Odds and probabilities
Although I have used the UK National Lottery as an example my question really goes much further.
The lottery is roughly 14m - 1 per ticket. It is a 6 from 49 random draw. You are allowed to pick 6 numbers per ticket and must match them all (in no particular order) to win the jackpot.
My question is:
If you buy 7 random tickets (all different combinations) then odds seem to be 7/14m = just under 2m.
If you picked 7 numbers and then permed all '6 group' combinations (7) odds = just under 2m.
This is the part I dont really get...:
Would it be better to have 7 tickets entered in a 14m - 1 shot, OR 1 ticket entered in a 2m - 1 shot.
I contend that although it appears that they are the same odds the 1 ticket in 2m is the better bet.
Because the 7 tickets in the '14m - 1' shot all have a '14m - 1' chance of winning. So you have 7 chances at '14m to 1'. Or to put it another way there are 13,999, 993 chances of losing.
Whereas the 1 ticket in a 2m to 1 shot has a 2m to 1 chance of winning or 1,999,999 chances of losing.
Therefore the 1 ticket in the 2m lottery has a far lower number of non winning chances... (around 12,000,000 less chances!) so it must be a better bet...
Am I right???
any math proffessors out there or where could I look. I will admit that the math would seem to say that they are even, but if they are I cant understand how.
You can't go by how many chances there are absolutely, but by the ratio of possible wins to losses. So you have to take into account the total amount. 13,999,993/14,000,000 is close to 1,999,999/2,000,000, even though there is a difference of 12,000,000. Your approach of just look at the possibility of wins is inappropriate. For example, if you have a 50% chance of winning in the 14,000,000, or 7,000,000 this is about 5,000,000 more chances of losing than 1,999,999 out of 2,000,000, but its clearly the better option. An even easier example would be 1/5 chance versus a 5/10 chance. There's 4 ways to lose in the first one, and 5 ways to lose in the 2nd, but 5/10 = 1/2 is a much higher chance of winning than 1/5.