Mathematical expectation of Zip Bingo

In summary: The wizardofodds website also provides the probability of getting a specific number of bingo's (e.g. 3). The probability of getting all 4 corners is ((35C4/75C4)*(1-0.043078695))^2. The total cost of the tickets is the sum of the individual probabilities. In this example, the probability of getting a bingo with 35 numbers is (.50+0.75+0.41+0.65) = $2.31, and each ticket costs $2.
  • #1
O Great One
98
0
Hello everyone,
This really has me stumped! The Washington state lottery has a new game called Zip Bingo. Every ticket costs $2 and consists of 2 regular Bingo cards with 35 call numbers. The prizes are as follows:

Regular bingo on card 1: $2
Regular bingo on card 2: $3
Regular bingo on both card 1 and card 2: $5
Match 4 corners on card 1: $10
Match 4 corners on card 2: $15
Match X pattern on card 1: $25
Match X pattern on card 2: $35
Match 4 corners on card 1 and X pattern on card 2: $45
Match Z pattern on card 1: $100
Match Z pattern on card 2: $200
Blackout on card 1: $500
Blackout on card 2: $20,000
Only one prize per ticket.

I tried to calculate the average return from this game, and in order to simplify things just considered the regular bingo and the four corners. It seems a little bit tricky because the events are not mutually exclusive.
The probability of a bingo with 35 numbers is 0.271983.
The probability of getting all four corners with 35 numbers is 0.043078695.
So:
(0.271983)*((1-0.043078695)^2)*2 = 0.50
(0.271983)*((1-0.043078695)^2)*3 = 0.75
(0.043078695)*(1-0.043078695)*10 = 0.41
(0.043078695)*15 = 0.65
0.50 + 0.75 + 0.41 + 0.65 = $2.31 but each ticket only costs $2!

So, where did I go wrong in my math? :confused:
 
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  • #2
"Regular bingo" means a line, right? What if a line overlaps with 4 corners? I guess what I am asking is how you calculate your probabilities. Also, are you assuming independent draws? What if the draws are correlated?
 
  • #3
1. Yes. A 'regular bingo' means a line.
2. Yes. A line could occur at the same time as 4 corners. That's why it is necessary to multiply the probability of getting a bingo by the probability of not getting four corners.
3. Yes, the draws are independent from ticket to ticket. There is one group of 35 numbers and 2 bingo cards on each ticket. The player uses the same group of 35 numbers for both cards.

I got the probability of getting a bingo with 35 numbers from the wizardofodds website. It required the use of a computer program. The probability of getting four corners is (35C4/75C4).
 

1. What is the mathematical expectation of Zip Bingo?

The mathematical expectation of Zip Bingo is a statistical measure that represents the average outcome of a game of Zip Bingo over a large number of trials.

2. How is the mathematical expectation of Zip Bingo calculated?

The mathematical expectation of Zip Bingo is calculated by multiplying the probability of winning by the amount of money that can be won and subtracting the probability of losing multiplied by the amount of money that is lost.

3. Why is the mathematical expectation of Zip Bingo important?

The mathematical expectation of Zip Bingo is important because it can help players determine the overall expected value of playing the game. This can be useful in deciding whether or not to play, as well as how much to bet.

4. What factors can affect the mathematical expectation of Zip Bingo?

The mathematical expectation of Zip Bingo can be affected by the number of players, the amount of money being bet, and the rules of the game, such as the number of cards being played and the payout structure.

5. Is the mathematical expectation of Zip Bingo a guarantee of winning or losing?

No, the mathematical expectation of Zip Bingo is not a guarantee of winning or losing. It is simply a theoretical average over a large number of trials and does not guarantee any specific outcome for an individual player.

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