Ask Lemmy
A Fediverse community for open-ended, thought provoking questions
Rules: (interactive)
1) Be nice and; have fun
Doxxing, trolling, sealioning, racism, and toxicity are not welcomed in AskLemmy. Remember what your mother said: if you can't say something nice, don't say anything at all. In addition, the site-wide Lemmy.world terms of service also apply here. Please familiarize yourself with them
2) All posts must end with a '?'
This is sort of like Jeopardy. Please phrase all post titles in the form of a proper question ending with ?
3) No spam
Please do not flood the community with nonsense. Actual suspected spammers will be banned on site. No astroturfing.
4) NSFW is okay, within reason
Just remember to tag posts with either a content warning or a [NSFW] tag. Overtly sexual posts are not allowed, please direct them to either [email protected] or [email protected].
NSFW comments should be restricted to posts tagged [NSFW].
5) This is not a support community.
It is not a place for 'how do I?', type questions.
If you have any questions regarding the site itself or would like to report a community, please direct them to Lemmy.world Support or email [email protected]. For other questions check our partnered communities list, or use the search function.
6) No US Politics.
Please don't post about current US Politics. If you need to do this, try [email protected] or [email protected]
Reminder: The terms of service apply here too.
Partnered Communities:
Logo design credit goes to: tubbadu
view the rest of the comments
Yup. There's no number of scratchers you can buy that gives you a 100% chance of winning. Sure, your chances go up the more you buy, but it never reaches 100%.
The formula is:
1 - (1-p)^Nwherepis the chance of winning andNis the number of scratchers you buy. Basically, you have to NOT win for N scratchers, so we multiply (since this is an AND condition, ie: you must lose scratcher A and scratcher B and scratcher C, etc) the chance of not winning (1-p) by itself for the number of scratchers bought. That's the overall chance of not winning, so we subtract that from 1 to get the chance of winning. You could instead use the chance of winning directly, but the formula is much longer (until you simplify the equation, which would give you the same answer as above) since you'd need to add (in this case we are using OR conditions) the chances of winning 1 scratcher or 2 scratchers or 3 scratchers, etc.1 in 30 is a 3.33% chance of winning (a 96.67% chance of not winning, for those still following along). If you buy 30 scratchers, your chance of winning is only 63.83%. For 300, it's 99.9962%. The chance will never reach 100% because you have a number between 0 and 1 raised to the power of a positive number in the formula. The chance of winning at least 1 of N scratchers can only be 100% if the chance of winning a single scratcher is already 100%, and they don't sell those.
However! There are rules dictating the distribution of winning scratchers in a roll. It's obviously not 1 every 30 exactly, but it's also not perfectly random (which could lead to long strings of losing scratchers or long strings of winning scratchers). That's why sometimes you'll have to wait in line behind someone while they make the gas station attendant open a whole new roll because they want to buy 100 contiguous scratchers and there were only 99 left in the old roll.
Turns out, humans don't think true randomness "feels" random. There's actually a game design trick where you tell the player odds that are lower than reality because the true odds "feel" lower than the reported number. Pokemon did not use this trick, so Hyper Beam (reported accuracy of 90%) feels unfair, since you remember more strongly all the times it missed when you really, really needed it to hit vs. all the times it hit.
If you buy all the scratchers you will win, you probably wouldn't net a positive amount, but you would win.
Ah, yes, bask in the "technically correct"ness. 🤌🏼