more lottery fun

uzless
Posers and Puzzles 22 May '09 16:51
1. uzless
The So Fist
22 May '09 16:511 edit
Let's take the standard 6/49 lottery. (out of 49 numbers 6 are drawn randomly)

Assume each time you buy a ticket containing 6 numbers it costs you 1 dollar and you are going to spend 100 dollars on 100 tickets.

Are you better off to just let a computer randomly pick you 100 tickets with 6 numbers randomly chosen on each ticket,

or

are you better off picking a small subset of numbers (say 30) and rearranging them 100 different ways hoping that out of the 30, you pick the correct numbers that are chosen from the 49.

The payouts are as follows:

3 correct numbers: 10 dollars
4 correct numbers: 100 dollars
5 correct numbers: 100,000 dollars
6 correct numbers: 1 Million dollars
2. 22 May '09 17:00
Your expected gain/loss is exactly the same in all cases.

If you mean something else by "maximise your winnings" you need to be a bit more specific. Different strategies will give you different answers for things like "maximise your maximum possible winnings" or "maximise the probability of making a profit", etc.
3. uzless
The So Fist
25 May '09 17:202 edits
Originally posted by mtthw
Your expected gain/loss is exactly the same in all cases.

If you mean something else by "maximise your winnings" you need to be a bit more specific. Different strategies will give you different answers for things like "maximise your maximum possible winnings" or "maximise the probability of making a profit", etc.
The idea I was trying to get across goes like this.

If YOU pick 30 out of 49, your chances of getting at least 3 of the correct numbers are about 60%.

So, if you do get at least 3 numbers correct, then re-arranging the 30 numbers 100 different ways would hopefully result in you getting mulitiple winning tickets. Your chances of multiple winning tickets would increase if you got 4,5,6 numbers correct.

So, if you could get a 60% chance of getting 3 numbers correct by taking 30 of 49, would you do it? Or would it make no difference.

Assume you could only play the lottery for this one draw and never play it again for the rest of your life.
4. 26 May '09 16:04
Originally posted by uzless
The idea I was trying to get across goes like this.

If YOU pick 30 out of 49, your chances of getting at least 3 of the correct numbers are about 60%.

So, if you do get at least 3 numbers correct, then re-arranging the 30 numbers 100 different ways would hopefully result in you getting mulitiple winning tickets. Your chances of multiple winning tickets ...[text shortened]... could only play the lottery for this one draw and never play it again for the rest of your life.
Depends what you're trying to achieve - that's what I meant. "Maximize your winnings" can mean different things to different people.

If you want to maximise your chances of winning something, that approach might be sensible (there'll be an optimal strategy - I might try and work out what it is at some point).

If you care about your expected loss/gain, then it makes no difference.

If you wanted to maximise your potential winnings, then you'd pick the same 6 numbers on every ticket (since there's no mention of sharing a jackpot) - get the right 6 and you win 100 jackpots.

etc.
5. uzless
The So Fist
26 May '09 18:24
Originally posted by mtthw
Depends what you're trying to achieve - that's what I meant. "Maximize your winnings" can mean different things to different people.

If you want to maximise your chances of winning something, that approach might be sensible (there'll be an optimal strategy - I might try and work out what it is at some point).

If you care about your expected loss/ ...[text shortened]... re's no mention of sharing a jackpot) - get the right 6 and you win 100 jackpots.

etc.
let's go with scenario 1 shall we?