# Are my chances greater or lower

Here's what I'm trying to work out but I don't know how to do it.
I run a lottery syndicate based on the Patent ticket method of the irish lottery.
The numbers available are between 1 and 47. The draw each week is made up of 6 numbers.
I have 5 stakes of 3 numbers each.
The patent rules are, you choose 3 numbers, you win £7 for any one of 3, you win £75 if any two come up, and you win £905 if all three come up.
Now I can't work out, if it's better or not to have a larger pool of numbers or not.
So with 5 stakes I have 15 numbers available that might come up in any one of the six drawn.
but with that the share has to be split 15 ways.
So is it better to have less numbers say 12 numbers (4 stakes) and split the winnings 12 ways, or have 18 numbers (6 stakes) and have to split the winnings 18 ways.
Hope you can get what I'm asking?
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Principal Software EngineerCommented:
Write an equation to determine the expected value for n stakes.  Then either differentiate the equation with respect to n and find the zeros, or (possibly easier) pick the largest expected value for some reasonable range of n.
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