The half billion Powerball jackpot got me thinking about this.
“Give me two bucks and guess a number between one and 175,223,510. If you guess right, I’ll give you half a billion dollars.”
Simple. But how do I extend that to the other prizes while keeping the comparison to the jackpot, e.g.:
“Give me two bucks and guess a number between one and 175,223,510. If you guess the number within X either way, I’ll give you a million bucks/ten thousand bucks/whatever.”
The odds of winning are:
$1 million: 1 in 5,153,632.65
$10K: 1 in 648,975.96
$100: 1 in 19,087.53 and 12,244.83
$7: 1 in 360.14 or 706.43
$4: 1 in 110.81 or 55.41
I know the analogy breaks down if the secret number is 2 or something, but you see what I’m getting at.
I would guess: divide 175,223,510 by 5,153,632 == 34. Now break 175,223510 into 34 bit chunks (with no overlap). If the user chooses a number in the correct 34 number chunk, they win. Do the others similarly.
J.
p.s. And actually, no, the analogy does not break down if the number is “2”. 2 works like all of the other numbers in the 175 million possible numbers.
I meant because the numbers don’t loop, the odds are less for 2 because there are fewer numbers below it than above it, so the range wouldn’t accurately reflect the odds.
But since all you want is a simple rule, you can say “within X, looping allowed”.
Thats the simplest way to fix your rules keep the calculation of odds simple.
You could of course merely say “If Buy N numbers out of M, then your odds of winning are N in M…” 5 out of 10 is the same as 10 out of 20… 50% …
A term you didn’t use was expected result, or average result…
This is used to differentiate between winnings and costs paid.
Is it a system you can use to make a profit ?
If you play 10,000 times, then sum the winnings and divide by 10,000 … So you might be paying $500 each time but the expected winnings is an average of $400 , you definitely paid $500 * Y , but only received back $400 * Y… If you spent $5m in 10,000 games, most likely you only received $4m back… (law of large numbers .) You have lost $1m.
BTW, The game of roulette has this spelled out for you… you buy 12 squares, the return is three times your bet… problem is the chance of winning is 12/37 (the 0 square…) … No matter which type of bet you make, the law of large numbers says your return is 36/37 of your bets.