Electricity on the Underground

Both positive and negative rail are equally capable of electrocuting you, and you don't need to be touching both - you just need to provide a path from one to ground (which you almost certainly will if you are touching anything else). The running rails are not normally electrified but under certain conditions can be so are best treated with equal caution. I haven't watched (and don't particularly want to watch) the video so I don't know why they were not electrocuted but good fortune will have played a part.

The ruling from the various track courses be it NR or LU “ DONT STEP ON ANY RAIL “

simples it will hurt

There is a common belief that negative is OK in this case - it’s not. Negetivr only refers to the “direction” of the current. The effect of -200 volts on your body is exactly the same as +200 volts.

To be pedantic about it, you have to provide a path back to the source, not to "ground" (or earth). It happens that the traction current source is bonded to "ground" so there is a path from the running rails (and the concrete around them).

Also, since I'm being that way, electricity doesn't take the path of least resistance, it takes all paths in proportion to their impedance.

I don't plan on watching the video, either.

Although the 210 volts will have a lot more current than the 230 / 240 volts home supply, so the overall effect is likely to be worse.
Power = volts x current.

More dangerous than being electrocuted at home, firstly because it is not the voltage that kills you but the ampage, (the quantity of electricity*), and secondly because the underground runs on direct current and this holds you to the source while alternating current throws you off it. 

*electric bills are charged in amps.

oops sorry.

Obviously on third-rail electrified lines the running rails carry the return current and this is also the case where the three and four rail trains run on the same track (e.g. Wimbledon and Richmond branches, Bakerloo north of Queen's Park) where the fourth rail (negative) is typically bonded to the running rail.
It's also possible for running rails to be electrified in various fault scenarios. This is why, as rincew1nd and @aetearlscourt note upthread the advice is to treat all rails as live.

There are places where the negative rail is at 0V, usually where track is shared with NR trains. But surely any requirement for on board supply at less than line voltage is taken from the main supply using a potential divider, not by a separate feed from one or other rail?

As for the effects of electricity on the human body, it depends more on thevroite it finds through the body and therefore which muscles are triggered than on whether it's AC or DC. A shock to the leg muscles can make you hurl yourself across a room. To the fingers can cause you to be unable to release your grip. To the heart can stop it. You can also get severe burns.

The amps are relevant, but the current flowing through you will depend largely on the electrical resistance of your body (and anything between you and the electric supply or the ground, such as your shoes). If the short circuit from rail to ground passes only from toe to heel of one foot, the resistance is low and the current therefore high. You will get a very nasty burn but the current will only pass through your foot. If it passes from one foot to the other the resistance will be greater and the current less- but it will pass through more vital organs (and those powerful leg muscles)

15v through the running rails if memory serves

1/10 of an ampere (amp) of electricity going through the body for just 2 seconds is enough to cause death. The amount of internal current a person can withstand and still be able to control the muscles of the arm and hand can be less than 10 milliamperes (milliamps or mA).

Not sure what you mean by amps being "available". Either the current is flowing at that rate or it isn't. It is electric charge which can be stored (measured in coulombs)

A billion amps across 1 volt gives a power of 1GW, or about 1.3 million horsepower. (The resistance would be tiny, 1 nano-ohm!) You could do that sort of thing, but only for fractions of a second, by short circuiting a million coulomb capacitor in one millisecond, but please let everyone know beforehand so they can get along way away first!

Lightning is the other way round, huge voltages but tiny currents. The power, and energy, delivered is the same either way. Power is the product of volts and amps, energy is power multiplied by the time the current flows.

Sorry, I thought that was obvious. Any power source will only be able to supply a certain current (limited by, e.g. a fuse, or it's internal resistance). Thus 30 PP9's in series can't be used to satisfactorily power a 2kw electric fire, even for a few seconds.

That seems to cover the bases.

Indeed, but I meant 'available' in the sense that it could be supplied at all, not how long it could be supplied for.

The billion amp figure was supposed to be hyperbolically illustrative, not a figure to be used in circuit calculations.

Sorry, that's just plain wrong. Yes, the voltages are extremely high but the currents typically reach tens of thousands of amps.

5v to 15v but open circuit voltage is 100v and believe me it does hurt