6a. Megabucks vs. state lottery
Date: Mon Nov 30, 2009 7:35 pm ((PST))Is it reasonable to assume that one has a better chance of hitting the $1
Megabucks jackpot than the TX State Lottery (or any other state's lottery? Does
anyone know the Megabucks odds?Thanks for any insight/help.
It is not reasonable to assume anything, but one can find out. For every state I've seen, the state lottery jackpot is easier to hit than the Megabucks or Powerball jackpot, but also pays less on average (obviously, when the "big" lotteries re-set after being hit, it's possible for a state lottery to have a bigger jackpot); whether the state or multi-state lottery is a better deal is dependent not only on chance of hitting, but also on the amount paid if hit.
Of course, some would say that using the concept of EV on a lottery ticket is absurd, but the concept can in fact be applied; the problem, like a (hypothetical) progressive that only pays on a dealt sequential royal in a designated suit, is that the jackpot's effect on EV is substantial, and it is a rare occurrence -- only magnified (I think) over the dealt sequential royal (someone here can tell the odds of that as well, I know how to calculate that one, but don't have the time), probably by an order of magnitude or more.
Both Megabucks and Powerball have websites with all the details of the odds for winning each prize, including the jackpot. Every state I've checked also has a similar website for their own lottery, with similar information.
You can make an estimate of the necessary jackpot for positive EV (usually easiest to calculate by ignoring all the smaller prizes, but those actually do have value too, of course) for each lottery. Some sites actually tell you the probability of winning "any prize" -- but that is not useful without knowing the average amount of that "any prize" -- however, with the probability of EACH prize being given, you could calculate the average prize amount -- except that sometimes there are some top prizes that are variable amounts depending on how many hit it, just as with the top jackpot.
The only variable impossible to incorporate into the estimate is the factor of more than one winner, causing a split jackpot, although I suppose you can at least estimate the number of tickets sold based on historical sales at that jackpot level, if the particular lottery commission will share that information with you, and then I guess you can calculate / estimate the probability of more than one winner as well.
Don't forget to factor in the reduced amount actually received for the jackpot if you take cash option, as well as (ugh) taxes withheld. Not surprisingly, if you factor in everything, it takes a pretty big jackpot to make a positive EV for buying a lottery ticket, possibly bigger than any historical jackpot to date for many (most?) state lotteries. I think that even with everything factored in, some of the record multi-state jackpots have been high enough to make it theoretically a "good play" to buy one of every possible ticket, although this is practically impossible to do, due to the time involved to buy those tickets.
Personally, I just take the likelihood of hitting the jackpot (let's say it's 10 million to one for a given lottery) and when the jackpot is twice the odds, i.e. $20 million in this example, I start buying tickets at what I consider a low purchase amount, and over time, increase my purchase amount as the jackpot grows. I do this both for multi-state and state lotteries, although I don't go out of my way to participate in lotteries outside my own state (but will consider them when driving thru). The actual positive EV starts at a much higher level than I use, but like most lottery players, I figure it's not much money to buy a ticket, but would change my financial situation significantly for the rest of my life if I won -- I just moderate the philosophy a little bit by not "wasting" (lol) my money on the smaller jackpots.
--BG
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