Probabilities Inquiry

[Mcducky]

This may be a stupid question, but can someone explain the below to me?

Place bets on the nine at craps illustrate a situation where the house has an edge. These bets have 40 percent chance of winning and pay 7-to-5, giving the bosses 4 percent edge.

If the bet has a 40 percent chance of winning and it pays 7 to 5 (7/5 =1.4), how does the house have a 4 percent edge?

[LT Profits]

7/5 odds has break-even of 5/12 = 41.7%
True odds are 40.0%
.417/.400 = 1.04 = 4% edge

[Mcducky]

So you are basically saying 2 things:

When the house gives you 7/5 odds on a bet, you need to win at a 41.7% frequency to break even?

The difference between the break-even percentage and the payout for winning percentage is the house's edge?

Thanks for the quick reply.

[LT Profits]

So you are basically saying 2 things:

When the house gives you 7/5 odds on a bet, you need to win at a 41.7% frequency to break even?

The difference between the break-even percentage and the payout for winning percentage is the house's edge?

Thanks for the quick reply.

Correct.

[indio]

So you are basically saying 2 things:

When the house gives you 7/5 odds on a bet, you need to win at a 41.7% frequency to break even?

The difference between the break-even percentage and the payout for winning percentage is the house's edge?

Thanks for the quick reply.

While all the %'s you have been given are correct, sometimes it's good to visualize the basics to get an understanding of an edge.

If I roll two dice, there are 36 possible ways for it to land, six of those will be 7's, and four of those will be 9's. So obviously I should roll six 7's for every four 9's when I roll dice (thanks to variance, that only has a 25% chance of happening on the first 10 results, but that's for another thread).

Let's say I roll dice and bet $10 on every roll and receive $24 back (7/5 odds) when I roll a 9, and
all rolls other than 9 or 7 don't count. If I bet $10 on ten rolls that count, I would bet $100 total. If four of those ten rolls are 9's, I would get back $96 ($24 x 4). So out of my $100 in bets, the house has paid back $96 and kept $4, hence, 4% hold.