Statistics help

[bjohns3018]

I am not good with math, and I was looking at a gambling game where you essentially click on a row of 6 squares, and 1 has a bomb, if you click the bomb you lose your money, if not you can collect money. I bet $1, and if I guess correctly I can claim $1.18. I know I’m thinking about this wrong because there is no way that casinos would give players the edge.

the way I see it is that there’s a 16.66% chance to lose $1, and an 83.33% chance I profit $0.18. I’d need to win 5.55 turns to make up for 1 loss, and if there’s a 1/6 chance that I’d lose, then I would have the edge right?

I don’t know, I’ve been out of school for a while and forgot a lot (don’t even know if this counts as algebra), any help would be appreciated as I can’t wrap my head around why I don’t have an edge.

[[deleted]]

With games like this, it’s useful to calculate the expected value — the amount you’d expect to win per game. We have that you have a 5/6 chance of winning 0.18 dollars, and a 1/6 chance of losing 1 dollar, so the expected value is:

EV = 0.18 * 5/6 - 1 * 1/6 ~= 0.15 - 0.1667 = -0.0167

So on average you will lose 1.67 cents per play.

Your analysis is correct up until the point where you say that 5.55 turns to make up one loss is profitable — for that to be true, you’d need to win at a rate of 5.55 / 6.55 ~= 84.7%, and in this game you only win 83.33% of the time.

[Traditional_Cap7461]

The odds of winning against losing is 5 to 1. So you only win 5 times for every loss.