Ah, right. I understand now. If that's the case, would it be easier to send the maximum amount available (without slippage) on one exchange to both exchanges?
Ie: exchange 1 has ask price 550 with amount 5, exchange 2 has bid price 600 with amount 10. You then place buy/sell orders for an amount of 5 on both exchanges. Ensuring no slippage.
That would be a possibility yes, but usually a discrepancy between prices tends to last a little bit. So it would be better to wait until you have enough liquidity to match your exposure. For example you don't want Blackbird to trade for $24 when the exposure you set is $5,000. I think it's better to wait until you have enough liquidity to send $5,000 orders.
Out of curiosity do you only examine the order book prices to a depth of 1? Seems like by doing so there'd be a few missed opportunities. However to examine with a depth of two the maths is much more involved.
During the liquidity check, Blackbird reads the order book in depth until it reaches a price that would cover its liquidity needs. So it doesn't just examine the first depth but the following ones as well, if necessary.