Find expected profit of gambles,

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Question statement

A roulette table has $\var{number}$ numbers and pays at $\var{odds1}$ to $\var{odds2}$ if the winning number is chosen.

Find the expected profit to the casino if $\var{10^{r}}$ bets of £ $\var{bet}$ are placed independently.

Give any introductory information the student needs.

			Name	Type	Generated Value

profit	number	135135.14
numberbets	number	100000
number	integer	37
r	integer	5
bet	integer	50
odds2	integer	1
odds1	integer	35

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
precround(numberbets*bet-numberbets*bet*(odds1+odds2)/(odds2*number),2)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `number`

135135.14

← Depends on:

bet
number
numberbets
odds1
odds2

This variable doesn't seem to be used anywhere.

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1. Gap Number entry
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Expected profit=£Unnamed gap

Enter to two decimal places.

Advice

The probability of winning is $\dfrac{1}{\var{number}}$ and the odds of $\var{odds1}$ to $\var{odds2}$ tells us that each winning choice realises

$\text{£}\simplify{{odds1+odds2}/{odds2}}\times \var{bet}=\text{£}\var{(odds1+odds2)*bet/odds2}$ on a bet of £

$\var{bet}$ .

Hence the expected payout on a bet of £ $\var{bet}$ is £ $\frac{\var{(odds1+odds2)*bet}}{\var{odds2*number}}$

So the expected payout on $\var{numberbets}$ bets of £ $\var{bet}$ is $\var{numberbets}\times \frac{\var{(odds1+odds2)*bet}}{\var{odds2*number}}$

Hence:

Profit = Income - Payout

$=\text{£}\var{numberbets}\times \var{bet}-\var{numberbets}\times \frac{\var{(odds1+odds2)*bet}}{\var{odds2*number}}= \text{£}\var{profit}$ to 2 decimal places.

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Taxonomy: mathcentre

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `number`

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Find expected profit of gambles,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`