Lottery- Buy $40 now, or $30 now and $10 next drawing?

AA Suited · #1 09-05-2006, 10:10 AM

Let's say the odds of winning is 1 in a Million.

Current Prize is $1.5 Million cash.

The lottery is in another state 500miles away. You're there on vacation, but are leaving that day. You decide to spend $40 on the lottery.

Is it better to Buy $40 worth of tickets for the current drawing? Or buy $30 for current, and $10 for next, incase no one hits the current? (You're not going back to that state for a while.)

avfletch · #2 09-05-2006, 01:15 PM

I think we need to know how much it'll increase to if no one wins to figure this out. Its certainly true if the new prize is 1 billion and the same if it stays at 1.5 million.

Edit: And a guess at how many entries there will be this time.

Kerth · #3 09-05-2006, 01:51 PM

How many tickets are bought for the current drawing?
How many tickets will be bought for the next drawing if no one wins the current one?
How many tickets will be bought for the next drawing if someone wins the current one?
How much does one ticket cost?
How much will the new prize be if no one wins the current drawing?
How much will the new prize be if someone wins the current drawing?

AA Suited · #4 09-05-2006, 10:58 PM

$1 per ticket.

no idea about # of entries.

if noone hits, then the jackpot is $2M.

If it hits, then it's reset to 150k.

BiPolar_Nut · #5 09-06-2006, 01:09 AM

[ QUOTE ]
Let's say the odds of winning is 1 in a Million.

Current Prize is $1.5 Million cash.

[/ QUOTE ]

[ QUOTE ]
$1 per ticket.

[/ QUOTE ]

A +EV lottery? Every lottery I've seen was a tax for those that suck at math. How did this happen?

BiPolar_Nut · #6 09-06-2006, 02:13 AM

[ QUOTE ]
A +EV lottery?

[/ QUOTE ]

(I know it's not +EV w/ multiple winners nor if there are more than a certain number (1.5M?) of tickets bought by others)

Without knowing the other data asked for, there is really no way to answer the original question accurately other than making guestimates based on historical data for that particular and other similar lotteries...in similar jackpot amount situations. Still seems like an interesting question, just insufficient data to calcuate a good answer.

PairTheBoard · #7 09-06-2006, 12:27 PM

If you ever decide on sufficient assumptions for making the calculation then I think it will be an all or nothing decision. If the $10 has higher EV by waiting for the next lottery then so does the other $30. The assumption that could make this true would be a small increase in the number of entrants to the second lottery with a large carryover of the prize pool if nobody hits the first.

PairTheBoard

MediaPA · #8 09-07-2006, 12:36 AM

[ QUOTE ]
[ QUOTE ]
Let's say the odds of winning is 1 in a Million.

Current Prize is $1.5 Million cash.

[/ QUOTE ]

[ QUOTE ]
$1 per ticket.

[/ QUOTE ]

A +EV lottery? Every lottery I've seen was a tax for those that suck at math. How did this happen?

[/ QUOTE ]

There was a rigged lottery (which we won't count).

I also want to say that there was at least one other time where a group decided to buy every combination since there was an overlay and hope that no one else hit. I think that worked out ok, even though they were scared to death because they missed a batch due to problems with the machine at a convenience store or whatever.

http://www.maa.org/devlin/devlin_6_00.html Proof of +EV lotteries. Not my above story.

40 now. Don't feel like doing the math, too many unknown variables.

PairTheBoard · #9 09-07-2006, 07:20 PM

[ QUOTE ]
[ QUOTE ]
Let's say the odds of winning is 1 in a Million.

Current Prize is $1.5 Million cash.

[/ QUOTE ]

[ QUOTE ]
$1 per ticket.

[/ QUOTE ]

A +EV lottery? Every lottery I've seen was a tax for those that suck at math. How did this happen?

[/ QUOTE ]

It's not necessarily a +EV lottery with just that information. It depends on how the $1.5 million prize pool got there. For example, suppose 15 million tickets were sold with 10 cents out of every dollar going into the prize pool. Chances are 1 in a million of winning but there likely will be 15 winners. Clearly not +EV.

Suppose on the other hand, all the money goes into the prize pool and each week sells 100,000 tickets. Suppose it hasn't been hit for 14 straight weeks and all the prize money has carried over to make this week's pool $1.5 million. Suppose only 100,000 tickets are again sold this week. Your $1 ticket is clearly +EV in this case.

If you further assume that 100,000 tickets will continue to be bought every week you could now calculate whether it would be better to buy a ticket now or wait till next week. With these assumptions you should be able to caluclate the inflection point where it is better to bet now than wait a week.

I don't think these assumptions are very realistic though. Larger prize pools generate a lot of extra interest.

PairTheBoard