Question

A standard roulette wheel has 38 numbered slots for a small ball to land in: 36 are marked from 1 to 36, with half of those black and half red; two green slots are numbered 0 and 00. An allowable bet is to bet on either red or black. This bet is an even-money bet, which means if you win you receive twice what you bet. Many people think that betting black or red is a fair game. What is the expected value of betting $500 on red

Answer 1

Answer:

The expected value of betting $500 on red is $463.7.

Step-by-step explanation:

There is not a fair game. This can be demostrated by the expected value of betting a sum of money on red, for example.

The expected value is calculated as:

$E(G)=\sum p_iG_i$

being G the profit of each possible result.

If we bet $500, the possible outcomes are:

- Winning. We get G_w=$1,000. This happens when the roulette's ball falls in a red place. The probability of this can be calculated dividing the red slots (half of 36) by the total slots (38) of the roulette:

$P(R)=R/T=18/38\approx0.4737$  

- Losing. We get G_l=$0.  This happens when the ball does not fall in a red place. The probability of this is the complementary of winning, so we have:

$P(not \,R)=1-P(R)=1-18/38=20/38\approx 0.5263$

Then,  we can calculate the expected value as:

$E(G)=\sum p_iG_i=p_wG_w+p_lG_l=0.4637*1,000+0.5263*0=463.7$

We expect to win $463.7 for every $500 we bet on red, so we are losing in average $36.3 per $500 bet.