On Probability

eternal_noob

eternal_noob

Let's pretend there is a game and the prize is the thing you ever wanted. There are several tickets which have a certain probability to win that prize.

Ticket 1:
Probability to win: 15%
Price: $120

Ticket 2:
Probability to win: 9%
Price: $60

Ticket 3:
Probability to win: 6%
Price: $20

Which ticket offers the best value for money if you buy as much tickets until you win. Of course you want to spend as little money as possible.
 
hruodr said:
I need 100/6 tickets, for 20*100/6 = 333 1/3 $ for winning, the other are 666 2/3 and 800 $.
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Crivens said:
That's not how this works..
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If anything you can calculate on that few info that's given then it's % to win per $, that would be:
15/120=0.125
9/60=0.15
6/20=0.3
So 1 and 2 are almost equally bad, and 3 is by far best.
However, you're dealing with probability, which means even when you buy tickets together come >100% you still can lose, while you can win by buying a single ticket with lowest probability.
 
- Which ticket offers the best value for money
------> compare 3 fractions,
- if you buy as much tickets until you win.
------> there is a distribution for this, but i forgot which one.
---------------------> like 1 + 0.3¹ +0.3 ² +...... = 1/(1-0.3)
 
I would say all are the same irrespective of percentages or currency then. I would look to trade a few tickets in exchange for a burger or a pizza pie.

Something along those lines
 
Ticket 1:
Probability to win: 15%
Price: $120

Total change to win :

0.15+ (1-0.15)*0.15 + (1-0.15)^2*0.15+.....
=0.15*[ 0.85⁰ +0.85¹ +0.85² +++++]
=0.15/(1-0.85)
=1

Ok we see where this is going.
I would bye Ticket 3.
 
hruodr said:
I need 100/6 tickets
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Understandable reasoning, but it assumes when you buy 100 tickets you're guaranteed to have 6 winning ones. Each individual ticket of the 100 has a 6% chance of winning. Not that 6% of the tickets are winning tickets.

It's an interesting math problem, and some statistics thrown in. But you're never guaranteed to win, regardless of the amount of tickets you buy. Unless you buy a significant portion of the total amount of available tickets. But we don't know how many tickets there are.
 
The more chance you win the first time, the lower the change you first win the second time , because it gets multiplied by the not winning the first time. So the series start higher but go down faster. :)
 
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