My guess is the following.
Lets say that the numbers in the game are in the range [1..N]. Lets further assume that there are M slots (or squares where numbers are placed). Suppose M is about 3*N.
So, on average, you'd expect each number to occur 3 times.
If you see that number occur only once in the (visible) column on the right, then you are pretty sure that it'll occur at least once or twice in the (hidden) column on the left. So if you see 3 numbers in a row (or column) that each occur only once in the right hand side, then you can be fairly certain that they'll occur at least once in the left side; so you're pretty sure to win the prize.
All you need is some basic knowledge of statistics, uniform distribution, etc. I don't see a need for high-falutin' cryptographic analysis and higher order math.
If you're dealing with online stuff, then some knowledge of PRNGs can help. I remember (a long time ago) hearing about some online poker algorithm which was just calling rand(), and had been seeded with unix time. That leaves a really small number of possibilities to try, and you can reconstruct the stream of random numbers it would generate.
That makes sense, but theres still the problem that, even if you have 3 in a row that you think have a higher probability of occurring in the hidden part, they can still be X or O, not necessarily winning. Maybe theres a statistical edge in knowing that, but I doubt that would give you an edge of 90%.
Also, that seems to indicate the issue is due to the overall structure of the problem of choosing numbers for a game like this, while I got the sense from the article that the problem was more due to the algorithm the company used to control winners and losers (maybe I'm wrong on that). If it is due to how the company controls wins in some way, I could see how observing 3 in a row of singles more often than expected by a random distribution (whatever the distribution is for choice of number and choice of spot on the board) is a giveaway to some nonrandomness introduced by their algorithm. But if you were to approach it by finding divergences from this distribution, wouldn't you need a lot of tickets before you could infer this?
In any case - any guess on the expected number of tickets you'd have to have to discover a flaw like this?
All you need is some basic knowledge of statistics, uniform distribution, etc. I don't see a need for high-falutin' cryptographic analysis and higher order math.
If you're dealing with online stuff, then some knowledge of PRNGs can help. I remember (a long time ago) hearing about some online poker algorithm which was just calling rand(), and had been seeded with unix time. That leaves a really small number of possibilities to try, and you can reconstruct the stream of random numbers it would generate.