Posted Thu Jun 23, 2005 3:36 pm GMT by p3nguin
I got into a discussion today online about odds and such and since I feel I have learned a lot here I flexed my muscles a bit in the thread. So I will post snipits of it here in order to have you guys who really know your stuff tear me apart 
He said:
| Quote: | | Lottery = tax on people who are bad at math. |
I said:
| Quote: | Not really.
The local powerball here has a 1:120,000,000 chance of hitting or so.
If the payoff is greater than $120,000,000 then the dollar you risk is a "good bet" considering the payoff is greater than your odds of winning it. |
Someone else said:
| Quote: | Not really.
It's only a "good bet" if you can buy enough tickets to boost your chance of winning above 50% AND the payoff is greater than the ammount you spent, any other time it's just an astronomically wild gamble. |
I said:
| Quote: |
If you look at losing a dollar as taking a risk, then I agree you should never play the lotto. I agree it would be an even better bet if you could inflate your odd to greater than 50%, or 75% or 90%.
But anytime the odds of paying off are less than the ratio of return a single bet is justified. This is true in poker and in the lotto. Of course it is all gambling. |
Someone said:
| Quote: |
The Powerball jackpot would have to be at least $200-million to make it a good bet on account of the tax. Plus, it's only a "good bet" if you can cover all the possible combinations. Offering 40-to-1 on a roulette wheel is a great bet to take because you can bet all 38 numbers rather easily. $200-million for a 120,000,000-to-1 bet isn't that great because it's hard to come up with $120-million and even harder to punch in every possible combination. Plus, if someone else hits it, then you share the jackpot and lose money (depending on what the consolations pay). |
I said:
| Quote: |
The Powerball jackpot would have to be at least $200-million to make it a good bet on account of the tax.
Touche`, I stand corrected.
I didn't say it was a "great" bet, just justified by the pot odds.
Sharing the jackpot would not cause you to "lose" money, just get less return value on the initial bet. That being said the initial bet is still justified. |
He said:
| Quote: | If you give me $10,000, I will let you pick a number between 1 and 100 million. If you get the number correct, then I will give you 1 billion dollars, otherwise I keep the $10,000.
Since the payoff is 10 times your odds of winning, surely it is a no-brainer. I do this out of the goodness of my heart, and only for you. |
I said:
| Quote: | If I were a kajillionare sure. Any money you "Gamble" with must be assumed to be lost as soon as you put it in the pot. Once you are willing to lose it, you can bet it smartly to minimize the risk of losing it or maximize gain.
Changing the stakes does not change the math as long as my bankroll is big enough./i |
It goes on, but I just wanted to know, am I getting it, or am I jaut talking out of my arse?
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Posted Thu Jun 23, 2005 3:55 pm GMT by Loonbat
Regarding the Powerball example, there are a couple of problems:
Assume the chance is 1 in 120,000,000 (I'll take your word for it - not sure of how many balls are being used).
All lotteries of this nature have an annuity value equal to the jackpot, but a cash value equal to half (eg a $100 million jackpot would pay you $50 million on the spot, before taxes). So, given a tax rate of nearly 40%, including state, capital gains, etc, you would have to clear nearly $200 million as a cash value in order to make the pot break even IF there was just a payout on the jackpot and no smaller prizes were taken into account. Thus, an annuity value of approximately $400 million is required for a positive EV. However, given smaller tier prizes, I would expect only a value of $370 million is needed in order to make it a break even prospect.
"If you give me $10,000, I will let you pick a number between 1 and 100 million. If you get the number correct, then I will give you 1 billion dollars, otherwise I keep the $10,000.
Since the payoff is 10 times your odds of winning, surely it is a no-brainer. I do this out of the goodness of my heart, and only for you."
BAD numerical example and bad odds - the payoff is 10 times as great as the possibilities, yet you are not risking $10 ... you are risking 1000 times as much.
Posted Thu Jun 23, 2005 4:14 pm GMT by p3nguin
| Loonbat wrote: |
BAD numerical example and bad odds - the payoff is 10 times as great as the possibilities, yet you are not risking $10 ... you are risking 1000 times as much. |
Yikes, I see that now.
OK, bad odds. I should have checked the numbers.
Posted Thu Jun 23, 2005 4:31 pm GMT by snoogins47
"It's only a good bet if you can boost your chances of winning over 50%" is quite possibly the stupidest thing I've read with regards to odds in a long time. Until:
"Plus, it's only a "good bet" if you can cover all the possible combinations."
His roulette example is absolutely mindblowingly stupid. The standard deviation of his system is clearly much lower than betting individual numbers (duh) but it has no effect on the bottom line expectation.
You're right about his last example: I'm pretty sure that betting $10k on that would be way sub-optimal as far as the Kelly Criterion on most human being's bankrolls would be. But it's a great bet if you have the money. My rudimentary understanding of the Kelly Criterion and trying to run it from memory would put your optimum bankroll on that bet for long term growth at One Trillion Dollars, roughly. You'd probably want to be more conservative than that in practice. Man, why did I waste my time figuring that out, when I probably screwed up the math anyway? ;P
You're right about the fundamentals of the lottery being +EV, and we also have to remember the fact that a lotto win after an investment of say, $10, is life changing money. In a lot of people's minds, this more than justifies the negative expectation, because spending $5-10 a week isn't going to alter their lives significantly, but winning $100 Million clearly would.
Posted Thu Jun 23, 2005 4:33 pm GMT by suitedaces84
| p3nguin wrote: |
| Quote: | | Lottery = tax on people who are bad at math. |
|
I can think of a few less than complementary things I'd replace "bad at math" with.
| p3nguin wrote: | | Quote: | Not really.
The local powerball here has a 1:120,000,000 chance of hitting or so.
If the payoff is greater than $120,000,000 then the dollar you risk is a "good bet" considering the payoff is greater than your odds of winning it. |
|
You're logic here is certainly correct, but you fail to factor in tax. And based on the previous post do not know the subtleties of the lottery, which I don't either. But you are correct that if you had a 1 in 12M chance of winning 120M for $1 it would be EV.
What the hell can you do with 120M that you couldn't do with 10M or so(don't answer this one)? The extra money is really not worth the decreased chance of winning. It would be a better (less worse) deal if you had a 1 in 10M chance of winning 10M for $1, IMHO.
Posted Thu Jun 23, 2005 4:47 pm GMT by p3nguin
Well, this was just an excercise to find out if I am starting to get the EV thing in theory.
From the responses it sounds like I am.
The conclusion that we came to in the discussion was that in theory the bet can be justified mathmatically.
In reality there are lots of reasons not to play lotto, math not being one of them.
Would you guys agree with that?
Posted Thu Jun 23, 2005 6:32 pm GMT by THNKNBG
It was funny to read this since I was just talking to a friend about it the other day. He is on the side of the fence where you should never play the lottery.
You are very correct about math not being a reason to aviod the lottery.
You have to remember the people that are raising the powerball jackpot for everyone else from the original 10 million to the absurd 300 million (not that i would mind the money) are not good investors becuase of the pot odds but i am glad that there are people in the world to do that.
Hopefully when the jackpot gets over 120 million, or over 200 million depending on your tax thoughts, i will win it.
Posted Fri Jun 24, 2005 4:36 pm GMT by snoogins47
Math is clearly a reason to avoid the lottery, but as far as practical applications go, when you deal with things like life-changing risk, life-changing reward, astronomical odds, etc... A straight up expectation calculation isn't going to tell the story. For many, it might be worth losing on average $5 a week, if there's a 0.001% chance that they'll win enough money such that they'll never have to work, be able to buy everything they want, maybe start a business, make sure their kids are always well off and get great educations, etc. Or, it might be worth it if there's a chance they can buy a lot of cocaine. Whatever.
These people might not know that they're losing on average every time they buy a lottery ticket, but if you told them, it wouldn't stop many of them, and that doesn't mean they necessarily lack intelligence.
Intuitively, and probably from most human being's viewpoints, a bad gamble isn't necessarily a bad idea if the risk in minimal and the possible payout is life-changing. On the flip side, a great gamble might not be the best idea if the risk is life-changing.
There was some modestly famous piece about somebody who had two choices: one was to walk over an old rickety bridge that had a certain (albeit low) chance of breaking, or to walk an extra 10 minutes to a bridge that had no chance of breaking. He had to do this daily, to and from work, or something. Mathematically, if you counted the extra ten minutes daily as time that was "wasted," it was clear that you should take the gamble. But this isn't poker, this is life: we can't just keep trying over and over again until our actual lifespan and our expected lifespan converge.
Interesting stuff to think about.
Posted Fri Jun 24, 2005 5:16 pm GMT by Sean_in_NJ
| snoogins47 wrote: | | But this isn't poker, this is life: we can't just keep trying over and over again until our actual lifespan and our expected lifespan converge. |
I often wonder when I will reach that point where the combined running time of my DVD collection is greater than the amount of time I have left to watch them.
Posted Sat Jun 25, 2005 1:48 pm GMT by snoogins47
| Sean_in_NJ wrote: | | snoogins47 wrote: | | But this isn't poker, this is life: we can't just keep trying over and over again until our actual lifespan and our expected lifespan converge. |
I often wonder when I will reach that point where the combined running time of my DVD collection is greater than the amount of time I have left to watch them. |
At that point, start trimming the fat by sending me a new DVD every 90-180 minutes. We wouldn't want you to feel obligated to live longer, now would we?
Posted Mon Jun 27, 2005 2:03 pm GMT by PuckJunkieNY
| Sean_in_NJ wrote: | | snoogins47 wrote: | | But this isn't poker, this is life: we can't just keep trying over and over again until our actual lifespan and our expected lifespan converge. |
I often wonder when I will reach that point where the combined running time of my DVD collection is greater than the amount of time I have left to watch them. |
You do have some control to this problen Sean. Sleep less. Just one hour less/per night will yield approx. 180 more DVD's to be viewed/year. Not counting bonus material of course.
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