Rollover probabilities for Powerball at $400M annuity.

Reply #10

Stack47 — Tue, 17 Sep 2013 02:44:12 GMT

I use the simple approach by projecting the number of five number matches. It should require about $206 million in sales to produce 20 five number matches. Based on sales from past jackpots of this size, the total ticket sales could reach $250 million and around 25 five number matches. With each of them having a 1 in 35 chance of matching the bonus number, the chances of the jackpot being won should be over 50%. Based on projected sales of $145.6 million, there is less than a 50% chance.

I'm... [ More ]

Reply #9

Jon D — Tue, 17 Sep 2013 02:05:14 GMT

There is no mathematically legitimate way to declare the expectation value as undefined because the odds are large.

I didn't say the EV was undefined. As I said in my original reply: The EV for the PB/MM return is 0.5 and does not change. You wanna talk about the return for a single draw, that is one thing, but that is not the same as the EV for the game. The odds and prize share percentage do not change, and the rollovers and variable jackpots are just part of the game and the long term aver... [ More ]

Reply #8

Prob988 — Tue, 17 Sep 2013 00:53:26 GMT

There is no mathematically legitimate way to declare the expectation value as undefined because the odds are large. Indeed in mathematical physics, one often defines improbable events in terms of expectation values, in the case of so called quantum mechanical tunneling for example.

It is simply a ratio of potential reward to risk, and there is no arbitrary place at which it is undefined except where the risk is non-existent. If the ratio of the sum of cash jackpots awarded to each winner tim... [ More ]

Reply #7

RedStang — Mon, 16 Sep 2013 18:26:30 GMT

Roll one more time then someone will prevent it from breaking the MM record.

Reply #6

Jon D — Mon, 16 Sep 2013 13:39:27 GMT

I just have this problem with ever calling MM or PB a good bet even when the jackpot is high, that's just my pet peeve.

EV is more appropriate for low odds gambling like blackjack or craps, but really has no place with high odds jackpot games with pari-mutuel top prizes. But anyway, the return for this draw is either quite a bit lower than 0.75, or quite a bit higher if you include the wager itself for all combos. And it makes way too many assumptions that you win the jackpot with your bet, o... [ More ]

Reply #5

Prob988 — Mon, 16 Sep 2013 04:30:21 GMT

The expectation value as calculated includes values for all of the lower prizes, which amounts to about .18, as well as the weighted values calculated from the probabilities of numbers of winners based on projected sales, as calculated from a Poisson distribution assuming randomized tickets, as well as the advertised cash value and the odds of any particular ticket winning, which are of course constant. In this case, the chief contribution is a single winner, which adds 0.51 to my calculated exp... [ More ]

Reply #4

Jon D — Mon, 16 Sep 2013 01:29:12 GMT

One thing I'd caution you on is quoting an expectation value or EV for Jackpot games.

There are many times where return/payout and EV can be used interchangably, but never for a single draw of a Jackpot game like MM or PB. The EV for the PB/MM return is 0.5 (or -50% or whatever) and does not change. You can talk about the theoretical return if you played all combinations with no other players winning for this draw, but that is not EV for the game.

The top prize is pari-mutuel, based on sal... [ More ]

Reply #3

LottoMetro — Mon, 16 Sep 2013 00:33:46 GMT

MUSL projects sales of approximately 87 million tickets; this is likely a conservative projection but it will be updated Wednesday afternoon. At this figure just under 40% of all combinations will be sold. Even if sales hit 125 million tickets only 51% of combinations would be sold. Thinking in terms of cumulative probabilities, we are getting close to the 90% level.

Reply #2

Stack47 — Mon, 16 Sep 2013 00:26:49 GMT

If we use past ticket sales on $400 million jackpot as a starting point, sales should be at least $250 million or 125 million tickets.

Reply #1

Uff Da! — Sun, 15 Sep 2013 14:32:14 GMT

Thanks for this information, Prob988. I always find the probability of a rollover to be of interest.

Rollover probabilities for Powerball at $400M annuity.

Prob988 — Sun, 15 Sep 2013 13:17:56 GMT

The Powerball jackpot is advertised as a 400M annuity jackpot. This means, based on cash values of this jackpot and the previous jackpot that the lottery anticipates sales of $145.6M or about 72.8M tickets. If these projections are accurate, the probability of various numbers of winners is as follows:

k, number of winners p(m,k)

0 66.04%

1 27.40%

2 5.68%

3 0.79%

4 0.08%

5 0.01%

The expectation value - with 1.00 being thought of as a good bet - is 0.75.... [ More ]