hoops78 wrote: ``I spoke to a lottery representative and she kindly gave me all of the numbers on the 20$ lucky times 20 ticket.``
Not really.
She might have given you all the numbers she knows. But they are deficient in some obvious details. "There must be a lot" of remaining wins for the $20, $25, $50 and $100 prizes is not sufficient.
Also note that the odds 1:3.89 are for the outset of the game. (I assume you are talking about the Rhode Island game #321.) It may or may not be the current odds. That depends on the missing information.
Moreover, I believe "usually 8-10 winners per book of 30" is incorrect. I would say there was "usually" 6 to 9 winners among 30 tickets, the closest to 50% or more of the wins centered around the 50 %ile, which is between 7 and 8. Alternatively, you might say there was "usually" 8 or more winners among 30 tickets [1], representing (the upper) 50% or more wins. The point is: to me, "usually" means 50% or more.
But the operative word is "was". Again, that is based on the initial odds of 1:3.89. (By the way, that might be rounded from 1:3.885 to less than 1:3.895.) There is insufficient information to know the current odds [2].
In any case, I hope you are not seriously considering investing $600 in scratcher tickets -- the cost of 30 tickets. So whether there are 6 to 9 or 8 or more winners in 30 tickets is irrelevant to you.
(OMG, based on another one of your posting, you did invest $600 in scratchers -- even more!)
Your probability of winning something -- that is, one or more winners -- in n tickets is about 1 - (1 - 1/3.89)^n. For n = 1 to 5 ($20 to $100 investment), the respective probability is about: 26%, 45%, 59%, 70% and 77%. And "something" can be as little as $20 everytime.
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hoops78 wrote: ``What would you all do as for as purchasing? Go for it and keep playing?``
That really depends on your financial situation. But you might consider the following.
Making some wild assumptions [3] about the distribution of the remaining wins for the $20 to $100 prizes, your expected return might be about $14.72 per $20 investment. In other words, you can expect to lose $5.38 per $20 investment.
Of course, that is not real, since I had to make so many wild assumptions. I offer it just as an illustration. And of course, that is the average ("expected") return.
Also note that if you buy one $20 ticket for the Lucky Times 20 game, the probability of winning something was about 26% at the outset: 1/3.89.
But if you buy four $5 tickets for the Blackjack Tripler game, for example, the probability of winning something was about 75% at the outset: 1 - (1 - 1/3.39)^4.
Of course, that's 26% to win as little as $20 v. 75% to win as little as $5. And that is based on odds at the outset of each game, not necessarily current odds.
We cannot make accurate predictions without a complete breakdown of the number wins per prize and the total number of tickets.
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[1] The probability of 6 to 9 winners among 30 tickets was about 60%. The probability of 8 or more winners among 30 tickets was about 52%.
[2] Absent information to the contrary, it might be reasonable to assume that the current odds are the same as the initial odds.
[3] For the remaining number of wins for the $20 to $100 prizes, I assume the following distribution. My choice is arbitrary insofar as you offer no information to justify it. And I cannot find any details online about the distribution of prizes for the Rhode Island game. So I prorated another distribution of similar prizes. I also assume the current odds are the same as the initial odds.
| Prize | #Wins |
| $20,000 | 47 |
| $1,000 | 9 |
| $500 | 250 |
| $200 | 2,900 |
| $100 | 3,700 |
| $50 | 11,766 |
| $25 | 22,200 |
| $20 | 22,200 |
245,352 Total remaining tickets (306960 * 80%)
63,072 Total remaining wins (245352 / 3.89)
59,866 Remaining wins for prizes $20 to $100 (63072 - 47 - 9 - 250 - 2900)