How Does Betting on a Corner in Roulette Affect Your Expected Returns?

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In summary: Thanks for you help!In summary, the conversation discusses the probability distribution and expected value for a $1 bet on a corner in a roulette wheel with 37 slots. The probability of winning a corner is 4/37, while the probability of not winning a corner is 33/37. The expected value of a $1 bet is calculated to be approximately -2 cents, indicating a negative expected value for gambling on a corner.
  • #1
nicholasch
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Homework Statement



This particular roulette wheel has 37 slots - 0,1,2...36. A gambler can bet on different combinations of numbers. Louise loves to bet on a block of 4 numbers, called a corner. The payout on a corner is 8 to 1.

(a) Let X be a gambler's winning from a $1 bet on a corner. What is the probablity distribution for X? (Hint X can be negative)

(b) What is the expected value of a $1 bet on a corner.


2. The attempt at a solution

(a) Okay i figured that the chance of a corner would be.

Pr(corner) = (1/37)X4 = 4/37.

However, i don't think this counts as the probablity distribution?

Not quite sure how to approach this.

(b) Excepted value for a $1 bet. Need to take account both winning and losing?

Pr (corner) = 4/37
Pay out is 8 to 1.
therefore is excepted value is 4/37 X $8 = 32/37

Pr (no corner) = 33/37 ((1-(4/37))
Expected value is 33/37 X -$8 = -264/37

Excepted value of 1 dollar bet = (-264/37) + (33/37) = -232/37 = -6.27

You would expect to lose -6.27??

Thanks
 
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  • #2
A probability distribution is a listing of all outcomes and their respective probabilities. Obviously one can only win or lose at Roulette, so there are only two outcomes to worry about here. How much would one win and how much would one lose in a single bet? Find the probability of each occurring.

As for expected value - you have the right formula, but the incorrect values. Think about how much you're losing when you lose.

The answer should be negative (or casinos wouldn't exist), but not -6.27.

--Elucidus
 
  • #3
oh yes. i think i got it. if you put in 1 dollar you can only lose it. you can you more than you put in...

Pr(no corner) = 33/37
Excepted value = -1 X 33/37 = -33/37

Excepted value of one dollar bet = -33/37 +32/37 = -0.02702 = -2.7%

that shows slightly wrong though?
 
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  • #4
Can anyone help me through the probability distribution?
X is in the case refers to Winning a corner. You can only will or lose a corner..
If Pr (Corner) = 4/37, Pr(Corner) = 33/37
 
  • #5
nicholasch said:
oh yes. i think i got it. if you put in 1 dollar you can only lose it. you can you more than you put in...

Pr(no corner) = 33/37
Excepted value = -1 X 33/37 = -33/37

Excepted value of one dollar bet = -33/37 +32/37 = -0.02702 = -2.7%

that shows slightly wrong though?

Looks correct to me.

You've got the distributions. The variable X is the winnings.

The value of X when you lose is -1. The value of X when you win is +8.

The probability distribution is the probability for each value of X. You can give it as a table.

Cheers -- sylas
 
  • #6
Cheers Sylas,

I was thinking about the expected value of a $1 bet further.
Shouldnt the EXPECTED VALUE of the $1 bet be $1 minus $0.02 = 98 cents?

Got it from http://en.wikipedia.org/wiki/Expected_Value#Examples

Not very sure because the definition is E(X)= xP(x) well from my book...
 
  • #7
I suggest you look at your book again. The definition of expected value is the sum of xP(x) where x ranges over all possible values. Here, the two possible values of x are 8 (if you win) and -1 (if you lose). The expected value is 8Pr(win)- 1Pr(lose)= \(\displaystyle 8\frac{1}{37}- \frac{33}{37}\). You don't think you are going to have a positive expected value gambling do you?
 
  • #8
nicholasch said:
Can anyone help me through the probability distribution?
X is in the case refers to Winning a corner. You can only will or lose a corner..
If Pr (Corner) = 4/37, Pr(Corner) = 33/37
You mean "Pr (Corner) = 4/37, Pr(NOT Corner) = 33/37", of course.
 
  • #9
Thanks for the prompt reply. Oh my book is correct. I mistyped that.

It is the sum of xP(X), therefore it is (32/37) + (-33/37) = -1/37

Therefore, the expected value of a $1 bet is $(-1/37), which is approx -2 cents.

It was wikipedia confusing me.
 

FAQ: How Does Betting on a Corner in Roulette Affect Your Expected Returns?

1. What is the probability of winning in roulette?

The probability of winning in roulette depends on the type of bet you place. For example, the probability of winning on a straight-up bet (betting on a single number) is 1 in 37 or 2.7%, while the probability of winning on an even/odd bet is 18 in 37 or 48.6%. Overall, the house always has an advantage in roulette, with the odds of winning being slightly less than the true odds.

2. How is the outcome of a roulette spin determined?

The outcome of a roulette spin is determined by the random spinning of a ball on a spinning wheel with numbered pockets. The pocket that the ball lands in is the winning number. The wheel is designed to be completely random, so each spin is independent of the previous one.

3. What is the difference between American and European roulette?

The main difference between American and European roulette is the number of pockets on the wheel. American roulette has 38 pockets, including a 0 and 00, while European roulette has 37 pockets, with only a single 0. This means that the odds of winning are slightly better in European roulette compared to American roulette.

4. Is there a betting strategy that can increase my chances of winning in roulette?

There is no betting strategy that can guarantee a win in roulette, as the game is based on chance. However, some players may use strategies such as the Martingale system, where they double their bet after a loss in hopes of recouping their losses. It's important to remember that these strategies do not change the odds of winning, and can actually increase the risk of losing money.

5. Can I use previous outcomes to predict future outcomes in roulette?

No, previous outcomes have no impact on future outcomes in roulette. Each spin is completely independent and random, so there is no way to predict which number will come up next. This is why roulette is often called a game of chance.

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