Question

A bet on "black" in Roulette has a probability of 18/38 of winning. If you win, you double your money. You can bet anywhere from $1 to $100 on each spin. a. Suppose you have $10, and are going to play until you go broke or have $20. What is your best strategy for playing? Explain using information you learned in this module's material, such as expected value. b. Suppose you have $10, and are going to play until you go broke or have $30. What is your best strategy for playing? Explain using information you learned in this modules material, such as expected value.

Answer 1

Answer:-

Given That:-

A bet on “black” in Roulette has a probability of 18/38 of winning. If you win, you double your money. You can bet anywhere from $1 to $100 on each spin.

Given,

If we bet $x then the following table shows the possible outcomes with their corresponding probabilities:-

Outcome	-x	x
Probability	$\frac{20}{38}$	$\frac{18}{38}$

The expected value of each bet is
$E(bet)=-x\times\frac{20}{38}+x\times\frac{18}{38}$

  $=\frac{-2x}{38}$

$=\frac{-x}{19}$

The expected value is a decreaing function of the bet $x which means the more we bet the higher we may lose.

a. Suppose you have $10, and are going to play until you go broke or have $20. What is your best strategy for playing? Explain using information you learned in this module's material, such as expected value.

The above expected value is minimum at x = $1 as we cannot bet lower than that.

Therefore,

The best strategy would be to bet $1 on each spin.

b. Suppose you have $10, and are going to play until you go broke or have $30. What is your best strategy for playing? Explain using information you learned in this module's material, such as expected value.

As the the money that we have in hand is the same as (a) therefore the strategy would be the same and that is to bet $1 on each spin.

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