I've a probability question. "I bought a lottery ticket where just wins and blanks are possible. I don't know about the chance to win. With the first lottery ticket i won. Know it could be just luck or the chance to win is "good". I took a second ticket and won again. Was this now just luck again or can i say with a specific guarantee, the chance to win is "good" (whatever "good" means.)
Any approaches welcome. Thanks for your help and interest Max
Lotteries are just random, like flipping coins. Someone who wins once is just lucky, but isn't a "lucky person". Their odds for winning the next time are the same as if they'd never played before.
If someone wins twice in a row they are just a very lucky person, but their odds the next time are the same as if they'd never played.
If someone wins $100$ times in a row I would suspect fraud.
Here's the coin tossing analogy.
If you toss a coin and get heads the chance for heads on a second toss is still just $1/2$. The coin doesn't remember its history and try to "even things out".
Two tosses in a row will be heads $1/4$ of the time. The chance of a third head is still $1/2$.
If you see $100$ heads in a row check that the coin really has a head and a tail. $100$ heads in a row can happen but it's very unlikely. But $10$ heads in a row happens about once in a thousand tries. So if everyone in a city of $100,000$ people flips a coin $10$ times about $100$ of them will think their coin is a lucky coin. Another $100$ will think that about an all tails coin.
You might assume that the expected win in a lottery, after subtracting the cost of the ticket, will be negative - otherwise the lottery would be losing money, and they don't do that. If your assumption is true then winning once, or winning twice, and so on, is pure luck.
On gambling machines you could have a price that says "all winnings on your next twenty bets are tripled". Good for you. Your expected winnings in the next twenty bets will be quite positive, and you should continue playing. But apart from such special cases, your expected winnings should be negative.
Unless... there is some programming error, or an unknown benefactor who bribed the lottery company to put money in your pocket etc., in which case your expected winnings would be positive.
Anyway, if you are on a winning streak then your assumption of "negative expectations" might be wrong, and you can proceed carefully. Just calculate the probability of winning as much as you did if everything is fair, and guess the probability that the expected winnings are unexpectedly positive.
