Lottery Question

[sirlearie]

hi all
not sure if this is the right category but as it is always popular with clever people , here goes :
I have played lottery mini game monopoly gold many times but have recently suffered on 3 occasions from an immediate duplicate game
ie. the dice roll exactly the same combinations as the preceding game
( surprise , not a winning game ! )
I am assured by the lottery help line that it is completely random but I would be grateful if anyone can tell me the odds of this happening ?
thanks.

[Ken4155]

I don't know the answer to your question, sirlearie, but some time back, the same thing happened to me. I contacted Camelot who told me that there was only an infinite number of permutations and that identical rolls of the dice will occur from time to time. I stopped playing the game (and any of the others on line) there and then. They get enough out of me with their twice weekly draws.

[Ken4155]

By the way, i did ask if there were ever any cases where a winning game was immediately duplicated. They said they didn't know:-(

[JJ109]

How many dice are rolled and are we talking about combinations or permutations?
ie does 344 count as a duplicate of 443 ie the same three numbers but in a different order, or does it have to be 344 exactly?

[Ken4155]

You get 6 rolls of 2 dice - bonus roll for a double (which i didn't get). In my experience, the totals of the two dice (that's each roll) were exactly matched in the second game. And in exactly the same order. So if i moved 8 squares, followed by 9, 7, 8, 6 and 3 in the first game, then i did exactly the same in the second. Hope that makes sense?

[JJ109]

I am sorry Ken, I haven't played this and so don't understand what is required!

[Ken4155]

It's just an ordinary Monopoly board, jj.

[davebro]

are there just 2 dice in the game?

[Ken4155]

Yes Dave, and you get 6 tolls, as i said. The idea is that each square you land on becomes your property. There is a list of combined properties which earn prizes and if you match any on that list, you win the stated amount. What sirlearie and myself have both experienced is identical rolls of the dice (all 6 rolls) in two consecutive games. Both of which were losing games - otherwise i guess we'd both be quite happy:-/

[Ken4155]

That's 6 rolls, not tolls, of course.

[JJ109]

The probability of matching the exact two pip values of 2 dice in the exact same order = 1/6 x 1/6 = 1/36
The probability of matching the same scores but not necessarily in the same order = 2/36 = 1/18 ie 63 could be achieved by either 63 or 36

However it gets more complicated if you can get any permutation of numbers to achieve the same score. Say you scored 7, This has many permutations to achieve it
If you scored 7 with say 61, then it could be matched with
61,52,43,34,25,61 There are 6 permutations out of 36 that will match it
ie there is a 1/6 chance of duplicating the score of 7

There are 5 permutations that match 6 and 8
51,42,33,24,15 and 62,53,44,35,26
Therefore the probability of matching a score of 8 = 5/36
Similarly matching scores of 5 and 9 are each 4/36
scores of 4 and 10 are each 3/36
scores of 3 and 11 are each 2/36
scores of 2 and 12 = 1/36

Therefore if whether different pip values are allowed and count as duplicating the scores the overall probability will be affected.
Once you have the 6 probabilities of each individual throw you then multiply them together

However when the lottery say it is random they are not talking about the dice scores, They have preset a number of permutations that will give the desired probability of winning as displayed on their literature. Some of the actual dice permutations will not be used by the lottery, They say the overall 6 roll permutions are randomly selected from the ones they use. Therefore unless we know how many permutations they use, we cannot determine the probability of getting 2 duplicate permutations in a row.