How do I compare lotteries' chances of winning jackpot, when they differ in the maximum number of plays?
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Do the odds below factor in each lottery's different maximum (number of) plays? Or are these odds calculated for merely 1 play?
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Does each lottery's different maximum (number of) plays affect the probability of winning the jackpot?
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How can I deduce which lottery's jackpot is easiest to win, when they differ in the maximum plays?
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For example, which has the highest chance of winning : 10 plays of Lotto 649 vs. 5 plays of DAILY GRAND (assume I pick $7 million lump sum) vs. 2 plays of DAILY KENO?
Data for 3 lotteries from the Ontario Lottery and Gaming Corporation
| LOTTO 649 | DAILY GRAND | DAILY KENO | |
|---|---|---|---|
| Jackpot | $5 million | $1,000/day for life or \$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 | 5 | 2 |
1 answer
Do the odds below factor in each lottery's different maximum (number of) plays? Or are these odds calculated for merely 1 play?
You'd have to ask each lottery, but usually such published odds are the chance of any one ticket winning. That appears to be the case here too.
Does each lottery's different maximum (number of) plays affect its odds?
No. The chance of any one ticket winning are the same regardless of how many tickets you are allowed to buy. Buying more tickets increases your chance of winning, but not that of any one ticket.
How can I deduce which lottery's jackpot is easiest to win, when they differ in the maximum plays?
By comparing the chance to win per ticket. Since there is no rule that everyone always must buy the maximum number of tickets, you can only compare the probability of any one ticket winning. If you buy multiple tickets, then your overall chance of winning increases.
This is the same for any group of tickets. If all 10 people in the neighborhood each buy one ticket, then the neighborhood has the same chance of winning as an individual that bought 10 tickets.
For small numbers of tickets and small chances of winning per ticket (like all the lotteries you quote), then the chance of winning increases linearly with the number of tickets to a good approximation.
Note that the chance of winning isn't really linear with the number of tickets. Let's say each ticket has a 50% chance of winning, like flipping a coin. Two tickets have 75% chance of winning, and 5 tickets 96.9% chance.
For example, which has the highest chance of winning : 10 plays of Lotto 649 (5 million) vs. 5 plays of DAILY GRAND (assume I pick 7 million lump sum) vs. 2 plays of DAILY KENO (2.5 million)?
You can look this up yourself. Note that the payout is irrelevant to your question, which simplifies it considerably. The chance of winning has nothing to do how much you get if you happen to win.
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