Math/Statistics Question

[LuFins Dad]

Would you statistically have a better chance of winning a lottery if you picked the exact same set of numbers over and over or if you had a random set every time?

[Doctor Phibes]

Past numbers have no bearing on future results, so it doesn't matter which set of numbers you use, you're equally unlikely to win.

[LuFins Dad]

@doctor-phibes That was my original take, and every single drawing the odds would be the same, but over 1000 attempts? 10,000? 100,000?

Are the odds of losing 1000000 times in a row the exact inverse of winning once in 1000000 times?

[Doctor Phibes]

Each drawing of lots is an independent event. Take a simpler case - if you throw heads three time with an unbiased coin, your chance of throwing heads on the fourth throw is still 1/2. However, before you throw the first throw, your chances of throwing four heads in a row is 1/16.

[LuFins Dad]

@doctor-phibes said in Math/Statistics Question:

Each drawing of lots is an independent event. Take a simpler case - if you throw heads three time with an unbiased coin, your chance of throwing heads on the fourth throw is still 1/2. However, before you throw the first throw, your chances of throwing four heads in a row is 1/16.

Using that example, in a sequence of sixteen throws, each individual throw is going to be 50/50, but the odds that I roll eight heads and eight tails over the sequence would be the the highest probability, 7 of 9 either way would be the next highest probability, 6-10, and so on. So if I throw 4 tails in a roll, doesn’t it increase the chances (assuming the throws truly are random) that my next throw will be heads?

[Horace]

The only meaningful strategy for picking numbers in a lottery is to try to pick a number nobody else picked. So any pattern or logic that others might use should be avoided. Use a random number.

[Doctor Phibes]

@lufins-dad said in Math/Statistics Question:

So if I throw 4 tails in a roll, doesn’t it increase the chances (assuming the throws truly are random) that my next throw will be heads?

No, since the result of each throw is independent of the results of previous throws. It is somewhat counter-intuitive.

[Doctor Phibes]

@horace said in Math/Statistics Question:

The only meaningful strategy for picking numbers in a lottery is to try to pick a number nobody else picked. So any pattern or logic that others might use should be avoided. Use a random number.

That doesn't increase your chances of winning, but it does increase your chances of winning all of the money (i.e. not sharing with other winners) if the number comes up.

[Horace]

@doctor-phibes said in Math/Statistics Question:

@horace said in Math/Statistics Question:

The only meaningful strategy for picking numbers in a lottery is to try to pick a number nobody else picked. So any pattern or logic that others might use should be avoided. Use a random number.

That doesn't increase your chances of winning, but it does increase your chances of winning all of the money (i.e. not sharing with other winners) if the number comes up.

Yes that’s why it’s a meaningful strategy. Increased expected return on investment.

[Klaus]

I believe lottery numbers are often not truly random and some numbers have slightly higher probabilities than others. One should optimize for combinations that are rarely picked and more likely than average. Of course, even then the expected return is usually smaller than the investment.