Postulate that I shall always pick the lump sum for Daily Grand. The data below showcases that Pr(Keno's jackpot) > Pr(Grand's jackpot) > Pr(Lotto 649's jackpot). $\color{red}{\text{This probability inequality tips you to buy Keno!}}$
But the Expected Values of
1 Lotto 649 play= $= \dfrac{$5E6}{13,983,816} - \\$3 = -2.64$.
1 Daily Grand play = $= \dfrac{$7E6}{13,348,188} - \\$3 = -2.48$.
1 Daily Keno play $= \dfrac{$2.5E6}{2,147,181} - \\$10 = -8.84$.
Hence, E(Keno) < E(649) < E(Grand) < 0. $\color{red}{\text{This Expected Value inequality tips you to buy Grand!}}$ Plainly, the results from the Probability and Expected Value clash!
1. Why does Keno have the highest probability, but Daily Grand the highest Expected Value? How do I construe this contradictory information? My mind is freezing from this cognitive dissonance!
2. Presuppose a player can live snugly on any 1 of these lotteries' jackpot, and fancies winning whichever one. Then how ought this player construe the above computations? How ought this player decide which lottery to buy?
#### Data for 3 lotteries from the Ontario Lottery and Gaming Corporation
| | [LOTTO 649](https://www.playsmart.ca/lottery-instant-games/lottery/odds) | [DAILY GRAND](https://www.playsmart.ca/lottery-instant-games/lottery/odds) | [DAILY KENO](https://www.playsmart.ca/lottery-instant-games/lottery-daily-games/odds/)
|:-:|:-:|:-:|:-:|
| **Jackpot** | $5 million | <s>$1,000/day for life or</s> \$7 million lump sum | $2.5 million |
| **Odds of winning jackpot** | $\dfrac1{13,983,816}$ | $\dfrac1{13,348,188}$ | $\dfrac1{2,147,181}$ |
| **Matching numbers required to win jackpot** | 6/6 | 5/5 + Grand Number | 10/20 on a $10 bet |
| **Number pool** | 49 | 49 + Grand Number (7) | 70
| **Number of tickets one person can buy** | [10](https://i.imgur.com/rmjU10P.jpg5) | [5](https://i.imgur.com/5b5PMEM.jpg) | [2](https://i.imgur.com/h43DaJV.jpg)
| **Price per ticket** | $3 | $3 | $10 |
Chgg Clou
·
2023-06-01T06:38:47Z (over 1 year ago)