You take a coin and flip it a lot of times in a row, and you note every time that two different sequences of 3 results comes up.
Your initial reaction (and mine) was that all of the 2x2x2=8 results are equally likely to come up. Because if we flip a coin 3 times only this is true. You try and flip a coin 3 times and record weather your sequence came up or not and then start again. If you do this enough times (you'll need a few hours and nothing better to do) and you can easily show that all 8 results are just as likely. We are lead to believe this is true for the game above.
This isn't what happens, in a long string of results HTHHHTHTHTTHTHTHTHTTTHTHTH
I predict THH: T win! 1/3 done, H win! 2/3 done, T ignore what happened before, start again with the first one right , 1/3 done
I predict HHH: H win! 1/3 done, H win! 2/3 done, T ignore what happened before, start again with the first one wrong, 0/3 done
Pick a sequence where failing to get the end right means you are automatically in with a second chance. This means you can win far more often than you would think. The reason is just common sense, no deep maths, no psychology, no team thinking, no magic, just common sense.
As for how he predicted the lottery, there are dozens of equally plausible solutions, but however he did it I'll stab myself in the foot if a group of 24 people in a trance had the slightest involvement.