This is called "picking up pennies in front of a steamroller". You will make your $1 for many, many days, then the day comes where you continue doubling down and you lose a substantial amount of capital in the process.

Very similar to systematically trading options, i.e. selling covered calls, ...

See also: https://en.wikipedia.org/wiki/Martingale_(betting_system)

Source (FWIW, but it really isn't needed for this case): I worked at the most prestigious hedge fund/market maker in the US running their strategies on the servers colocated in all the major exchanges, so I know a couple things about arbitrage strategies. If a similar approach were to even remotely work, I would have most certainly seen it.

No need to reply (to me at least): I won't be convinced by any further argument that your trading system circumvents this basic paradox :-)