If you have a button, and everytime you press it there is a 51% chance you get 1 dollar...

That's still $250k a year, which is a damn good salary. Upper-middle class. Especially if you don't live in a city.

that's basically how any office workers live

...

No dude...

depends on whether or not you can go negative and if so how much you start out with

do you really lose a dollar if you don't have a dollar? how

lol read the question before answering

It's LIKELY you'll become a millionaire -- after a few years of button pushing.
Only statistically. Not guaranteed though.

In the meantime, you could go broke and be kicked out of the game, die of boredom, or be hauled away with the worst case of Carpal Tunnel Syndrome in history.

Its a pretty simple question. The answer is yes. As the number of presses approaches infinity; so does your funds

After 50 million presses the odds of being broke are astronomically low. It's essentially guaranteed you will have a good chunk of money.

One of you make a program and see how many presses it took QUICK

op didn't give enough information see

No.... That doesn't matter at all.

The expected value of one click is the weighted average of the cash flows under their respective probabilities. In this case, our variable CF has a distribution of:

CF 1 -1
P(CF) .51 .49

The expected value of one click, E(CF) = 1*(0.51) + (-1)*(.49) = 0.02 cents

The expected value of n clicks would be:
E(n*CF) = n * E(CF) = 0.02n

So if you clicked on it n = 1,000,000 times you'd get, on average $20000. A financial loss in this case is nearly impossible because you're talking about a value (-1cent or less) that greatly diverges from the mean. In fact, following this logic, the more you click, the lower the probability of losing money, (the greater the average of your financial inflow, so the more money you will make).

Those saying you can lose money and that "it's only statistical" implying that it isn't nearly impossible to lose money are clearly pseuds who should not be on this board.

You shouldn't either.

If you pressed the button enough times, you'd eventually have 51 cents.

Exactly. I'd press the hell out of that button. And if I started losing money, I'd press it even more. That's how statistics works. More presses means you get closer to the expected outcome. In the long run it's a guaranteed money maker.

then the problem is beyond trivial

Agreed. Your chances of going broke are only significant at the beginning.
But we can't tell how low because we don't know the OP's current finances. If his total assets are two bucks, quite possible. At 50 bucks I wouldn't worry.

It does matter. If you have unlimited assets, Martingales would work.
This game is biased in the player's favor, but it's still possible to lose. That's what statistics is all about.

Would do this job depending on how my boss is.

>It does matter. If you have unlimited assets, Martingales would work.
For the question of "would I eventually become a millionaire?" it doesn't matter. There's no time constraint.

...

Gambler's fallacy if you get extremely unlucky it doesn't mean you'll get more lucky because the expected value should eventually be beneficial to you. In this case it's still good to press it because it has a positive expected value no matter how many times you've pressed it before.

>When a poor person thinks they understand the economy

Sigh...

You would "probably" become a millionaire eventually, assuming you don't have to stop playing when you hit 0 dollars or something like that. But there's know guarantee that you would ever become a millionaire.

depends if these are real dollars or game dollars

I would create a stupid auto pusher and just wait for the Money. Think outside the Box you cunts

that's not gambler's fallacy you dumbfuck

statistically speaking if OP presses the button 100 times he will make 1 dollar, the chance of this happening will increase as the amount of times the button has been pressed also increases

if OP is to press it 100 000 000 000 000 times he'll make $1 000 000 000

it has nothing to do with luck, he'd be lucky to make more than $1 in 100 presses

This is known as the Drunkard's Walk Problem. Google this if you need to peek at a solution.

To calulate the expected value, it's your odds of winning by how much you make, minus your odds of losing per how much you lose, so
[math]EV=($1)(0.51) - ($1)(0.49) =
$0.02[/math]
So per average game you'l "make" 2 cents.
To get [math]$1,000,000[/math] you need to play the game [math]\frac{$10^6}{$2\cdot 10^{-2
} = 5\cdot 10^7[/math] times.
If you can push the button once every second then you need to push it every second for [math]579[/math] days.

So yes, you can become a millionaire if you are willing to do this for over 19 months with no rest.

>250k/yr
>upper-middle class
read rule number 2

>51% chance
Lrn2probabilly, Billy

>If you have unlimited assets, Martingales would work.
You not only need unlimited assets, but unlimited time and unlimited bet size as well

I think if k is the amount you have, and P is the probability to go up and 1-P is the one to go down, then the probability for the change [math]\Delta k[/math] is

[math]\Delta p(k, \Delta k) = P\, \delta_{\Delta k, 1} + (1-P)\, ( \delta_{\Delta k, -1} + \delta_{k, 0} (\delta_{\Delta k, 0} - \delta_{\Delta k, -1})) [/math]

At time n=0, you start with

[math] p(k,n=0) = \delta_{k,0} [/math]

money and each time step follows from the last one by integrating over the steps (+1, 0, -1).

ad. I'd want to make a longer simulation but it looks like exponential runtime in time steps
(disregard negative k in the pic)

n=13

simulation of the probability density and expectation value up to time n=16

Any half-intelligent person would automate the process