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Math brain teasers require computations to solve.

 

Puzzle ID:#1048
Fun:*** (2.65)
Difficulty:** (1.98)
Category:Math
Submitted By:vivek***

 

 

 



The famous playboy explained to a beautiful woman his system for playing roulette: "In each round, I always bet half of the money I have at the time on red. Yesterday, I counted and I had won as many rounds as I had lost." Over the course of the night, did the gambler win, lose or break even?


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Answer

He lost. Every time he wins, his money increases 1.5 times (with $100, he bets $50 and if he wins, he has $150). When he loses, his money is reduced by half. So a win-loss combination results in a loss of one quarter of his money. The more he plays, the more money he loses, even though he wins the same number of times as he loses.

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Comments

tec_ocd
Jan 09, 2004

nice. my friends method is each time he loses he bets three times his previous loss (which would cover all previous losses in that set of bets) and as soon as he wins he starts back at a low bet again. it seems this method would win small amount most of the time but lose insanely every once in a great while.... also i wonder how winning and losing streaks affect your theory.
tec_ocd
Jan 09, 2004

something like
1.5 ^ nw
versus
.5 ^ nl
where:
^ means to the power of
nw means number of wins in a row
nl means number of losses in a row

oh wait never mind he still loses on average
addspras**
Mar 14, 2014

the teaser doesn't mention that he would win 50% on every win, how are we supposed to calculate?
samuelurrea
Dec 05, 2014

I am mexican and a couple of minutes ago i was reading a spanish version of this riddle, the spanish version says:

If he has 16 euros and he wins 3 times and loses other 3 times (No matter the order) how much money does he end up with?

The solution they give is that he will end up with 6.75 euros, having a loss of 9 .25 euros.


They don't explain why they came out with that number, so i wrote down this in order to see if that argument was right or wrong...

If you have 16 euros and you bet 8 euros and you lose, (1st time) you end up with 8 euros, you bet 4 euros, and you lose (2nd time) you end up with 4 euros, you bet 2 euros and you lose (3rd time) you end up with 2 euros...

You bet 1 euro (4th time) you win, you end up with 3 euros..
you bet 1.5 euros (5th time) you win, you end up with 4.5 euros...
you bet 2.25 euros (6th time) you win, you end up with 6.75 euros having a loss of 9.25 euros

6.75 is the 57.813% of 9.25

So, what's up with that? in this riddle they don't mention the original amount of money the gambler has, neither the minimum bet possible, so, it's implicit the 25% of loss can happen in any kind of situation, and starting with 16 euros is a situation where that premise is totally wrong.
samuelurrea
Dec 05, 2014

Sorry, i made some mistakes in the comment i just wrote, this is the same comment without the errors...

I am mexican and a couple of minutes ago i was reading a spanish version of this teaser, the spanish version says:

If he has 16 euros and he wins 3 times and loses other 3 times (No matter the order) how much money does he end up with?

The solution they give is that he will end up with 6.75 euros, having a loss of 9 .25 euros.


They don't explain why they came out with that number, so i wrote thi down in order to see if that argument was right or wrong...

If you have 16 euros and you bet 8 euros and you lose, (1st time) you end up with 8 euros, you bet 4 euros, and you lose (2nd time) you end up with 4 euros, you bet 2 euros and you lose (3rd time) you end up with 2 euros...

You bet 1 euro (4th time) you win, you end up with 3 euros..
you bet 1.5 euros (5th time) you win, you end up with 4.5 euros...
you bet 2.25 euros (6th time) you win, you end up with 6.75 euros having a loss of 9.25 euros

9.25 is the 57.813% of 16

So, what's up with that? in this riddle they don't mention the original amount of money the gambler has, neither the minimum bet possible, so, it's implicit the 25% of loss can happen in any kind of situation, and starting with 16 euros is a kind of situation where that premise is totally wrong.
samuelurrea
Dec 05, 2014

Damn it, there was another error and you can't edit the comments xD

Here is the comment without the errors...

I am mexican and a couple of minutes ago i was reading a spanish version of this teaser, the spanish version says:

If he has 16 euros and he wins 3 times and loses other 3 times (No matter the order) how much money does he end up with?

The solution they give is that he will end up with 6.75 euros, having a loss of 9 .25 euros.


They don't explain why they came out with that number, so i wrote this down in order to see if that argument was right or wrong...

If you have 16 euros and you bet 8 euros and you lose, (1st time) you end up with 8 euros, you bet 4 euros, and you lose (2nd time) you end up with 4 euros, you bet 2 euros and you lose (3rd time) you end up with 2 euros...

You bet 1 euro (4th time) you win, you end up with 3 euros..
you bet 1.5 euros (5th time) you win, you end up with 4.5 euros...
you bet 2.25 euros (6th time) you win, you end up with 6.75 euros having a loss of 9.25 euros

9.25 is the 57.813% of 16

So, what's up with that? in this riddle they don't mention the original amount of money the gambler has, neither the minimum bet possible, so, it's implicit the 25% of loss can happen in any kind of situation, and starting with 16 euros is a kind of situation where that premise is totally wrong.



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