This one is hard. Take Cannae, for example. Can you really measure this as one outcome? It could be broken down into all kinds of things: * Varro's (or Paullus' if you happen to believe that Varro was indeed scapegoated for the disaster and that Paullus was really in command that day) decision to mass the legions in a phalanx, instead of their usual wide maniples. * Whether the Celts, Celtiberians and Iberians would have been able to hold the center against the legionaires without breaking. * Whether Hasdrubal would have managed to stop the Roman and Italian Cavalry * I cannot recall who was in command of he Numidians on the other flank, but if they had not been turned around when they went to pursue The Italian Allied Cavalry on their flank, that side of the battlefield would not have been enveloped by the Punic/African Heavy Infantry that Hannibal had held back And, one could continue, probably down to the level of "Did Legionaire Plebius manage to hurl his pila soon enough to impale the charging Celtberian Villoni in time to keep the aforementioned Celtiberian from eventually killing Plebius' centurian, who would have then gone on to kill Hannibal, just before he had time to issue the final order of the day?" So, how are you defining "A single event" here?

I don't think you get a single outcome even from the best specified event-- you'd get a big sheaf of outcomes. If you could see all the multiple futures branching off from the present and have some way of sorting through them, you could presumably make better choices than you do now, but it would still be very hard to optimize much of anything.