their own specific rules.
| | |
10-28-2009, 09:57 AM
| | Moderator | | Join Date: Sep 2001 Location: Mindlessly floating around.
Posts: 4,262
| | |
It is true that random number generation isn't always as easy as it sounds. However, simulating the problem above is really difficult to mess up. The difference in probability is quite large, and all that is required for a two chance strategy to prevail over time is that the numbers produced have a close to uniform distribution.
__________________
While others climb the mountains High, beneath the tree I love to lie
And watch the snails go whizzing by, It's foolish but it's fun | | |
10-28-2009, 11:06 AM
| | Exalted Member | | Join Date: Oct 2005
Posts: 2,647
| | Quote:
Originally Posted by Loki[D.d.G] Good point. It'll be pretty interesting to see just how random a random generated computer number is. After all, it is a machine coupled with a software that conforms to their own specific rules. | You can actually literally 'see' that, if properly implemented: Pseudo-Random vs. True Random - A Simple Visual Example
That site compares a pseudo random number generator with a true random number generator. RANDOM.ORG - Statistical Analysis ~ more info and where I found that link.
| | Thread Tools | Search this Thread | | | | | Display Modes | Rate This Thread |  Linear Mode | | 
Posting Rules
| You may not post new threads You may not post replies You may not post attachments You may not edit your posts
HTML code is Off
| | | |
