From a strict probability and quant viewpoint you don’t know if the next trades will be 270 consecutive winners.
How can you keep faith? By knowing that your backtests are truly accurate, by using the system in a live account and seeing the performance. By asking yourself why there is such a huge discrepancy between the live account and backtest performance.
Also, if someone thinks they have a system with 90% winrate and it generates 30 consecutive losses, they could attribute it to a run of bad luck. The vastly more likely scenario is that their system is not 90% winrate no matter how hard they “think” it is or how the backtest turns out. Reality and live trading with emotions and money on the line is where it really counts.
I used to run a system that had an 75-90% winrate. If it generated 1 loss I would very reluctantly kinda attribute it to bad luck. If it generated 2 losses in a row the warning lights would fire in my trading room and in my personality and I had to figure out why I was taking losses and whether I was following the rules of my system. I would never tolerate more than 2 losses in a row.
Generally if you are trading a system with such high win rates, you should know pretty exactly what causes your trades to succeed or fail. You should know why your trades succeed or fail to a fairly precise degree.