Firstly, I've never heard of this so called "deep maths" and I can't find mention of it on the channel 4 website anywhere.
However, in the coin trick he showed up, I would expect that Derren's "team" would win on average 7 times to Andrew's 1.
The reasoning is as follows, remember that Andrew requires HHH, Derren requires THH.
Now consider the first three coin tosses, there is a one in eight chance that it is HHH, if it is, Andrew has won, if it is not this, then the coin must have come up with a T.
Now consider the three coin tosses directly after the T, if they are HHH, then Derren has won because the sequence has gone THHH, and thus the THH occured before the HHH. Therefore, once a T has been tossed, it is impossible for Andrew to win, because any HHH must directly follow a T, and Derren will win on the second H.
Therefore, Andrew needs to win before a T is tossed, i.e. in the first three tosses, giving him a 1 in 8 chance.
I'm not sure if this maths follows for when the sequence is different, but it makes logical sense that Derren's sequence should have as its last two tosses the first two tosses of Andrew's sequence.
In any case, we only saw the HHH version and for all we know, the stunt was filmed a few times until someone picked HHH or TTT as appropriate.
As for wisdom of crowds, if they were wiser, they wouldn't have predicted 63 as an average lottery number. I'm unsure as to how this could occur, and it hardly seems a foolproof system, in this example it could be conveniently switched to 36, but what if it had been 55, 56, 57, 58, 59, 65, 66, 67, 68, 69 etc etc etc etc.
Furthermore, it seems to be that this "free writing" is just a way for people to shut their eyes and notice that Derren and "accomplices" are looking at the numbers been given, adding them up, comparing to the actual numbers and then using a plant to submit balancing numbers.
In this video
here if you pause it at 3.09 you get a nice overhead shot of the numbers. The 9th person seems to have huge numbers, enough to send the predictions non-sensical. Only one person is making these large predictions.
Now, if you subtract this person's figure from the total, and then divide the new total by 22, what do you get?
1449 - 874 = 575 /22 = 26.13
976 - 391 = 585 /22 = 26.59
506 - (-69) = 575 /22 = 26.13
299 - (-276) = 575 /22 = 26.13
450 - (-158) = 608 /22 = 27.64
598 - 23 = 575 /22 = 26.13
so what have we learned, that the wisdom of the crowd is no good, as previous draws do not influence future draws, thus all the numbers are guesses, and if you aggregate enough guesses, they tend towards 25, as 25 is the average value of the lottery balls.
If you look at it further, you see that in fact, this Tyler who found the technique of "writing the first number that comes into your head tricky" is more likely another plant, who perhaps destroys one random set of numbers and replaces it with the 9th ballot. In any case, numbers above 49 or negative are required in order to balance the average away from 25.
As long as Derren can convinvce the other 23, he gets to convince the public as the subjects' reactions are genuine, throw in a bit of fancy talk, such as "deep maths" and bob's your uncle, people get sucked in.