I planning to wire up four lengths of 12v WS2811 led strings in a tree in my garden. 200 leds total and i have an 20 amp 12v power supply.
I want to mount the power supply innside the house, so the cable from the power supply to the first led is about 10 meter.
How big cable would i go for here?
It's not just for the first LED. The power needs to be supplied to both ends of the strips and possibly in the middle as well.
The sort of cable used for household wiring would be a good start or the heavy sort of speaker cable.
Remember that you will have to mount the Arduino (Nano would be a good start) in a waterproof case at the start of the LED strip as you cannot easily feed the data signal down a long cable. Remember also the 1 mF capacitor across the power at the start of the LED strip and the 330 Ohm resistor in series with the data line at the LED strip.
Why do i have to give power to two ends? It's nothing or very little Voltage drop with use of four 12v strings.
I had forgot the signal wire. I have to buy an waterproof box i think. Thanks 
Bjerknez:
Why do i have to give power to two ends? It's nothing or very little Voltage drop with use of four 12v strings.
How much current do you figure they need?
Incidentally there are different sorts of 12 V strings. You must specify what they are. If they have three LEDs per WS2811 chip, then 200 LEDs would require 4 Amps which is probably not too bad. If they have only one LED per WS2811 chip, then they would require 12 Amps which is a ridiculous amount for the thin foil.
If you use #14AWG with 10 Amp load you will get about 10.5 Volts at the LEDs. You need to determine what voltage you want at the load, then use this calculator you can figure out your wire size. Voltage Drop Calculator I have adjusted the voltage output of some power supplys to 13 or so volts to make up the voltage drop but you must be very careful if it is not a steady state load.