Calculating Probability in Casino Games: A Case Study in Roulette Betting

In summary, when betting $5 on the number 7 in roulette at the Venetian casino in Las Vegas, there is a 37/38 probability of losing $5 and a 1/38 probability of making a net gain of $175. By calculating the expected values, it is determined that the overall expected outcome is a loss of $.26. However, it is important to note that the answer is likely not -.26 cents, as this would be a fraction of a penny.
  • #1
rowdy3
33
0
When you give the Venetian casino in Las Vegas $5 for a bet on the number 7 in roulette, you have a 37/38 probability of losing $5 and you have a 1/38 probability of making a net gain of $175.
There's a example close to this problem in my book and followed the steps. I made a table and did the following:
I did $-5 x 37/38(.974) = -4.87
I did $5 x 1/38(.026) = + 0.13
= -4.74. The answer is -. 26 cents. What did I do wrong?
 
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  • #2
Your second expected value should be 175*(1/38), which comes out to about $4.61.
-$4.87 + $4.61 = -$.26,

Note that the answer is probably NOT -.26 cents, which would be a fraction of a penny.
 
  • #3
Thanks.
 

FAQ: Calculating Probability in Casino Games: A Case Study in Roulette Betting

1. What is the probability of winning at a casino?

The probability of winning at a casino varies depending on the game being played and the specific rules of the casino. Generally, the probability is always slightly in favor of the casino, known as the "house edge". This means that in the long run, the casino will make a profit, but individual players may still win in the short term.

2. How do casinos determine the probabilities of their games?

Casinos use mathematical models and statistics to determine the probabilities of their games. They calculate the expected payouts for each game and adjust the odds in their favor to ensure a profit. This is why it's important for players to understand the rules and odds of each game before playing.

3. Is it possible to beat the odds and consistently win at a casino?

While it is possible to win at a casino, it is highly unlikely to consistently beat the odds. As mentioned before, the house always has a slight advantage, and games are designed to be random and unpredictable. Strategies and skills can help improve the chances of winning, but they cannot guarantee a win every time.

4. What is the difference between odds and probability in a casino?

Odds and probability are related concepts, but they are not the same thing. Probability is the likelihood of a particular outcome occurring, expressed as a fraction or percentage. Odds, on the other hand, compare the number of favorable outcomes to the number of unfavorable outcomes. In a casino, odds are often displayed as the ratio of winning to losing.

5. Can casinos manipulate the odds in their favor?

Casinos do not need to manipulate the odds as they are already in their favor. However, they may use certain tactics such as changing the rules or payouts of a game to increase their advantage. It is important for players to be aware of these potential manipulations and choose games with fair odds.

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