Keno 10 spot

A question to the wizard and anyone that can help.

The odds of winning the keno 10 spot is around 1 in 8.9 million. This is I assume for one game. What would the odds be if I played 50 games with the same numbers or even 200 games? Also would it be better to play 200 games with one set of numbers or split it into 4 sets of numbers for 50 games each? Or doesn't it make a difference. Thanks for the great site.

The odds are 1 in 8,911,711. Let's call the probability p = 1/ 8,911,711. The probability of hitting at least once in n games is 1-(1-p)^n.

So, in the case of 200 games, the probability of hitting at least once is 1-(1-p)^200 = 0.0000224421 or 1 in 44559.

You can get a close estimate by just dividing 8977711 by 200, as long as the answer is still very small.

It does not matter how you choose the numbers. The same ones 200 times or a different set each time, makes no difference.

Wiz -

I agree that for 200 games, it doesn't matter if you use one set all 200 times, for a different set each time.

But what about 200 different sets for only one game. Does the overlap affect anything?


On a somewhat related note, I rarely buy lotto tickets, but when I do, it's usually a multiple line quick pick. I get bummed out if I see numbers repeated. Should I?

I realize I'm not the Wiz, but what overlap? I'm confused by your question.

Multiple tickets for the same game means that numbers will appear on multiple tickets. With 200 tickets, all the numbers will get used multiple times. The distribution of the repeats is the overlap. I'm just not sure if it matters at all or not.

Quote: DJTeddyBear

Multiple tickets for the same game means that numbers will appear on multiple tickets. With 200 tickets, all the numbers will get used multiple times. The distribution of the repeats is the overlap. I'm just not sure if it matters at all or not.

Ah... I mis-read your question...sorry about that.

I don't think it affects the odds of the 10 hits.. I do think it affects the odds of the lower hits, when you have overlap.

If the payouts of the lesser prizes are fixed, isn't the EV the same, regardless of overlap (greater variance, tho)? If it is parimutuel (prize = total prize pool / # of winners), then yes, you would win less if the same winning numbers were on different tickets. But if, say, you hit a 4/10 on two tickets, the same 4 winning numbers would have to be on the two tickets.

BTW, DJTB, interestingly enough, Wikipedia says that for Powerball, the lesser prizes are fixed, except in California, where they are parimutuel. So, no worries as long as you buy your tickets in the other 49 states! Unless the quick-pick selected the same 6 numbers on 2 lines. Then, yeah, super-bummer!

I think ultimate EV is the same... but if you have a lot of overlapping numbers on the smaller prizes, the probability of winning is less, but you win more because you could have multiple wins.

I think I'm just repeating what you are saying.