Math for Grownups (31 page)

As she’s watching, Zoe notices something else—it’s very difficult to win at roulette. For one thing, each time the ball is dropped, the chances are the same. In other words, it doesn’t matter how long she plays, she’ll have exactly the same chance of winning on every single bet.

Second, the odds of each win are pretty small. Take the straight-up bet, for example. There are 38 possible outcomes: the numbers 1ߝ36, along with 0 and 00. (You can’t bet on 0 or 00 on a straight-up bet.) Zoe is betting on only one of those outcomes. So the odds of her winning are 1:38. The odds of winning any of the other bets are also low, although calculating those odds is more complicated. What if Zoe put down an outside red bet? What would be her chances of winning?

Two of the roulette slots are green, so that means 36 of them are red or black. Half of those 36 are actually red, so Zoe has 18 chances to win. The odds of her winning are 18 out of 38. Hmm, that doesn’t look so bad, does it?

If she changed the fraction to a percent (that is, if she divided 18 by 38), she’d find out that her chance is 47%. That’s less than her chances of getting heads when she flips a coin.

Zoe’s enthusiasm is dropping like a stone. This gambling thing is looking less and less like a sure thing.

Just to be sure, Zoe considers one more bet: the basket. If she bets that 00, 0, 1, 2, or 3 will come up, how are her chances? Turns out, not so good. She wants 1 of 5 possibilities, but there are 38 possibilities in all:

Estimating, she sees that her chances of winning are between 1:7 and 1:8, or between 13% and 14%.

Why does she do this instead of finding out what 5 / 38 is?

First, she notices that 5∕38 does not reduce easily. But she also notices that 38 is between 35 and 40, which are multiples of 5. And she knows that 5∕35 reduces to 1∕7 and that 5∕40 reduces to 1∕8.

Make sense? Good.

Now, Zoe happens to know that 1∕7 is about 14%. You may not have that little bit of information in your mental reserve. But you may know that 1∕8 = 0.125, or 12.5%. And you probably know that 1∕7 is a little bit bigger than 1∕8.

So you can check Zoe’s mental math—the odds of a basket bet are a bit higher than 13%.

Zoe’s too cautious to play such terrible odds. But maybe another game is a better choice? She strolls over to the craps table to see.

The payout for casino gambling is the amount paid on each winning bet. So if the payout is 15:1, you get 15 times the bet you placed, plus the amount you bet. Here’s an example:

Original bet
→ $4

Payout
→ 15:1

Amount won
→ (4 • $15) + $15 = $75

You’d think these payouts are related to the odds—and they are, but not exactly. For example, the payout on roulette is expressed by this formula:

So, if you made an outside black bet, you’d have 18 chances to win. That means your payout would be

In this case, you’d get back the amount you bet, plus your bet.

Appendix

Fabulous Formulas

Amount-Due Formula (
Chapter 2
)

A
=
P
(1 +
r
)
ⁿ

where
A
is amount due on the loan,
P
is the principal,
r
is the compound interest rate, and
n
is the number of compounding periods in the loan

Area (Chapters 4 and 6)

AREA OF A SQUARE

A
=
s
²
, where
s
is the length of a side

AREA OF A RECTANGLE

A
=
l
•
w
, where
l
is length and
w
is width

AREA OF A TRIANGLE

A
= ½
hb
, where
h
is the height of the triangle and
b
is the base

AREA OF A CIRCLE

A
=
πr
²
, where
π
is 3.14 … and
r
is the radius

Basal Metabolic Rate, or BMR (
Chapter 9
)

BMR
_women
= 655 + 4.3
w
+ 4.7
h
– 4.7
a

BMR
_men
= 66 + 6.3
w
+ 12.9
h
– 6.8
a

where
w
is weight,
h
is height, and
a
is age

Body Mass Index, or BMI (
Chapter 9
)

Brzycki Formula (
Chapter 9
)

where 1RM is the 1-repetition maximum,
w
is the weight used, and
r
is the number of repetitions

Debt-to-Income Ratio (
Chapter 8
)

debt/income

Monthly Payment Formula (Chapters 2 and 8)

where
M
is the monthly payment,
P
is the principal (or the amount borrowed),
r
is the monthly interest rate, and
n
is the number of months in the loan

Monthly Lease Payment (
Chapter 2
)

Monthly lease payment = depreciation fee + finance fee + sales tax Depreciation fee = (cap cost – residual value) / lease term Finance fee = (cap cost – residual value) • money factor Sales tax = monthly payment • sales tax rate

where the
cap cost
is the amount financed (the cost of the vehicle, plus any dealers costs) and the
money factor
is the interest rate

Maximum Heart Rate, or MHR (
Chapter 9
)

MHR
= 220 –
a
, where
a
is age

Net Worth Formula (
Chapter 8
)

Net worth = assets – liabilities

Principal Formula (
Chapter 3
)