Chances vs. Probability

What's the math that supports the smarter decision?

0.0019 x $176,000 = $334.40 per chance
$334.40 x 11 chances = $3,678.40

0.0152 x $25,000 = $380 per chance
$380 x 16 chances = $6,080

this assumes you can win the jackpot multiple times. If not the value of the $25,000 drawing would drop by a few pennies

Fairly confident that is accurate, but someone please correct me if I'm wrong

…and the numbers if the jackpots can only be won once.

E[first option] = (1 – (1 – 0.0019)¹¹) * 176000 = 3643.65
E[second option] = (1 – (1 – 0.0152)¹⁶) * 25000 = 5433.70

The second option is the way to go.

So what do the final numbers represent?

Quote: Chodempole

So what do the final numbers represent?

The expected value of the return—or, on average, how much money you’ll make from each option.

So if you define “smarter decision” as the one which provides the greater return—go with the second option.

But evaluating money decisions like this may not always be idea—they can be complicated with crap like diminishing marginal utility of money and crap. Consider I offer a 100% chance at $10 million or a 1% chance at $1.5 billion. I think most people would take the $10 million even though the latter option has a higher expected return. It depends how you value money and whatnot.

True. $1000 to one guy is $100 to another.

But the other issue is that with such low percentages, luck plays a huge role. So do you just let that extra 1.3% go and hope to win more money or use that extra to try and hit multiple smaller jackpots?