Okay, I've been reading (to the limit of my comprehension, it seems) responses here to the following puzzle:
You are in hell and facing an eternity of torment, but the devil offers you a way out, which you can take once and only once at any time from now on. Today, if you ask him to, the devil will toss a fair coin once and if it comes up heads you are free (but if tails then you face eternal torment with no possibility of reprieve). You don’t have to play today, though, because tomorrow the devil will make the deal slightly more favourable to you (and you know this): he’ll toss the coin twice but just one head will free you. The day after, the offer will improve further: 3 tosses with just one head needed. And so on (4 tosses, 5 tosses, ….1000 tosses …) for the rest of time if needed. So, given that the devil will give you better odds on every day after this one, but that you want to escape from hell some time, when should accept his offer?
The replies have gotten over my head somewhat, but I'm wondering if they are all missing the boat on what the answer is. Or do I just not understand probability mathematics?
It would seem to me that you should take the devil's offer on the very first day. Because wouldn't your odds remain the same - 50% - each day, regardless of how many flips of a coin you get each day? Isn't it incorrect to make the assumption 'if I have x number of flips today, my chances are greater that one of them will be heads'? Don't you have to take each flip individually, as a separate entity unto itself? And don't the odds remain the same - 50% - for each flip?
In other words: with one coin flip, there's a 50/50 chance it'll turn up heads. In a thousand coin flips, there's also a 50/50 chance that each flip will turn up heads. Am I wrong in assuming that your odds don't improve the more times you flip a coin?
If I am wrong, then am I also wrong in my assumption that the 649 Atlantic from Atlantic Loto is a rip-off? They are selling you the notion that because it's only played in Atlantic Canada, you have a better chance of winning (winning a much smaller jackpot, by the way), when in fact, you still have to match 6 of 49 numbers. They (or, we the gullible buyers) incorrectly imply that you are competing against fewer people so your chance of winning is greater. But you're not competing against others. Your competing against the odds of matching 6 of 49 numbers. So, your chance of winning the 649 Atlantic is as slim as winning the national 649. Or am I wrong on that too?