A question for the mathematicians on this site

[edeholland]

Hey all, I have a question inspired by a bar I visited not too long ago. The bar has a lucky wheel. For 10 euros, you can spin the wheel once, and you get the prize that you spin. Possible prizes include: four shots of vodka, a bottle of prosecco, 5 beers, etc. There one prize that's different from the rest: it gives you four shots and you may spin the wheel again. This means that's in possible in theory to spin that specific prize 5 times in a row and get 20 free shots.

However, this is their advertisement: Translated it says: you can win an infinite amount of shots or a bottle of prosecco.

My question is the following: is it actually possible to win an infinite amount of shots? Let's say there are 16 different prizez you can win. If you calculate 1/16 * 1/16 * 1/16 * 1/16 ..... doesn't that equal 0? Doesn't that mean there is a chance of 0 to actually win an infinite amount of shots?

I'm currently discussing this with a few friends but nobody is actually good at proofing this, so I hope @RefluxSemantic or @iNcog or @Goodspeed can share their thoughts.

[RefluxSemantic]

I believe that 1/x in the limit of x->infinity indeed does go to zero.

[Mr_Bramboy]

My question is the following: is it actually possible to win an infinite amount of shots? Let's say there are 16 different prices you can win. If you calculate 1/16 * 1/16 * 1/16 * 1/16 ..... doesn't that equal 0? Doesn't that mean there is a chance of 0 to actually win an infinite amount of shots?

Your maths are wrong. If you want to calculate the chance of spinning the free spin, you do not only factor in the chance of that circumstance (1/16) but also the chance of any other circumstance (15/16).

The chance of one free spin is (1/16 * 15/16) = 0.058.

[harcha]

My question is the following: is it actually possible to win an infinite amount of shots? Let's say there are 16 different prices you can win. If you calculate 1/16 * 1/16 * 1/16 * 1/16 ..... doesn't that equal 0? Doesn't that mean there is a chance of 0 to actually win an infinite amount of shots?

Your maths are wrong. If you want to calculate the chance of spinning the free spin, you do not only factor in the chance of that circumstance (1/16) but also the chance of any other circumstance (15/16).

The chance of one free spin is (1/16 * 15/16) = 0.058.

could you explain why, i feel dumb reading this

also prize not price wtf @edeholland

[Goodspeed]

My question is the following: is it actually possible to win an infinite amount of shots? Let's say there are 16 different prices you can win. If you calculate 1/16 * 1/16 * 1/16 * 1/16 ..... doesn't that equal 0? Doesn't that mean there is a chance of 0 to actually win an infinite amount of shots?

Your maths are wrong. If you want to calculate the chance of spinning the free spin, you do not only factor in the chance of that circumstance (1/16) but also the chance of any other circumstance (15/16).

The chance of one free spin is (1/16 * 15/16) = 0.058.

??

That would be the chance of getting the free spin first, and then anything else the second time you spin it.

[iNcog]

-- deleted post --

[Mr_Bramboy]

My question is the following: is it actually possible to win an infinite amount of shots? Let's say there are 16 different prices you can win. If you calculate 1/16 * 1/16 * 1/16 * 1/16 ..... doesn't that equal 0? Doesn't that mean there is a chance of 0 to actually win an infinite amount of shots?

Your maths are wrong. If you want to calculate the chance of spinning the free spin, you do not only factor in the chance of that circumstance (1/16) but also the chance of any other circumstance (15/16).

The chance of one free spin is (1/16 * 15/16) = 0.058.

??

That would be the chance of getting the free spin first, and then anything else the second time you spin it.

Wasn't that the question? Maybe I understood it wrongly.

[harcha]

what i think ede was saying is that one of the outcomes of a spin includes both of the following: 4 shots and another spin, so getting infinite shots would mean to infinitely land on this option

[Goodspeed]

Show hidden quotes

My question is the following: is it actually possible to win an infinite amount of shots? Let's say there are 16 different prices you can win. If you calculate 1/16 * 1/16 * 1/16 * 1/16 ..... doesn't that equal 0? Doesn't that mean there is a chance of 0 to actually win an infinite amount of shots?

Your maths are wrong. If you want to calculate the chance of spinning the free spin, you do not only factor in the chance of that circumstance (1/16) but also the chance of any other circumstance (15/16).

The chance of one free spin is (1/16 * 15/16) = 0.058.

??

That would be the chance of getting the free spin first, and then anything else the second time you spin it.

Wasn't that the question? Maybe I understood it wrongly.

The question is can you win an infinite amount of shots.

It would depend on whether 1/16 ^ infinity = 0, which appears to be the case: https://math.stackexchange.com/question ... s-infinity

[iNcog]

-- deleted post --

[princeofcarthage]

It never becomes absolute zero, it tends to be zero

[iNcog]

-- deleted post --

[RefluxSemantic]

Show hidden quotes

My question is the following: is it actually possible to win an infinite amount of shots? Let's say there are 16 different prices you can win. If you calculate 1/16 * 1/16 * 1/16 * 1/16 ..... doesn't that equal 0? Doesn't that mean there is a chance of 0 to actually win an infinite amount of shots?

Your maths are wrong. If you want to calculate the chance of spinning the free spin, you do not only factor in the chance of that circumstance (1/16) but also the chance of any other circumstance (15/16).

The chance of one free spin is (1/16 * 15/16) = 0.058.

??

That would be the chance of getting the free spin first, and then anything else the second time you spin it.

Wasn't that the question? Maybe I understood it wrongly.

The question is can you win an infinite amount of shots.

It would depend on whether 1/16 ^ infinity = 0, which appears to be the case: https://math.stackexchange.com/question ... s-infinity

at what value of n for 1/16 ^ n does it become 0?

infinite

[edeholland]

It never becomes absolute zero, it tends to be zero

If it never becomes zero, does that mean it's possible to win an infinite amount of shots?

[princeofcarthage]

It never becomes absolute zero, it tends to be zero

If it never becomes zero, does that mean it's possible to win an infinite amount of shots?

Mathematically yes, practically probably no.

[edeholland]

It never becomes absolute zero, it tends to be zero

If it never becomes zero, does that mean it's possible to win an infinite amount of shots?

Mathematically yes, practically probably no.

The issue with that is I can rephrase it to say "With infinite luck, you can win infinite shots" which would mean that it's not possible to win infinite shots.

[RefluxSemantic]

Mathematically this is the question:
f (x) = 1/(16^x)
What is f(x) in the limit of x -> inf

And the answer to that is that
lim x->inf (f(x)) = 0

[princeofcarthage]

Well it isn't exactly luck based, weather the spin will stop on infinite shots depends on factors, most of which are beyond absolute human control. Hence it gives the impression of luck. If you could for ex control the circumstances with absolute certainty say for ex with a robot, in a controlled environment you can get infinite free shots.

[RefluxSemantic]

No, the chance that you get infinite shots is zero.

[fightinfrenchman]

Well it isn't exactly luck based, weather the spin will stop on infinite shots depends on factors, most of which are beyond absolute human control. Hence it gives the impression of luck. If you could for ex control the circumstances with absolute certainty say for ex with a robot, in a controlled environment you can get infinite free shots.

Getting the spin right every time would be difficult if you're doing 4 shots of vodka every time.

[iNcog]

-- deleted post --

[RefluxSemantic]

Show hidden quotes

My question is the following: is it actually possible to win an infinite amount of shots? Let's say there are 16 different prices you can win. If you calculate 1/16 * 1/16 * 1/16 * 1/16 ..... doesn't that equal 0? Doesn't that mean there is a chance of 0 to actually win an infinite amount of shots?

Your maths are wrong. If you want to calculate the chance of spinning the free spin, you do not only factor in the chance of that circumstance (1/16) but also the chance of any other circumstance (15/16).

The chance of one free spin is (1/16 * 15/16) = 0.058.

??

That would be the chance of getting the free spin first, and then anything else the second time you spin it.

Wasn't that the question? Maybe I understood it wrongly.

The question is can you win an infinite amount of shots.

It would depend on whether 1/16 ^ infinity = 0, which appears to be the case: https://math.stackexchange.com/question ... s-infinity

at what value of n for 1/16 ^ n does it become 0?

infinite

that's not a real number, it's an idea

I'm sure there would be a very basic way to mathematically demonstrate that

Maybe like

(inf + 1) - inf is not equal to 1

Yes. In maths 1/infinite is 0.

[princeofcarthage]

Well it's for practical purposes of solving equations. The correct answer is infinitesimal, which is extremely small or close to zero. However it's never absolute zero

[iNcog]

-- deleted post --

[princeofcarthage]

The correct possibility is simply 1/16^n where n = infinity, I don't understand why it is complicated more than it should be.