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Coin Trick
2012
unknownj
Regarding Derren Brown.. Brilliant show, by the way..

It's not "deep maths". It's very simple.

Unless you throw HHH on your first go, then there will be a tails within the first three throws. In which case the person who predicts THH will always win.

So if you miss out on that 1/8 chance to score HHH immediately, then you cannot get a subsequent HHH without first gifting the other player THH - you can't get to your third H without the other player already getting THH on your second H.

So in the long run, you'll lose with a score ratio of 7:1.

Bloody good trick, really love it, but it's not "deep maths", and doesn't relate to the lottery :o)

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(Deleted comment)
Nope.

Well, not exactly.

If I pick HTH then your strategy needs to be to pick either HHT or THT. In either case, my third coin toss only goes ahead the 50% of the time that the second coin toss didn't fulfil your victory conditions.

Now for obvious reasons, THT would be a bad choice, since we would have opposing sequences, and actually the trick would cancel out. So I've picked HTH and you pick HHT - smart move.

Now for me to score, I must get HT and then throw an H. So I've got a 1/8 chance of scoring on the first three throws. But so do you.

If we're beyond the first three throws, then for any instance of HT, there's a 50% chance that the preceeding throw was an H, in which case you win and the point is over. In the 50% chance that that didn't happen, there's then a 50% chance that I get the H I need in order to score. Which means that for each instance of HT, there's a 50% chance that you've just scored, and a 25% chance that I will go on to score.

Which means that we'd end up with a score ratio of 2:1. You still win, but the effect isn't so pronounced.

Which is why he probably tried the trick with a few groups, until he got the one where it works best. It always works, but to different extents, and he'd want to show off the best one :o)

Man it's good to be good at maths :D

(Deleted comment)
Because I was describing a special case where you win 7:1. Very pronounced effect, looks very good on TV.

But there is one where you only win 2:1. On average. Which means that if you play only a handful of times, you might still lose. Odds of 67% aren't exactly great :o)

(Deleted comment)
Split screen.

Probably.

But it's not important. What's important is the showmanship that went into it - he spent all that time giving us the whole "wisdom of crowds" thing, which was obviously total bull.. And the one risk in that would be that somebody would say "So then I take it that you proved that they gave you the right numbers, by showing the working afterwards, and that you'd taken the correct set of balls from the case, right..?"

BAM! Illusion is destroyed, because he can't prove that.

So he comes up with the whole "Or maybe I rigged the lottery". By joking about that, it gets him off the hook when it comes to proving that he used what the crowd said. Hell, he even admits it - he said (with a smug grin) that perhaps he didn't use what they gave him at all! And now that he's trying to keep it ambiguous (with a joke answer), he doesn't have to prove that the crowd thing had anything to do with it.

Absolutely brilliant...

The trick isn't in how he did it. It's in how he convinces everyone else that he did it.

(Deleted comment)
I mean that at a certain point, when Derren and the TV were on the right of the screen, and the balls were on the left, the left hand side was "frozen" (or more accurately, looped a bit). Which meant somebody could nip in, change the balls around, and then nip out before the real footage was displayed.

It requires that the hand-cam is mounted to make sure everything joins up correctly (no movement), and that everything is very fast and controlled.. Still, it's possible.

And yes, that was how I knew that the averages thing would be complete bollocks - you just don't end up with an average of two, it's really improbable..

(Deleted comment)
I didn't come up with it, it just seemed like the most plausible answer on the Internet.. At this point, I can only claim credit for working out the probabilities in the coin trick as it was going on - nothing more :o)

Also, yeah, "I did the calculations myself because we didn't want to know the numbers beforehand" -- oh okay.

Ah, but that's the genius of it. Because he's basically said "Or maybe I didn't use their numbers, and just rigged it". So that uncertainty is in there, but he's taken care of it, by basically saying "Yeah, if I didn't use their numbers, then I guess I must have rigged the lottery - how do you like THAT?!"

Brilliant :o)

(Deleted comment)
Yeah, ed and I were talking about running a simulation with one of the decomissioned machines, to see what weight imbalance would be required to guarantee an outcome (I don't think 20% would be enough to make certain of all six).

I think they were satisfied that it worked based on the trial runs they did.. And then his apparently getting it right on the night.. He said "this is what success looks like" and then showed it to them - of course they'll think it was them :o)

I don't think he was trying to keep it ambiguous. I think the entire show was geared to convince people that he rigged it.

I had just replied here saying something sort of similar :o)

Or at least, that he basically set up the false dichotomy of "either this bullshit average stuff happened, or I rigged it" with the expectation that your only logical conclusion would be the latter :o)

(Deleted comment)
Simple probability, Carrie.. While the probability of a single set of coin tosses is fixed, having victory conditions that reset the game means that certain outcomes are less likely to arise due to the fact that pre-requisite conditions are proportionately more likely to have resulted in a reset.

Let me put it like this. You bet me that you can throw a coin twice and have it come up Heads-Heads. I tell you that if you throw a Heads, I'll take the coin and go home. Even though Heads-Heads still has a 1/4 chance in theory, in practice you'll never achieve it because the game will end before you get the chance.

(Deleted comment)
Thank you. It was obvious to me that by picking THH it made it impossible for the other person to get HHH once there'd been a single T, but I was completely unable to verbalise it.

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