# Pick a number - in practice.

FabianFnas
Posers and Puzzles 12 Sep '08 07:14
1. 12 Sep '08 07:14
I'm referring to the "Pick a number, any number" thread,
This will be an experiment of the above game "Pick a number".

The rules are as follows:
Pick a number, any number (but it has to be a positive integer). He/she who choose the lowest number has won. You bet a (virtual) dollar and you win the pot of the round.

How it is done here:
Put the bet in a personal mail to me (FabianFnas), use "Pick a number" as the title and in the mail body you write "I bet on 3" or something, and send it.
Every day from now, at this approximate time, I collect the mails, and decide the lowest number and give him the (virtual) amount of dollars betted. I will make the bettings and choosing of the numbers public, so we cn make conclusions, in this thread.

Only for fun, no real dollars involved.
Any questions?

Okay, here we go. Place your bet on a number by mail.
2. 12 Sep '08 08:26
For those who may not have read the other thread, it's the lowest unique number that wins. So don't all send in "1".
3. 12 Sep '08 08:54
Originally posted by Jirakon
For those who may not have read the other thread, it's the lowest unique number that wins. So don't all send in "1".
Sorry, yes of course, the lowest unique number.
Thank you Jirakon
4. wolfgang59
Mr. Wolf
12 Sep '08 10:03
mmmmmmmm the strategy will depend on the number of players. My guess is that with N opponents an optimal strategy is to randomly choose 1 with probability 1/N to choose 2 with probability 1/N^2
etcetera.
5. 12 Sep '08 11:28
Originally posted by wolfgang59
mmmmmmmm the strategy will depend on the number of players. My guess is that with N opponents an optimal strategy is to randomly choose 1 with probability 1/N to choose 2 with probability 1/N^2
etcetera.
Noone will know how many there is beting. I won't tell until I present the outcome.
6. 13 Sep '08 07:13
This is the result of this first round, round 1, of betting in the game of "Pick a number:

3 betters (in alphabetical order): forkedknight, golfer1, and wolfgang59.

Every bet cost one (virtual) dollar so before I present who won, they have an individual account of -1 dollar.

The three guesses were (in numerical order): 1, 7, 7.

And the today's winner is (*drums*) forkedknight!

Here are the accounts after the round 1:
forkedknight: 2
golfer1: -1
wolfgang59: -1

Now starts round 2, please put your bettings. Tomorrow at this time I will present the new winner.

Okay, that's it. This is how I will present every round. I don't want to tell what each and one of you guessed, but I will present who betted, and what they guessed, but no individual info. This is about strategy, and I don't want to reveal any strategy of the participants. If anyone will reveal their strategy, it's their business. Today it's not hard to know who guessed what, but with more betters than this, it will be harder.

7. 14 Sep '08 07:20
This is the result of this round 2 of bettings in the game of "Pick a number:

3 betters (in alphabetical order): doodinthemood, golfer1, heinzkat , and Scheel.

Four guesses were (in numerical order): 1, 2, 3, 7.

The winner (4 dollar) of this round is (*drums*) doodinthemood.

Here are the accounts after the round 2:
doodinthemood: 3
forkedknight: 2
wolfgang59: -1
Scheel: -1
heinzkat: -1
golfer1: -2

The lowest possible guess (1) has won two times. Isn't it a good affair to bet on 1 again?

(Round 3 will be presented two hour earlier than today.)
8. 15 Sep '08 04:37
This is round 3 of "Pick a Number" game.

These players (presented alphabetically) golfer1, greenpawn34, Scheel
has bet a dollor on 3, 4, and 7.

Winner is (*drums*) Scheel !

Here are the accounts after the round 3:
doodinthemood: 3
forkedknight: 2
Scheel: 1
wolfgang59: -1
heinzkat: -1
greenpawn34: -1
golfer1: -3
9. TheMaster37
Kupikupopo!
15 Sep '08 07:00
Originally posted by FabianFnas
This is round 3 of "Pick a Number" game.

These players (presented alphabetically) golfer1, greenpawn34, Scheel
has bet a dollor on 3, 4, and 7.

Winner is (*drums*) Scheel !

Here are the accounts after the round 3:
doodinthemood: 3
forkedknight: 2
Scheel: 1
wolfgang59: -1
heinzkat: -1
greenpawn34: -1
golfer1: -3
I've played a similar game.

"What percentage of participants answer this question correctly?"

I'm guessing around the 20.000 people participated. I was one of the winners with 7% I believe. The correct answer depends greatly on the number of participants.

Very nice!
10. 16 Sep '08 04:30
This is round 4 of "Pick a Number" game.

These players (presented alphabetically) doodinthemood, golfer1, TheMaster37, wolfgang59 have bet a dollar on 1, 1, 2, and 7.

Winner is (*drums*) wolfgang59 because he bet on 2, the lowest unique number.

Here are the accounts after the round 3:
doodinthemood: 2
forkedknight: 2
wolfgang59: 2
Scheel: 1
heinzkat: -1
greenpawn34: -1
TheMaster37 -1
golfer1: -4
11. 16 Sep '08 15:28
Originally posted by TheMaster37
I've played a similar game.

"What percentage of participants answer this question correctly?"

I'm guessing around the 20.000 people participated. I was one of the winners with 7% I believe. The correct answer depends greatly on the number of participants.

Very nice!
The answer is to pick the percentage which you represent:
If there are 2 people, then you pick 50% and if the other person picks anything other than 50% then you win.
If there are 3 people, then you pick 33% and the same is true for neither of the others picking it.

For 20,000 people, if you round the answer, 0% wins.
12. TheMaster37
Kupikupopo!
17 Sep '08 06:23
Originally posted by doodinthemood
The answer is to pick the percentage which you represent:
If there are 2 people, then you pick 50% and if the other person picks anything other than 50% then you win.
If there are 3 people, then you pick 33% and the same is true for neither of the others picking it.

For 20,000 people, if you round the answer, 0% wins.
Ah, but if more people use that reasoning 0% would be one of the worst answers.

My reasoning at that time was that alot of people would pick the lowest percentages, to anything under 6% would be wrong. People who thought of that would go for 7 -10 %. At this time I figured most would then go for 8 or 9%, leaving 7% for the people who really put some thought into it :p
13. 17 Sep '08 08:07
First I have to give heinzkat an apology. He did in fact guess "1" in round two and doodinthemood guessed "2". Therefore doodinthemood falsely got 4 dollars and heinzkat didn't. As a consequence from my error, I take 4 dollars from doodinthemood's account and give to heinzkat.

So here is the result of round 5:

I sense some lost interest of this game, only Wolfgang has made a bet. He quessed 2 and as this was the only bet he won back his dollar.

The accounts is as follows, corrected from my previous mistake:
heinzkat: 3
forkedknight: 2
wolfgang59: 2
Scheel: 1
greenpawn34: -1
TheMaster37 -1
doodinthemood: -2
golfer1: -4

wolfgang59 has made a bet for round 6, but I think that round 5 will be the last round. I thank you all for the interest.
14. wolfgang59
Mr. Wolf
17 Sep '08 09:40
Originally posted by FabianFnas

So here is the result of round 5:

I sense some lost interest of this game, only Wolfgang has made a bet. He quessed 2 and as this was the only bet he won back his dollar.

After the house took its cut I only got 90 cents ... :'(
15. 17 Sep '08 11:47
It seems I won the competition then... :-))) (you should have put a footnote somewhere that correspondence about the outcome is prohibited)