Sherlockx's Cenote, Sherlockx's Brain Cenote.
The similarities are scary: One was a place of sheer human malevolence, where blood, pain and tears flowed freely.
The other is one of Sherlockx's damnable riddles.
I just realized that in the "staff members" contest under "date" I should have been entering the time of the snapshot, and not the posting time. Not that it differs by more than a couple of minutes in most cases, but hopefully that isn't a problem...
Sorry, I'm no longer re-uploading expired releases.
In 3 consecutive games of Double or Nothing there are 8 possible outcomes (2 possibilities each time, cubed). If we call them W and L for win and lose, they are:
1. WWW
2. WWL
3. WLW
4. WLL
5. LWW
6. LWL
7. LLW
8. LLL
If you bet the same amount (call it B) each time, then the pay-offs are:
1. +3B
2. +1B
3. +1B
4. -1B
5. +1B
6. -1B
7. -1B
8. -3B
Each of the 8 outcomes is equally likely. So to find the average outcome (the “expected value” in math jargon) we just add up the B's and divide by 8. The result, without payback, is 0. With payback, however, the pay-off for outcome 8 changes to 0 and the sum is 3B. Now the average pay-off is 3/8 x B.
BUT... things are actually even better than that: if you keep playing, with outcomes 2, 4 and 6 you still have a chance of getting a payback. So let's look at what happens if you go to 4 games. Now there are 2^4=16 possible outcomes. Here they are, with their pay-offs:
1. WWWW -> +4B
2. WWWL -> +2B
3. WWLW -> +2B
4. WWLL -> 0
5. WLWW -> +2B
6. WLWL -> 0
7. WLLW -> 0
8. WLLL -> -2B (with payback, +1B)
9. LWWW -> +2B
10. LWWL -> 0
11. LWLW -> 0
12. LWLL -> -2B
13. LLWW -> 0
14. LLWL -> -2B
15. LLLW -> -2B (with payback, +1B)
16. LLLL -> -4B (with payback, -1B)
Without payback the average pay-off is still zero (the +B's and -B's cancel out). But with payback the average is now 9/16 x B. Importantly, 9/16 is more than 3/8 (=6/16).
Similarly, if you play five times the average pay-off (with payback) rises to 24/32 (or 12/16) x B. After six games it's 56/64 (or 14/16) x B.
There's obviously a formula in here somewhere for "n" games, although I haven't figured it out yet (it's been a frighteningly long time since I pottered around with probability theory in university). Most likely it's quite messy and involves both factorials and the number 3. I suspect that as you keep on playing (n gets bigger and bigger) the average pay-off is going to converge on 1B. Whether or not that is correct, it's going to be some positive multiple of B. And that suggests that you should make your bet as large as possible – although small enough that you can afford to keep repeating it.
1. WWW
2. WWL
3. WLW
4. WLL
5. LWW
6. LWL
7. LLW
8. LLL
If you bet the same amount (call it B) each time, then the pay-offs are:
1. +3B
2. +1B
3. +1B
4. -1B
5. +1B
6. -1B
7. -1B
8. -3B
Each of the 8 outcomes is equally likely. So to find the average outcome (the “expected value” in math jargon) we just add up the B's and divide by 8. The result, without payback, is 0. With payback, however, the pay-off for outcome 8 changes to 0 and the sum is 3B. Now the average pay-off is 3/8 x B.
BUT... things are actually even better than that: if you keep playing, with outcomes 2, 4 and 6 you still have a chance of getting a payback. So let's look at what happens if you go to 4 games. Now there are 2^4=16 possible outcomes. Here they are, with their pay-offs:
1. WWWW -> +4B
2. WWWL -> +2B
3. WWLW -> +2B
4. WWLL -> 0
5. WLWW -> +2B
6. WLWL -> 0
7. WLLW -> 0
8. WLLL -> -2B (with payback, +1B)
9. LWWW -> +2B
10. LWWL -> 0
11. LWLW -> 0
12. LWLL -> -2B
13. LLWW -> 0
14. LLWL -> -2B
15. LLLW -> -2B (with payback, +1B)
16. LLLL -> -4B (with payback, -1B)
Without payback the average pay-off is still zero (the +B's and -B's cancel out). But with payback the average is now 9/16 x B. Importantly, 9/16 is more than 3/8 (=6/16).
Similarly, if you play five times the average pay-off (with payback) rises to 24/32 (or 12/16) x B. After six games it's 56/64 (or 14/16) x B.
There's obviously a formula in here somewhere for "n" games, although I haven't figured it out yet (it's been a frighteningly long time since I pottered around with probability theory in university). Most likely it's quite messy and involves both factorials and the number 3. I suspect that as you keep on playing (n gets bigger and bigger) the average pay-off is going to converge on 1B. Whether or not that is correct, it's going to be some positive multiple of B. And that suggests that you should make your bet as large as possible – although small enough that you can afford to keep repeating it.
Last edited by avoran on May 25th, 2014, 12:40 pm, edited 2 times in total.
Sorry, I'm no longer re-uploading expired releases.
Help! I changed the site format setting under user preferences from 'ppz' (I think it was called) to 'Mobilism 2.0'. Now I want to change it back but can't, since the equivalent page under user preferences (ucp.php?i=165) no longer has the option. (!) Where do I go??
BTW staff take note - there really ought to be a generic 'Help' forum accessible from the main forum page. I couldn't find one.
BTW staff take note - there really ought to be a generic 'Help' forum accessible from the main forum page. I couldn't find one.
Sorry, I'm no longer re-uploading expired releases.
avoran wrote:Help! I changed the site format setting under user preferences from 'ppz' (I think it was called) to 'Mobilism 2.0'. Now I want to change it back but can't, since the equivalent page under user preferences (ucp.php?i=165) no longer has the option. (!) Where do I go??
BTW staff take note - there really ought to be a generic 'Help' forum accessible from the main forum page. I couldn't find one.
Try this:
bandicoot wrote:In beta stylesheet switch to mobile style.
Then click on settings button in top-right corner.
Then select User Control Panel.
Then click on overview.
Then select board preferences.
Then select my board style.
Change it to 'ppcw' and click on submit.
Now click on switch to full style.
Back to normal.
Don't know why there is no direct option to change from beta to ppcw style...
I am going to hold off posting another riddle so you can all try to get your heads round the 40 questions.
It did occur to me that I get to have all the fun so I am inviting you to think up a guest riddle to see if you can beat your colleagues.
Now a lot of the fun is seeing all the wrong guesses so if you can think of a worthy riddle your reward will be ten times the number of posted replies. in WRZ$. so 40 posts in your riddle gets you 400WRZ$.
pm your riddle and the answer to any of the contest managers together with your choice as to whether you wish to moderate the replies yourself or which of the Contest managers you want to do it.
It did occur to me that I get to have all the fun so I am inviting you to think up a guest riddle to see if you can beat your colleagues.
Now a lot of the fun is seeing all the wrong guesses so if you can think of a worthy riddle your reward will be ten times the number of posted replies. in WRZ$. so 40 posts in your riddle gets you 400WRZ$.
pm your riddle and the answer to any of the contest managers together with your choice as to whether you wish to moderate the replies yourself or which of the Contest managers you want to do it.
a million dollar question
is the contest "move on the other side" ever gonna start?
is the contest "move on the other side" ever gonna start?
Guy, I have been waiting (patiently) for four months for you to put the spares to the test as you said here: viewtopic.php?p=1701323#1701323 I demand you do it!
Just kidding, of course, but can we officially declare an end to the Go 4 it! contest?
Next we shall put the spare players to the test....
Just kidding, of course, but can we officially declare an end to the Go 4 it! contest?
On a more serious note, however, have we looked into a new form of the "contests tournament"?