European Lotto 150 million

[Killme00]

If you have to choose 5 number from 50 and 2 from 9 and match all seven...what are the odd of getting all seven numbers. I tried to work this out but kept comg up with 8million to one. At 2 euro per ticket it would then make sense to buy up all the combinations. This is because it would cost 160 million but the jackpot plus alot of smaller prizes would be greater than 160 million. The only risk is that the jackpot is shared. Is 80 million to 1 correct on getting a combination of 5 numbers from 50 and 2 from 9.
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[BruceZ]

[ QUOTE ]
If you have to choose 5 number from 50 and 2 from 9 and match all seven...what are the odd of getting all seven numbers. I tried to work this out but kept comg up with 8million to one. At 2 euro per ticket it would then make sense to buy up all the combinations. This is because it would cost 160 million but the jackpot plus alot of smaller prizes would be greater than 160 million. The only risk is that the jackpot is shared. Is 80 million to 1 correct on getting a combination of 5 numbers from 50 and 2 from 9.
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[/ QUOTE ]

76 million-to-1.

C(50,5)*C(9,2) = 50*49*48*47*46/(5*4*3*2*1) * 9*8/2 = 76,275,360.

[donkeyradish]

Dont forget to deduct the cost of all the pencils you'd go through.

[Killme00]

thanks

just got the result

no winner

it up to 175 million euro next week

[MathEconomist]

Well, in order to make this investment, you already need price*combinations money to begin with. And people who have that much money probably don't keep enough of it liquid to do something like this nor does the ROI really justify it I think compared to other options. But I always buy the powerball (American equivalent) when I notice the jackpot bigger than odds of winning just for the hell of it.

[matrix]

Not sure how many tickets you'd need to cover all your bases for that kind of seven number system.

There was a syndicate that scooped the UK lottery a while ago (standard 6 number pick from 49 - ~14mill:1 )

they worked out a system that screened out very unlikely results like 1,2,3,4,5,6 etc and bought around 1 million tickets - they hit the jackpot and a bundle of smaller prizes and made a huge profit.

To work a similar system with a 7 number pick you'd need to invest somewhere in the region I'd guess of 5 million.

Personally I'd hate to risk that much money - but I'm sure you'd scoop enough smaller prizes to recover your initial investment if you missed the big one and cover the price of a bumper box of pencils as well.

[AaronBrown]

If you had bought one ticket for each of the 76,275,360 combinations in this lottery, I project you would have made €193,980,989 on your investment of €152,550,720. The table below gives the number of each prize you would have won (the first number is the number correct out of 50, the next is the number correct out of 9, the third is the number of prizes you get by playing every combination, the last is my estimated payoff, taking into account that you have altered the prize pool and distribution):

5 2 1 €153,901,946
5 1 14 €578,630
5 0 21 €75,178
4 2 225 €6,004
4 1 3,150 €221
4 0 4,725 €87.18
3 2 9,900 €69.31
3 1 138,600 €21.17
2 2 141,900 €19.72
3 0 207,900 €11.39
1 2 744,975 €8.29
2 1 1,986,600 €6.53

But you would have been lucky in that no one else hit the big prize, which was only a 24% chance given the number of tickets sold. There was also a substantial deficit in the other high prize categories, because the numbers did not match up well with popular combinations to play.

With average luck, your payoffs would have been reduced to the numbers below, with a total return of €99,424,527, a big loss on your investment. And that's just average, if some popular numbers had come up, you could have done much worse.

€63,190,394
€374,287
€62,345
€4,424
€193
€84.52
€60.93
€20.83
€18.18
€12.16
€7.82
€6.68

[el capitan]

[ QUOTE ]
they worked out a system that screened out very unlikely results like 1,2,3,4,5,6 etc and bought around 1 million tickets

[/ QUOTE ]

Please explain to me how 1,2,3,4,5,6 is more unlikely than 7,15,26,35,40,50

[AaronBrown]

As El Capitan pointed out, you can't screen out any combinations for being unlikely, they're all equally likely. On the other hand, it is smart to screen out popular combinations, because they pay off less when they win. I don't know if 1, 2, 3, 4, 5, 6 is played more or less often than average. On one hand, most people avoid it because the chance it its winning is obviously low (unlike more random-looking combinations, that appear to be similar to the numbers that win every day); but you only need one person in 76 million to disagree, or pick the numbers by mistake.

You won't make money from the smaller prizes. Everything but the top prize adds up to about $0.24 per $1.00 bought. That cuts your losses, it doesn't make a profit. You can increase that only a little by selecting unpopular numbers. With any large number of tickets, you can't show a profit without hitting the jackpot, and it takes millions of tickets to have any significant chance of hitting the jackpot.

[wiper]

please do this, and please report back!

i was trying to explain to a couple people the last time the powerball was at 300million or so that the odds were with you at that point, but nobody understood...

[tomdemaine]

[ QUOTE ]
If you had bought one ticket for each of the 76,275,360 combinations in this lottery, I project you would have made €193,980,989 on your investment of €152,550,720. The table below gives the number of each prize you would have won (the first number is the number correct out of 50, the next is the number correct out of 9, the third is the number of prizes you get by playing every combination, the last is my estimated payoff, taking into account that you have altered the prize pool and distribution):

5 2 1 €153,901,946
5 1 14 €578,630
5 0 21 €75,178
4 2 225 €6,004
4 1 3,150 €221
4 0 4,725 €87.18
3 2 9,900 €69.31
3 1 138,600 €21.17
2 2 141,900 €19.72
3 0 207,900 €11.39
1 2 744,975 €8.29
2 1 1,986,600 €6.53

But you would have been lucky in that no one else hit the big prize, which was only a 24% chance given the number of tickets sold. There was also a substantial deficit in the other high prize categories, because the numbers did not match up well with popular combinations to play.

With average luck, your payoffs would have been reduced to the numbers below, with a total return of €99,424,527, a big loss on your investment. And that's just average, if some popular numbers had come up, you could have done much worse.

€63,190,394
€374,287
€62,345
€4,424
€193
€84.52
€60.93
€20.83
€18.18
€12.16
€7.82
€6.68

[/ QUOTE ]

Good analysis, but does this include the fact that ~50% of the money you spend on tickets will be added to the prize pool? another ~75mill could make the difference.

[Skjonne]

[ QUOTE ]
they worked out a system that screened out very unlikely results like 1,2,3,4,5,6 etc

[/ QUOTE ]

/images/graemlins/smile.gif /images/graemlins/smile.gif /images/graemlins/smile.gif /images/graemlins/smile.gif /images/graemlins/smile.gif

I use the same system. I screen out all unlikely results (i.e. I don't play the Lotto)

[Lestat]

<font color="blue">The only risk is that the jackpot is shared. </font>

This is NOT insignificant! Nor is the amount in taxes (if any), you'll have to pay if you win.

[Bez]

Because it only goes up to 49, therefore your numbers would have 0 chance of winning instead of ~14 million to 1. /images/graemlins/smile.gif