>>12719113I'll give you an actual answer.
Consider the following problem: You have CURRENCY 1 and can trade CURRENCY 2 at EXCHANGE A. However, the exchange rate at EXCHANGE B is different.
Write out, as carefully as possible, precisely how you would determine whether to move CURRENCY A to EXCHANGE B, return CURRENCY B back to EXCHANGE A, and exchange CURRENCY B for more CURRENCY A than you started with.
This is actually a ridiculously complicated problem you could investigate forever, but just try to play with it for half an hour.
There is one solution I've found where I ask myself, "I wish to make THIS MUCH money... how many trading loops must I go through to do so?" whence, given fees to move from EXCHANGE A to EXCHANGE B, plus the split in buy/sell orders at either exchange, an exact logical expression (which you will certainly write) becomes an exact and analytical algebraic equation (which I would write down here in this post, except I did this ten years ago so fuck knows where I put my paper or if I'm even saying this correctly).
If you try to map all possible relationships across all currency pairs across all exchanges with all fees, splits, transfer times, errors in estimated value of GO OR NO GO ("motivation"), you get a cool lopsided star pattern and you also get some inequalities, moduli and other funny stuff in your logic. More importantly, intra-exchange pairs are treated identically as intra-exchange pairs as might be a wallet or bank account as well... and finally the logic is split into four parts:
- GO OR NO GO given initial condiions, no time variance and no error
- Statement of time variance... varying... over time and over the depletion of trading opportunities/change in time of "motivation"
- Errors
- Exact and analytical expression for a very simple case which we confuse with "motivation" but is really irrational.
You find that, if V and E are higher-order functions of the first two items, then...
