I have just had a disagreement with a friend who thinks that your chance of winning the lottery is greater if your buy five tickets in one week than if you were to buy one ticket per week over five consecutive weeks.

What does every think about this?

I agree with your friend, assuming you're buying different numbers -- you should take this over to General Gambling > Probability for more information.

Assuming the same lottery and for example a 1/1000000 chance of winning for theory's sake:

5 different numbers one week:
1/1000000 + (999999/1000000 * 1/1000000) + (999998/1000000 * 1/1000000) + (999997/1000000 * 1/1000000) + (999996/1000000 * 1/1000000) = 4.99999 × 10-6 =~ 0.000004999 or 0.0004999% (4.999 in a million)

5 weeks with one ticket each week:
1/1000000 * 5 = 0.000005 or 0.0005% (5 in a million)

Your friend is correct. Although as far as the realities of playing and real odds go, you have pretty much about the same chance of winning with either way, or for that matter about the same chances as when not buying tickets at all.

the interest you make on the money from only doing 1 per week might outpace the expected value you gain by doing it all in one week

only doing 1 per week also leaves open the possibility that you'll die partway through and not get to buy those 3rd, 4th or 5th tickets, which is a nice way to maximize your EV

Mega Millions has 175 Million possible combinations. If you bought all 175 million combinations you are 100% guaranteed to win. If you bought 1 ticket a week for 175 million weeks you only have a 63% chance to have won after that time.

But you have the chance to win multiple times.

That 63% number IS the chance to win one or more times. Not just exactly once.

I've always wondered this. Not that I play the lottery anyway.. Biggest win was like $25 after 2 years of playing