Selecting the right GAUGE wire to power your Rov through the tether can make or break your Rov. (so to speak)
Gauge or AWG (American Wire Gauge) is the standard system (in the USA) of determining the diameter of the conductor of wire. The first thing I should point out is when it comes to Gauge size is the lower the number the thicker the conductor is. (so 14 Gauge is thicker than 20 Gauge.) Selecting too thin of a wire gauge will result in a huge power loss at the thruster because of the voltage drop.
Voltage Drop is just what it sounds like, it is the loss of voltage between the power source (battery) and the load (thrusters) To put it in layman's terms...the more power (amps) your thrusters use (draw) the greater the voltage loss will be which means less thrust your thrusters will make. To complicate things even more.....the longer your tether is, the more voltage drop you will have also.
Because of many factors such as the draw of your particular thrusters, length of tether, ect. I can't tell you exactly what size Gauge wire to use on your Rov but there are a lot of voltage drop calculators on the web you can use to figure what would be best for you. Formulas are good and all but I have done a few actual tests on a few common gauges that should serve as actual examples of what to expect, below are those results.