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I'm lucky. (Scratching Cards #1, "buying" 1000 fake(simulator) scratch cards.)

Warning: Scratching cards is not a way to live. I'm just pretty lucky.
So right now I'm really bored. After knowing lottery simulators a few months ago, I was "addicted". Yeah not really my luck was bad. But just today, I founded about scratch cards simulator. Just buying randomly without intention is really boring. So thanks to MrBeast, I have an idea: Buying 1000 scratch cards. In the website http://scratchlogic.com/, It also has luckiness. I created my scratch card price : 1$. And made six rewards:
Free ticket. 1 in 10 chance (I will not call "chance" next times)
Two dollars. 1 in 20. (I will type numbers and $ next times)
5$. 1 in 50.
20$. 1 in 100.
50$. 1 in 200.
And the grand prize, 100$, 1 in 500.
I mean if there's a real scratch card like this the chances of winning will probably be way lower, but the luckiness also changes with the price. My mission : Luck 100% or more. I destroyed that. (not really)
I got 121%! Actually, I set out to be 80% first because I know this was hard.
Let's look at the results.
I got 123 free tickets which 9 of them COMES from the FREE tickets.
46 times won 2$,
20 times won 5$,
14 times won 20$,
4 times won 50$
and 5 times won the grand prize, 100$. How did I got it more than half of it?
If you want to test your luck in a "serious" way try it. Don't try lottery simulators. because it's TOO HARD to win, also there are no other simulators than this that has luckiness.
Edit: You need to click on your own. There's also no auto "scratches per second/minute."
Plus my profit is 172$.
Let E be the expected gain of one ticket.
Then we have
E=1/10+2/20+5/50+20/100+50/200+100/500.
So E=4/10+1/5+1/4+1/5=21/20.
And thus E=1.05$.
So the expect gain of one ticket is strictly larger than the ticket price. Which means if you start selling these tickets you will go bankrupt.
@polylogarithmique said in #2:
> Let E be the expected gain of one ticket.
> Then we have
> E=1/10+2/20+5/50+20/100+50/200+100/500.
> So E=4/10+1/5+1/4+1/5=21/20.
> And thus E=1.05$.
> So the expect gain of one ticket is strictly larger than the ticket price. Which means if you start selling these tickets you will go bankrupt.
That's some serious calculating right there. I will make a harder scratch card next time.

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