Can We Hit the Lotto Again?

[IRV]

The company I work for had an individual win the Florida lottery about 6 years ago. Can it be proven mathematically that our odds are worst now since we already had a winner?

Another related question. What has a more +EV, spending $1 per week on lotto or $5? I can't see your win percentage changing much.

[knsmith85]

[ QUOTE ]
The company I work for had an individual win the Florida lottery about 6 years ago. Can it be proven mathematically that our odds are worst now since we already had a winner?

Another related question. What has a more +EV, spending $1 per week on lotto or $5? I can't see your win percentage changing much.

[/ QUOTE ]

1) There is no change to your company's chances, unless Florida has changed the way they do the lotto. In fact, there is just as much chance that 1-2-3-4-5-6 will be the winning numbers tomorrow as any random combination. It turns out, though, that playing these numbers is unwise solely because there are a handful of people out there that play these every time, and so if it does hit you'll be splitting with a larger number of people than most other number combinations.

2) The lottery is NOT +EV. Play $1/day gives you BETTER EV, but NOT +EV. Doing $1/day has an EV that is negative, but closer to 0 than $5/day.

[other1]

I've always thought buying multiple tickets was pointless. Lets say it's a huge megamillions jackpot.. The odds of winning, if I calculated it correctly, are 1 in 135,145,920. Is 5 in 135,145,920 really any better? I'd say it's a pretty insignificant change in the odds.

[knsmith85]

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I've always thought buying multiple tickets was pointless. Lets say it's a huge megamillions jackpot.. The odds of winning, if I calculated it correctly, are 1 in 135,145,920. Is 5 in 135,145,920 really any better? I'd say it's a pretty insignificant change in the odds.

[/ QUOTE ]

Well, you have a 5 times greater chance of winning. It's just that to get to a significant level, you need like a 10,000 or 100,000 out of 130 million chance in winning.

The key with the lottery is the "Utility Function". Now, I don't even really know what it means, but I saw someone else mention it and from what I can gather it's that even though the lottery is -EV you can justify it because the result of winning is so life-changing that the losses from playing are reasonable. I'm not sure how you'd use this "Utility Function" in an actual mathematical equation, though - can someone enlighten me?

Realize that this is just the opposite of a common situation in poker - you're in a NL tournament where you are by far the best player. On the first hand, you pick up a flush draw, and someone moves all-in and there is a call behind them. You have the pot odds here to make the call, but the risk of going out when you can win anyways is much too great to justify a call. That's why it can be good to enter -EV situations as well as avoid +EV ones.

[Marm]

That was always my contetnion, but now I have a name for it, The utility function, I like it. I play every now and then, just for S&G's (S**ts and Giggles), but the Reward for winning far far far out weighs the $5 I spend a week on it.

ANd since the odds for the MM jackpot are 135,145,920, and taxes take out 48%, then the jackpot would have to be higher than $200,015,961.60 to make this +EV. And it has hit that high on occasion.

[knsmith85]

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That was always my contetnion, but now I have a name for it, The utility function, I like it. I play every now and then, just for S&G's (S**ts and Giggles), but the Reward for winning far far far out weighs the $5 I spend a week on it.

ANd since the odds for the MM jackpot are 135,145,920, and taxes take out 48%, then the jackpot would have to be higher than $200,015,961.60 to make this +EV. And it has hit that high on occasion.

[/ QUOTE ]

I think this is actually pretty easy to represent in an equation.

Without the Utility Function (U), the EV equation is:

EV = -x + J*(x/p)

Where p = probability, J = jackpot value, and x = bet amount. If we take x to be 1, when the Jackpot exceeds the reciprical of the probability, you have a +EV. Since this doesn't really happen (because of multiple winning and more notably taxes), you always have a -EV.

However, things change when we consider U. Say your net income is $36.5k per year, or $100 per day (we'll say there are no taxes whatsoever on typical income). Of that $100/day, a loss of 1% of it is what we'll say the cutoff is for significance. So we have part of the utility function... that which we take from our willingness to lose a small amount of money.

Now, we need the part of U that comes from the enormous signifiance in winning a certain amount. For this exercise, we'll call that amount $1 million dollars.

So U is applicable when x <= $1.

So we can call U = J/1000000 as long as x <= $1.

Simply adding this to our original EV equation, we get:

EV = -x + J(x/p) + U, or EV = -x + J(x/p) + J/1000000

This value now becomes positive when J and p are in a certain ratio.

I think I probability messed this up somewhere, so if someone could please correct me, I'd appreciate it.

Thanks,
Kyle

[Marm]

Check that and correct that. I did the 48% math wrong, but you get my point.

[Hack]

Doesn't the lottery become +EV when the jackpot exceeds your odds of winning it? If the jackpot reaches say, 300 million, and the odds of winning it are 200 million to 1, then isn't it +EV to buy a ticket?

[niin]

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Doesn't the lottery become +EV when the jackpot exceeds your odds of winning it? If the jackpot reaches say, 300 million, and the odds of winning it are 200 million to 1, then isn't it +EV to buy a ticket?

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Only if you're the only one to win... if multiple people win, then it's no longer a positive bet.

[shummie]

Your place of employment may have even greater odds of hitting now if this win has encouraged others to play.

- Jason