Let X_t+1 = X_t b_t where +b_t and -b_t occur with equal probability b_t is measurable !1_t, and the outcome b_t is measurable !1_t+1 (in other words, my "bet" b_t can only depend on what has happened so far and not on the future, but my knowledge !1_t includes the outcome of all past bets). Then {X_t|!1_t} is a martingale.

The Martingale System is commonly compared to betting in a casino with the hopes of breaking even. When a gambler who uses this method experiences a loss, they immediately double the size of the next bet. By repeatedly doubling the bet when they lose, the gambler, in theory, will eventually even out with a win.

Bots can be setup to bet at a custom time, with custom staking plans and custom trade-out/hedge rules pre-event or in-play. Bots can bet in your own customized way based on your manual selections. Bots can also find selections themselves and be 100% automated based on your selection criteria and betting instructions.

Yes, Betfair can detect VPN usage if you are using a shoddy virtual private network. With a reliable VPN, such as NordVPN, you can get a dedicated IP, change your location, and use obfuscated servers. That way, Betfair shouldn't detect that you are using a VPN.