Atheism and the Paranormal

[Tiberius]

Another misconception is how odds actually work. EG Here the odds of winning the major prize in the state lottery is 1 in 30 MILLION. Buying two tickets doe0s NOT reduce the odds to 1 in 15 million and so on. Buying 10,000 tickets means you have 10,000 chances,but the odds of any one ticket winning remain at 1 in 30 million.

Actually, that depends on what you mean.

If, for instance, there are 30 million different combinations of the lottery numbers, and you have 1 ticket (with one possible combination) then your odds of winning by chance are 1 in 30 million. If you buy 2 tickets, as long as they have different combinations on them, your odds are now 2 in 30 million, which is the same as 1 in 15 million.

You have doubled your chances, because you've doubled the number of tickets. Do it again and you'll get odds of 1 in 7.5 million. Yes, every winning ticket still has the odds of winning of 1 in 30 million, but you are combining the odds when you buy more.

In statistics, if one event is dependent on the previous, you multiply odds to get the result. For instance, if you wanted to pick out 4 Aces from a pack of cards, the odds are:

4/52 (for the first Ace) * 3/51 (for the second) * 2/50 (for the third) * 1/49 (for the fourth)

Picking out an Ace is one event, and since you want to do it 4 times in a row, you need to multiply the odds of each pick. The same goes for the actual lottery numbers (i.e. 1/49 * 1/48 * 1/47...)

However, if you want to find the odds of picking out an Ace OR a King, the calculation involves addition:

4/52 (for the Ace) + 4/52 (for the King)

Another way of looking at it is to create a hypothetical scenario where a man buys all possible combinations of numbers (i.e. 30 million). Are his chances still only 1 in 30 million? Well, for each individual ticket, yes, but for all tickets combined, his chance of winning is 1 (i.e. absolute certainty). If you have all the tickets in a raffle, you are going to win everything...same logic.

Of course, the reason why people don't buy 2 tickets (or at least shouldn't) is that 1 in 15 million odds aren't really much better. If you want to get 50% odds (which isn't that good either...) then you need to buy 15 million tickets. If you've got £15 million, you don't need to play the lottery.