So my friend is telling me that in games like lotto, you reduce your chances of winning if you limit your own number choices by only ever choosing, say, your family's birthdays. But surely since the winning numbers are random, you got the same chances of winning no matter what.

Who is right?

CookieJon wrote:So my friend is telling me that in games like lotto, you reduce your chances of winning if you limit your own number choices by only ever choosing, say, your family's birthdays.

Does he explain why that is the case?

John

If you enter only birthday dates, you limit your choice of number to between 1 & 31. That would limit your chances of winning where the choice of numbers rises to 49, for obvious reasons. You are relying on numbers from a more limited range than for other people in the lottery.

Makes no difference I'm afraid. If you only entered the numbers 1 to 6 every week you would still have the same chance of winning as everybody else.

John

chairman bill wrote:If you enter only birthday dates, you limit your choice of number to between 1 & 31. That would limit your chances of winning where the choice of numbers rises to 49, for obvious reasons. You are relying on numbers from a more limited range than for other people in the lottery.

That's what he said.

z8000783 wrote:Makes no difference I'm afraid. If you only entered the numbers 1 to 6 every week you would still have the same chance of winning as everybody else.

John

That's what I said.

He's further added that both are right and this is some sort of known paradox, but really?? I think he's thinking of something else.

How can both be right, either the probabilities change or they don't? In this case they don't.

There are a number of myths around probabilities, he's probably thinking of something else. For example, if you are playing roulette and 10 reds turn up in a row is it better to put you money on Black?

John

CookieJon wrote:So my friend is telling me that in games like lotto, you reduce your chances of winning if you limit your own number choices by only ever choosing, say, your family's birthdays. But surely since the winning numbers are random, you got the same chances of winning no matter what.

Who is right?

If you are talking about a single entry, you are, without doubt.

If you're talking about about a number of "lines" on a single ticket, your friend could be right, in a very obscure way. To take the simplest case, say you need to choose a minimum of 6 combinations of numbers when buying a ticket (I think that is the case here, although I've never actually bought one myself).

If you had (for the purposes of an example only) 7 numbers you were willing to choose, then obviously you're going to have a big degree of overlap on each entry - and the chances of the ticket being a winner (which I take as winning any prize at all, e.g. for having 4/6 numbers) are reduced. However if it did win, it would likely win on more than 1 line and thus win more money.

The chances of your friend referring to something like this though, are about the same as the chances of they winning the big prize.
/pedantry

z8000783 wrote:Makes no difference I'm afraid. If you only entered the numbers 1 to 6 every week you would still have the same chance of winning as everybody else.

John

True - but if the numbers 1-6 did somehow win, you'd take home less money, as apparently 1-6 is the single most popular entry in these games, so the prize would be shared with many more people.

z8000783 wrote:For example, if you are playing roulette and 10 reds turn up in a row is it better to put you money on Black?

No, you should put it on red, as that would be fairly good evidence that the wheel is not playing true.

virphen wrote:

z8000783 wrote:For example, if you are playing roulette and 10 reds turn up in a row is it better to put you money on Black?

No, you should put it on red, as that would be fairly good evidence that the wheel is not playing true.

mmmmm...possibly.

John

CookieJon wrote:So my friend is telling me that in games like lotto, you reduce your chances of winning if you limit your own number choices by only ever choosing, say, your family's birthdays. But surely since the winning numbers are random, you got the same chances of winning no matter what.

Who is right?

Let´s look at this:
Every combination is equally likely to be drawn, so this is uniformly random (random is a more general term - a uniform distribution with all possible outcomes equally probable is a special case). To elaborate further: If you look at the random variable "number of numbers you picked that are also drawn", it has the same distribution for any combination.

What your friend may have though of is something different:
When several people have the winning combination things like jackpots are split. This means that if you pick a common number combination, you are more likely not to be the only winner.
This in turn means that if you look at the random variable "winnings in money", it does not have the same distribution for any combination and in particular differes in it´s expectation value. Your expected winnings are lower, the more common your chosen numbers are.

Now treating playing the lotto for several rounds as a random walk, with increments of winnings in money - cost of tickets, picking less common numbers will lead to the expectation of the increments being closer to 0 (they of course are negative). This in turn means that the probability that you are ahead in money after a couple of plays does increase when you pick the latter.
Here´s a diagram based on the winnings of the lowest category (and hence with the broadest data) in the german lottery of the last year:

These are scaled winnings for the numbes, with 1 being the generally expected win. Error bars give the root of the sample variance.

z8000783 wrote:Makes no difference I'm afraid. If you only entered the numbers 1 to 6 every week you would still have the same chance of winning as everybody else.

John

And you think you are the only one who has this idea? Oh no, there are hundreds!

Also diagonals, etc., are tipped by great numbers of players.

Berthold wrote:

z8000783 wrote:Makes no difference I'm afraid. If you only entered the numbers 1 to 6 every week you would still have the same chance of winning as everybody else.

John

And you think you are the only one who has this idea? Oh no, there are hundreds!

I wasn't proposing it a suggested selection.

John

Chance of winning is exactly the same whatever you pick....

But if you wish to reduce the number of people you share the jackpot with pick 6 numbers over 31 in a random fashion.

CarlPierce wrote:But if you wish to reduce the number of people you share the jackpot with pick 6 numbers over 31 in a random fashion.

I've heard that too many players are doing this by now. It was a good tactic before it was popularised.

Your expected payout is affected by the likelihood of having to split prizes by choosing popular sets of numbers, but it's also affected when you have multiple entries by the overlaps between them (for all but the jackpot with an exact match). The bottom line, though, is that lotteries are a poor gambling choice, the payouts being pretty far off from a fair game. The main selling point for lotteries is the ratio between the jackpot and the cost of entry, with the utility of a single dollar or pound being, for most people who play, insignificant compared to the (minute) possibility of becoming instantly wealthy.

You'd have the same chance of winning if you picked numbers 1,2,3,4,5,6 as if you chose any random set of numbers, so I don't see how limiting your number pool will have any effect.

Somebody else already pointed out that you have less risk of having to split a jackpot by choosing a set of numbers not likely to also be chosen by somebody else.

Someone wrote:Somebody else already pointed out that you have less risk of having to split a jackpot by choosing a set of numbers not likely to also be chosen by somebody else.

That's fine, but the OP's conversation wasn't about reward/risk ratio, it was about chances of wining.

The last thing you want is multiple winning lottery numbers that split the pot. Even if certain lucky numbers did come up more often, large amounts of peole will be playing those numbers thus reducing your share of the pot.