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Server Time: 11/21/2008 6:13:14 PM PACIFIC |
 Powerball ticks, Snorbolus, 10. Jul 2003 10:01 | ||
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| The jackpot in last nights CT lottery, Powerball was $250 million. The odds of winning that jackpot were 1:120,526,770. So each $1 ticket had a positive expectation. As I checked the numbers this morning and discovered, to my disappointment, that I was not a lucky winner, I began to ask myself if having positive expectation on the ticket makes any real difference for a lotto player? I have no realistic possibility of ever buying sufficient lotto tickets for any mathematical expectation (positive or negative) to be realized. If you doubt this consider that there have been fewer than 1 million days since the start of the calendar, 0AD. So what do you all think. Are players, such as I, who buy a modest number (5 in my case), of tickets only when the jackpot prize is greater than the odds against winning it, making a logically sound decision. Or would we be better basing our decision to buy a lotto ticket or not only on whether we have a spare dollar kicking around while we are in the shop and if we fancy taking a shot at unearned riches this week, irrespective of the absolute size of the prize? Snorbolus | ||
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| Re: Powerball ticks, MozMan, 10. Jul 2003 11:40 | ||
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| Ya got me. All I know is that I put the winning numbers on my Powerball ticket three days ago, but they showed the wrong numbers on TV last night... those lottery people are really starting to piss me off. ITS ALL RIGGED I TELL YOU! -Moz "The reports of my assimilation are greatly exaggerated." | ||
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| Re: Powerball ticks, TKarrde, 10. Jul 2003 11:56 | ||
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| I can't explain why but I NEVER play the lottery. The odds are too bad. However, I do make the exception for $5 or $10 when it gets above $100M. I think the analytical side of me thinks it is a +EV play. But still... a million to one shot is still a million to one shot. I think the EV attribute of something can only be used when you can expect the situation to occur often enough that you will get an average result over a period of time. I think that leaves the lottery out of it. TKarrde "The next best thing to playing and winning, is playing and losing." | ||
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| Re: Powerball ticks, stdioh, 10. Jul 2003 12:35 | ||
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| First of all, I consider the lottery, in general, to be voluntary taxation. That said, you can have a positive expectation and it is worth betting on, since reward far outweighs risk in this case. Sure you are so unlikely to win in your lifetime, but the amount that you would win would be enough to ensure success for the next 5 generations of your descendants, cure a disease, stop an alien invasion, etc. I see nothing wrong with buying +EV tickets. Here is the real problem with lotteries when it comes to expectation. People do not factor in the chance of somebody else picking the same numbers and sharing the prize. This is a very common application made by innumerate people. Lets say that there is a lottery in which 3 single digit numbers are drawn and lets say that it costs me a dollar to play. Lets also say that the prize is $1,100. Now if I buy one of each possible ticket from 000 to 999 I've spent $1,100 and I am guaranteed to win. +EV. The problem is that if I win I don't necessarilly get all $1,100. If somebody else picks the same numbers, we each get only $550. Now if I bought all possible tickets I have a net loss of $450. Big -EV. So then you have to look at the chance of splitting the prize with 1, 2, 3, etc others. How many people play the game? How many tickets will be sold? Well, when there is a quarter of a billion dollars up for grabs you better believe that more people will be playing then before there was. You've got a 1 in 120M shot at winning the thing, sure. What happens when crazies go out and buy 1000 tickets each? What happens if they sell 120M tickets? If they sell 120M tickets then we have to look at the chance of somebody else having the same ticket as you. We can assume a poisson distribution and do the statistics exactly, but I think that approximation will serve us here. You see that there would be a very high chance for one person to share your number, since there is roughly one person per number in the system. If you assume that one person has your number, the chance of having a third person on that number is again relatively high, and since we have such a large sample, adding a person to your number doesn't reduce the field significantly. The chance of 1 other person having your number is 1/120M+(120M-1)/120M*2/120M, ... this is a very long sequence, but let us draw an analogy with the number 10. Another way to look at this is to look at the chance somebody will win if there are 120M tickets sold. That is almost identical to the chance that you will share if you win. So let us say that your chance of winning is 1/120M, but your chance of sharing in a 2-way split if you do win is X where X is the chance that somebody will win. There will be a chance of 1/120M*X that you win and share with 1 person, a 1/120M*X^2 that you share with 2 people, and 1/120M*X*3 chance that you win and share with 3 people, etc. The chance of you winning and not sharing with anybody is 1/120M*(1-X-X^2-X^3-.....) Now if X is a very small fraction, you are doing ok because the number in the right side will be close to 1. If X is a very large fraction then we see that the number will be very small. If instance, if X = 1/2 then the right hand side is (1-1/2-1/4-1/8-1/16-1/32-1/64) = 1/64. Now if our set was really infinite, we could keep on extending this and it would tend to zero, but it becomes unrealistic to expect more than 7 people to share a prize, so lets just ignore that small amount. So here if you win you would have a 1/64 chance of winning 250M, a 1/32 chance of winnign 125M, a 1/16 chance of winning half that, etc. Your expected amount of profit would only be 27.34375M - peanuts compared to the 120M you would have to shell out in order to be certain of winning. What are the chances of somebody winning if there is a 1 in 120M chance of winning and 120M tickets sold? Much more than 1/2. Thus your expected value would be much less than 27M. Now I'm sure that they didn't sell 120 million tickets, but how many did they sell? Since the money is not going into the prize pool, every ticket that is sold lowers your EV. Think of it like a rebuy tournament. When you rebuy, the prize pool increases. Yes you have less of a shot of winning than if you used the money to buy into a whole new tournaments, but other players' rebuying is building a much bigger prize pool, making it worth your while to buy back in. If the rebuy money went to the house and not into the prize pool, then there would never be a reason to play a rebuy tourney - the odds for all of the players would be terrible. A lottery is essentially a rebuy tournament where players can buy as much as they want with none of that money going into the prize pool. Here's another way to look at it. Lets say that I'm clever and want to win the 250M, so I send out a team of men to 7-11 stores each with a range of numbers and they are buying up tickets for weeks before the draw. Lets say that I spend 120M and actually buy one of each ticket. Lets say that somebody else does the same thing. Now no matter what number his, we split the 250M into 125M each, we each profit by 5M and go home smiling. Now we add a third player into the mix doing the same thing. Now we each get 83(1/3)M and are each out a total of 36(2/3)M. The long story short is that this lottery would only be worth playing if you could prevent others from playing, but the bigger the prize gets the more tickets people buy. Unless two players can win the jackpot without splitting the prize, there is almost never a lottery coffer that is actually worth playing. | ||
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| Re: Powerball ticks, Snorbolus, 10. Jul 2003 14:11 | ||
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| Stdioh, That is a good analysis, but I suspect that it misses the point. Consider a situation where somebody offered you an opportunity to invest a lump sum of $1 million now and recieve a guaranteed, index linked, $1 every day for the next 1 million years. That would be a 365 fold return on your investment! Would you accept the offer? Even if you were sure that they would be good for all of the payments I doubt it. I am forming the oppinion that thinking of lotto tickets in terms of an expectation which you have no opportunity to realize is a similar colour. That is to say it dosen't matter if the ticket is +EV or not. The real question is "what is worth more to me, $1 or a almost 0 chance of riches beyond the dreams of avarice?" The thing is that I would really like to have riches beyond the dreams of avarice. Snorbolus | ||
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| Re: Powerball ticks, MozMan, 10. Jul 2003 14:16 | ||
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| Good point. I find I look at the lottery like I look at casino house games; it's a small investment in fun and entertainment with no real hope of profit. If I could live long enough to play millions of times only when the jackpots odds justified the dollar, then I would consider +EV... but in reality I spend $1 or $2 on tix when the jackpot goes over $150m or $200m just because it's fun to think about what I would do if I won. -Moz "The reports of my assimilation are greatly exaggerated." | ||
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| Re: Powerball ticks, stdioh, 10. Jul 2003 14:26 | ||
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| In the case of the million dollars now and one dollar a day, it doesn't add up because of interest considerations. In the case of the lottery you don't know that you get paid at the end of one million years. You get paid as soon as you win. And there is no stipulation that you have to buy your tickets one at a time either. | ||
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| Re: Powerball ticks, Snorbolus, 10. Jul 2003 14:30 | ||
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| Index linked my friend, index linked ;-) Snorbolus on 10. Jul 2003 14:26 stdioh wrote: > In the case of the million dollars now and one dollar a day, it doesn't add up because of interest > considerations. In the case of the lottery you don't know that you get paid at the end of one > million years. You get paid as soon as you win. And there is no stipulation that you have to buy > your tickets one at a time either. | ||
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| Re: Powerball ticks, stdioh, 10. Jul 2003 14:36 | ||
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| The index is irrelevant. It doesn't cover interest, only inflation. Interest on $1,000,000 at 5% is $50,000 per anum which is almost $137 per day. Now I would give you a million if you paid me daily interest on the sum PLUS a dollar a day. Absolutely. I could then borrow the million, pay the interest through, and keep the dollars for myself. | ||
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| Re: Powerball ticks, Snorbolus, 10. Jul 2003 14:42 | ||
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| Yup, another sound argument but I still think that you are missing the point. Snorbolus on 10. Jul 2003 14:36 stdioh wrote: > The index is irrelevant. It doesn't cover interest, only inflation. Interest on $1,000,000 at 5% is $50,000 > per anum which is almost $137 per day. Now I would give you a million if you paid me daily interest on the sum > PLUS a dollar a day. Absolutely. I could then borrow the million, pay the interest through, and keep the > dollars for myself. | ||
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| Re: Powerball ticks, Snorbolus, 10. Jul 2003 15:36 | ||
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| My point was not that there aren't more profitable ways to invest $1 million. It is that, even if there weren't, this still wouldn't be a good one. Snorbolus on 10. Jul 2003 14:42 Snorbolus wrote: > Yup, another sound argument but I still think that you are missing the point. > > Snorbolus > > on 10. Jul 2003 14:36 stdioh wrote: > > The index is irrelevant. It doesn't cover interest, only inflation. Interest on $1,000,000 at 5% is $50,000 > > per anum which is almost $137 per day. Now I would give you a million if you paid me daily interest on the sum > > > PLUS a dollar a day. Absolutely. I could then borrow the million, pay the interest through, and keep the > > dollars for myself. | ||
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| Re: Powerball ticks, johnph77, 11. Jul 2003 04:53 | ||
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| The Powerball jackpot is also paid out over a period of time, rather than a lump sum - 25-30 years? If I'm not mistaken the lump sum cash option is between 50%-60% of the annuity option. Nice income, though. What that would do is raise the breakeven point of even-chance play to about $200 million, rather than the $120 million you asked about earlier. | ||
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| Re: Powerball ticks, Lottery Larry, 11. Jul 2003 12:27 | ||
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| well, $215 million to be more precise. but unless you're waiting for 2 years to take a shot, using the cash prize in your EV calculations is probably not worth it | ||
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| Re: Powerball ticks, shorn, 11. Jul 2003 13:36 | ||
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| I like to think of it as the opportunity cost of not playing. When it gets above $100 million, the opportunity cost is too high not to play. Hey, even in poker it is sometimes right to make a -EV play...why not in lottery? | ||
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| Re: Powerball ticks, foraces, 21. Jul 2003 19:42 | ||
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| So what your saying is that your hand can be counterfeited resulting in a split pot? | ||
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| Re: Powerball ticks, Lottery Larry, 10. Jul 2003 19:02 | ||
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| what did the title mean? thinking of terms of +/- EV when you are talking about vast sums of money for insignificant investment dollars is almost pointless. that being said, the two winners of the Powerball both ended up with positive EV at $130 million dollars.... so was that a good bet for them? i'm sure that LL wouldn't mind saying "EV- schmevie"... my point is primarily this- if you were one of the lucky two, would you care if you'd won $130 million or $50 million? only from a greed standpoint. i personally limit my exposure to the lottery by not playing until the annuity prize reaches over 9 figures. i won't really be looking at it as a +EV/ - EV situation when i could be creating a lifetime income of $2,000,000 or so every year..... investing a few dollars. if you wait until you have positive EV on the cash prize, even if you split, you'll play once every 2-3 years. i say, skip a lunch out, dream a little, maybe you'll get killed by 6 fireworks or struck by lighting 30 times or drown in the bathtub 150 times. Save the EV analyis for where it counts- at the felt. | ||
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| Re: Powerball ticks, stdioh, 11. Jul 2003 09:58 | ||
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| Results are irrelevant. It doesn't matter how much they won. Only the chance of sharing the prize with X other people vs. chance of winning. Why not have a lottery that pays out 1 billion dollars, but that you have a 1 in 100 billion chance of winning? Because nobody would want to play something with such an insignificant EV. What if you had a one in a million chance to win 10 million? That's great and I would play it very very often. I'd buy 1000 tickets a week, quite easilly and I would have a 1/1000 shot each week for $1000 of getting 10M. You better believe it would be worthwhile, so long as I had enough of a bankroll to play it. Damn hell, how about getting 10,000 tickets a week and you should win within about 2 years. The point is that systems like this regulate themselves. People are much more greedy than they are aware of mathematics and when something looks like a +EV on the surface, the rubes flock to it. Even if it were a genuine +EV there are arguments for and against buying tickets in terms of standard deviation, but that aside, I've never heard of a lottery getting to a point where it was an honest to god +EV. | ||
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| Re: Powerball ticks, Snorbolus, 11. Jul 2003 11:59 | ||
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| Stdioh, > Results are irrelevant. It doesn't matter how much they won........ This is where you and I disagree: Over a large (relative to the variance) number of trials, the outcome of any single trial is irrelevant. That I agree. But if you know for sure that there will be very few trials then, in my opinion, results are everything. Snorbolus on 11. Jul 2003 09:58 stdioh wrote: > Results are irrelevant. It doesn't matter how much they won. Only the chance of sharing > the prize with X other people vs. chance of winning. Why not have a lottery that pays out > 1 billion dollars, but that you have a 1 in 100 billion chance of winning? Because nobody > would want to play something with such an insignificant EV. > > What if you had a one in a million chance to win 10 million? That's great and I would > play it very very often. I'd buy 1000 tickets a week, quite easilly and I would have a > 1/1000 shot each week for $1000 of getting 10M. You better believe it would be worthwhile, > so long as I had enough of a bankroll to play it. Damn hell, how about getting 10,000 > tickets a week and you should win within about 2 years. > > The point is that systems like this regulate themselves. People are much more greedy than > they are aware of mathematics and when something looks like a +EV on the surface, the > rubes flock to it. Even if it were a genuine +EV there are arguments for and against > buying tickets in terms of standard deviation, but that aside, I've never heard of a > lottery getting to a point where it was an honest to god +EV. | ||
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| Re: Powerball ticks, Lottery Larry, 11. Jul 2003 12:39 | ||
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| on 11. Jul 2003 09:58 stdioh wrote: > Results are irrelevant. It doesn't matter how much they won. Only the chance of sharing > the prize with X other people vs. chance of winning. what is the chance of sharing? 120 million squared, or just 120M:1? and in this case they had a 120M:1 chance to win the $260M annuity (definately positive EV) and the winners "won" $130M annuity instead... still positive EV on the ticket price in results. so what is your point? Why not have a lottery that pays out > 1 billion dollars, but that you have a 1 in 100 billion chance of winning? Because nobody > would want to play something with such an insignificant EV. bet me. when they start the first federal lottery, or North American lottery, to fund government deficits, it will probably look just like that and there will be plenty of takers as long as the tickets are no more than $2-3 dollars. > > What if you had a one in a million chance to win 10 million? That's great and I would > play it very very often. I'd buy 1000 tickets a week, quite easilly and I would have a > 1/1000 shot each week for $1000 of getting 10M. You better believe it would be worthwhile, > so long as I had enough of a bankroll to play it. Damn hell, how about getting 10,000 > tickets a week and you should win within about 2 years. a poker player who didn't mention variance, standard deviation and the long run? well, you did say SD later on > > The point is that systems like this regulate themselves. People are much more greedy than > they are aware of mathematics and when something looks like a +EV on the surface, the > rubes flock to it. Even if it were a genuine +EV there are arguments for and against > buying tickets in terms of standard deviation, but that aside, I've never heard of a > lottery getting to a point where it was an honest to god +EV. so tell us at what level would the lottery have to be, as a factor of the odds of winning it, before it could be considered positive EV? at least for the jackpot amount. actually, in the amount of wasted money that my "system" saves me, by not getting involved with the lottery before it hits my "jackpot>odds" threshold, i claim positive EV right there! and again, would anyone be worrying about whether the play was positive or negative EV? for life-altering jackpot amounts, i submit that EV doesn't matter if you win and is always negative if you lose. back to you, stdioh | ||
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| Re: Powerball ticks, stdioh, 14. Jul 2003 07:22 | ||
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| > what is the chance of sharing? 120 million squared, or just 120M:1? and in this case they Much much much more than that. The actual number depends on the number of tickets that were sold, but there is a chance to share 2 ways, 3 ways, etc. > had a 120M:1 chance to win the $260M annuity (definately positive EV) and the winners "won" > $130M annuity instead... still positive EV on the ticket price in results. so what is your > point? The point is that they were lucky they only shared it two ways. > bet me. when they start the first federal lottery, or North American lottery, to fund > government deficits, it will probably look just like that and there will be plenty of takers as > long as the tickets are no more than $2-3 dollars. Well, it is true that there are a lot of stupid people in America. I would lose any such bet. > so tell us at what level would the lottery have to be, as a factor of the odds of winning > it, before it could be considered positive EV? at least for the jackpot amount. > actually, in the amount of wasted money that my "system" saves me, by not getting involved > with the lottery before it hits my "jackpot>odds" threshold, i claim positive EV right there! > and again, would anyone be worrying about whether the play was positive or negative EV? > for life-altering jackpot amounts, i submit that EV doesn't matter if you win and is > always negative if you lose. Feh. The amount of money is salient as it is finite. If it were a question of a lottery that pays out 100million and you say that anything over 1million is irrelevant, then share a ticket with 99 people. The point is that the numbers never lie. > back to you, stdioh I don't really care to argue about this anymore, since exact numbers are not available to me. If you can provide me with the number of tickets purchased (which is probably readilly available with a little googling) then I can do the math and tell you exactly what your EV is (though I would also need to know what prizes were available for partial wins, etc). | ||
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| Re: Powerball ticks, Lottery Larry, 14. Jul 2003 17:37 | ||
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| there is no point in considering the lesser prizes- even the 100,000 second prize is horribly bad EV based on a dollar's investment. i will not continue either, since my philosophy is closer to your "opportunity cost" comment than anything else. if i were so lucky as to win, i would't care if i split the prize 5 ways! | ||
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| Re: Powerball ticks, stdioh, 15. Jul 2003 10:12 | ||
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| Yes, but if there is a large prize pool divided into many small prizes then it certainly factors into the EV. $100,000 certainly factors in if it is awarded each to 100 people, follow? $10 factors in if 5% of players win it. | ||
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| Re: Powerball ticks, Easy E, 14. Jul 2003 18:08 | ||
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| on 14. Jul 2003 07:22 stdioh wrote: > > what is the chance of sharing? 120 million squared, or just 120M:1? and in this case they > > Much much much more than that. The actual number depends on the number of tickets that were sold, > but there is a chance to share 2 ways, 3 ways, etc. But what is the likelihood of THAT, stidoh? Isn't it the odds of catching the winning numbers times the odds of catching the winning numbers times the odds of catching the winning numbers.... or some huge amount of zeros that isn't even worth considering? > The point is that they were lucky they only shared it two ways. Or one of them was unlucky to have to share it? > Well, it is true that there are a lot of stupid people in America. I would lose any such bet. I'm not sure I agree that this is a STUPID bet, even if you had to split it. I guess the question becomes, can the lottery EVER become a "smart" bet ... and if not, does it matter anyway? Whatever- it's the LOTTERY! How much thought does this take, anyway? | ||
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| Re: Powerball ticks, stdioh, 15. Jul 2003 10:29 | ||
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| > But what is the likelihood of THAT, stidoh? Isn't it the odds of catching the winning numbers times > the odds of catching the winning numbers times the odds of catching the winning numbers.... or some huge > amount of zeros that isn't even worth considering? No! This is a falacy that many innumerate people fall into. If there are 100 marbles in a bag numbered from 0 to 99 then the chance of getting the winning marble is 1 in 100 if you guess a number. Now if 100 people guess a number, each person has a 1 in 100 chance of getting the right marble. We assume that you get the right marble and want to find out the chance that you are sharing the prize with somebody else. Well, Player 2 had a 1/100 chance of guessing the same number you did. Player 3 also had a 1/100 chance of guessing the same number you did. In fact there are 99 other players who have a 1/100 chane each of having your number. Thus chances are very good that you share with another person. Now if we assume that you share with another person there is only a slightly smaller chance that you share with 2 people. So let us say that there are 100 people playing the marble game with 100 marbles. On average there will be 1 person chosing each marble, but it could be more or less for any given marble. The chance that noboy else chose your marble is (99/100)^99 which is 37% Thus there is a 37/100 chance that you get the prize all by yourself and a 63/100 chance that you share with at least one person. If you share with one person or more, there is a (98/100)^98 chance that you don't share with more than one. That is about 14%. Thus there is a 37% chance you win alone, a 54% chance you share with one person, and a 9% chance you share with 2 or more people. To expand one more step, we see that there are (97/100)^97 ways to share with a fourth if you are already sharing with 3, so that is about 5% Thus it works out to being: a 37% chance you win alone a 54% chance you share with 1 other a 8.5% chance you share with 2 others a 0.5% chance you share with 3 others. In this small sample we see that it drops off rather quickly because we have such our fraction gets far away from 1 quickly. In a system with millions of participants, this fraction approximates a constant over each iteration so while we still have a monotonic convex down curve, it is very very very shallow. That means that if you were to sell one ticket for each dollar that is at stake, it would be reasonably likely to share with a dozen people (though much more likely to share between 2 or 3). I really don't want to run all the numbers (though if I keep getting argued with I may have to), but if I had to estimate it for this lottery scheme, I think it would look something like: 5% chance of winning alone 10% chance of sharing with 1 person 9% chance of sharing with 2 people 8% hance of sharing with 3 people 7% ... At leat it would approximate this sort of a functional shape. After the initial increase in probability, the decrease in probability would be close to linear. > > The point is that they were lucky they only shared it two ways. > > Or one of them was unlucky to have to share it? See the argument above. If enough people are playing the thing chances get very large that somebody else picks the same numbers as you do. > I'm not sure I agree that this is a STUPID bet, even if you had to split it. I guess the question > becomes, can the lottery EVER become a "smart" bet ... and if not, does it matter anyway? Like I said, it depends on what the chances are that you split it 3 or more ways. > Whatever- it's the LOTTERY! How much thought does this take, anyway? If you decide to not think about the lottery and not play it then that is reasonable, but it breaks my heart to see so many humans putting their money into something without the most rudimentary of investigations. As for why I like to look more in depth for these things - I like playing with numbers. That's why I'm a mathematician, I suppose. | ||
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| Re: Powerball ticks, Easy E, 15. Jul 2003 10:59 | ||
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| > No! This is a falacy that many innumerate people fall into. If there are 100 marbles in a bag numbered from 0 > to 99 then the chance of getting the winning marble is 1 in 100 if you guess a number. Now if 100 people guess > a number, each person has a 1 in 100 chance of getting the right marble. Okay, makes sense, they're independent actions as far as picking. But how can it be 120,000,000:1 that TEN people pick the winning number? > (though if I keep getting argued with I may have to), but if I had to estimate it for this lottery scheme, I think it would look something like: > 5% chance of winning alone > 10% chance of sharing with 1 person > 9% chance of sharing with 2 people > 8% hance of sharing with 3 people > 7% ... Well, the results don't bear out this even spread, since I can't remember ever hearing of more than 2 winning tickets for any 100 million:1 odds lottery.... or even that many for lower state lottery odds. I think you're going to have to grit your teeth and do the math for us idiots. I'm estimating that they sold $120M in tickets before the jackpot was hit, since the annuity went from $200M to $260M. I think that number is safe enough to use for this problem. Prizes for Powerball are: 5 numbers plus the Power Ball Jackpot 1 in 120,526,770 5 numbers without the Power Ball $100,000 1 in 2,939,677.32 4 numbers plus the Power Ball $5,000 1 in 502,194.88 4 numbers without the Power Ball $100 1 in 12,249 3 numbers plus the Power Ball $100 1 in 10,685 3 numbers without the Power Ball $7 1 in 261 2 numbers plus the Power Ball $7 1 in 697 1 number plus the Power Ball $4 1 in 124 Just the Power Ball $3 1 in 70 Let loose the EV calculation hounds! Don't waste your time with the lower-than-jackpot amounts, since they can NEVER be positive EV, given the vig that makes the jackpot amount possible. > > At leat it would approximate this sort of a functional shape. After the initial increase in probability, the > decrease in probability would be close to linear. > > > > The point is that they were lucky they only shared it two ways. NOT being a mathematician, I find it hard to believe that you have almost an equal chance of splitting 2 ways as splitting 10 ways, especially since the evidence doesn't bear this out. Then again, it IS a small sample size. > > Or one of them was unlucky to have to share it? > > See the argument above. If enough people are playing the thing chances get very large that somebody else > picks the same numbers as you do. See my "rebuttal" if you can call it that. > > If you decide to not think about the lottery and not play it then that is reasonable, but it breaks my heart to see so many humans putting their money into something without the most rudimentary of investigations. Sorry to hurt you, but the chance to win GOBS and GOBS of money for a few dollars doesn't need too much evaluation, in my mind.... even IF I get "unlucky" and have to share it with others. I'm happy with a simplistic "Annuity > Odds = Positive EV" calculation, as it keeps me out of the lottery for the most part AND lets me take a shot at moving up to $1000-2000 without learning how to play poker! (I mean, what ELSE would the money be good for?) And, as they say, SOMEONE has to win (besides the states, that is) > > As for why I like to look more in depth for these things - I like playing with numbers. That's why I'm a mathematician, I suppose. Geek.... :0 PS- Stray thought- should the Mob sue the state governments under monopolistic statues? I mean, the old number runners took out MUCH less than 50% vig (i've read 30% or so). | ||
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| Re: Powerball ticks, stdioh, 15. Jul 2003 11:51 | ||
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| I'll reply to this fully later, if I have time. Right now I'm up to my arse in alligators at work. I should point out that the argument hinges on a very large number of people playing in the thing. The larger the number of contestants compared the the ability to win, the flatter things become. Thus is 120M tickets were really sold there would be a very reasonable chance of splitting many ways, but in general much fewer tickets would be sold, so the curve would be much steeper and it would be very rare to split more than 2 ways. | ||
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| Re: Powerball ticks, Snorbolus, 15. Jul 2003 13:51 | ||
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| I still don't see how you think that being +EV helps when it comes to lotto tickets? Lets be generous and assume that the jackpot becomes sufficiently high to make the tickets truly +EV. You buy a ticket and loose. How are you better off than if you had bought a -EV ticket the week before and lost? You will never buy enough lotto tickets for their true expectation to be realized. Granted, in theory one could wait for a truly +EV lottery opportunity then go out, stand in line 1205268 times and buy every possible combination of numbers (ticket sales are limited to batches of 100 when the jackpot exceeds $100 million). However, I will NEVER do this. If you ever find me trying please just shoot me, or at least punch me squarely on the nose. In poker when you make a +EV play and loose its fine because you know that you will make similar plays sufficiently often for "the long run" to kick in and that, eventually, you will realize the expectation. This is not the case for lotteries. Now you might take the position that, because you are so astronomically unlikely to win, it is never worth playing the lotto. This is a defensible point of view. Indeed, I believe it to be the most prudent choice. However, I put it to you that if you are ever going to play the lotto then there is no practical reason to wait for a truly +EV situation because it will make no real difference. Snorbolus | ||
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| Re: Powerball ticks, johnph77, 15. Jul 2003 14:54 | ||
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| OK, I get this drift. It's a given that the odds on selecting one particular ticket is 1::120,526,770. Therefore, your odds of getting any combination of numbers is 1/120,526,770. The next person to buy a ticket has a 1/120,526,769 chance of obtaining a ticket with numbers differing from the numbers on your ticket. Therefore the chances of each of you having unique tickets are 1/120/526,770 + 1/120,526,769. And so on. I'm not going to pursue the math necessary to reach the point where the chances of a shared ticket reaches 50%, but the chances of that particular set of numbers being selected as a winner are the same as any other set. On the other hand, if you were to gather 75 people together at random the chances that two of them will share a birthday approaches 50%. | ||
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| Re: Powerball ticks, johnph77, 15. Jul 2003 16:58 | ||
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| I lied. When the 48,101,080th random ticket is purchased, the chances of 2 tickets being the same is 50%. | ||
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| Re: Powerball ticks, stdioh, 16. Jul 2003 10:51 | ||
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| Exactly. And the shared birthday phenomenon is just like people picking lotto numbers in a lottery that goes up to 365 (or 366 technically). Oh, and you don't need 75 people. There is a greater than 50% chance that two of them will share a birthday if you have 21 people. If you have 30 people the chance is over 70%. What would be interesting, but I'm still too busy to do, is collect 365 people and find the odds that 1 of them has a birthday of some randomly selected day, the odds that two of them share that birthday, three of them, etc. | ||
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| Re: Powerball ticks, Easy E, 16. Jul 2003 13:12 | ||
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| This still raises for me the question about why you don't see more split winners of the big lotteries, especially when they are selling 100M tickets... if it's that common for the split to happen. | ||
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| Re: Powerball ticks, MozMan, 16. Jul 2003 13:18 | ||
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| I've only been half-following this thread, so if I am off-base, then I apologize and you can dismiss me as an ignorant idiot. ;) I think the point is that there is a tremendous chance that multiple sets of numbers will be shared by multiple players; not that multiple players will win. In other words, there is a much greater chance that player A will have 1,2,3,4,5 and 9 and that player B will also have 1,2,3,4,5 and 9; but there are still 1:~1.2mil odds against 1,2,3,4,5 and 9 being drawn for the winning jackpot. -Moz "The reports of my assimilation are greatly exaggerated." | ||
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| Re: Powerball ticks, stdioh, 16. Jul 2003 13:49 | ||
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| It is a function of the chance of winning vs. the number of tickets sold. If the number of tickets sold goes through the roof then it becomes more likely for a multi-way split. I have no idea how many of the big wins get split, but don't forget that the whole thing hinges on somebody winning at all. My results were assuming that you won and were going to split it, but if you don't assume a winner, then everything drops down one level. Thus you have X chance nobody wins, Y chance 1 person wins, Z chance 3 people win, etc. Anyhow, I can't really argue it as I don't have any precise numbers for anything in front of me and it is getting a bit silly to argue without numbers, nor do I have the time to find out all of the numbers and do all the math. I will however point out that the issue has really been settled already by those who say, "even if you have a +EV you will never see the long run" | ||
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| Re: Powerball ticks, stdioh, 16. Jul 2003 13:50 | ||
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| And to reply to Moz' point, exactly. You don't care about your chance of winning. You care about the chance that X people have also chosen your numbers and the weighted average of what you will win if your numbers are drawn. | ||
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