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As soon as the Trisolarans receive Ye's transmission, the supreme leader orders their migration/invasion fleet, still under construction, to set out in the direction of the radio transmission as soon as they are able to launch. At this point in time they do not know how distant the destination is, and their vessels only have energy reserves to make a single deceleration. They have committed their entire fleet (although they do plan on building other vessels). It will be a long-term enterprise: the nearest star system will take 450 years to reach, but they don't know that that will turn out to be their destination and they must have reckoned on a much longer voyage, possibly thousands of years.

Although the Trisolarans are motivated by desperation ("God is a shameless gambler" so "we must become gamblers ourselves") there does appear to be a strategy that could mitigate some of the risk for them. Given that sophons are capable of FTL communication, and can travel at near lightspeed, they could send one or more as probes in advance of their fleet. Alternatively, if they had sent a sophon to their nearest stellar neighbour they could have discovered within 5 years that it was habitable, without the need to wait for a radio transmission.

We know that sophons are fantastically expensive to manufacture, since Project Sophon required them to cancel the building of a second fleet. However, once the equipment was in place it did not seem to take much time to successfully create 4 sophons. It's likely that the marginal cost of creating additional sophons would not have been great compared to the initial outlay.

Why didn't they adopt a strategy of exploration using sophons as probes, either as scouts in advance of their fleet, or prior to launching it?

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They did, after they produced a few. At the beginning of Death's End, it is briefly discussed that the Trisolarans launched multiple sophons through interstellar space at other star systems (and lost most of them to sophon-blind zones) as well as Earth. Presumably, the ones sent to Sol did not reach the system until after Ye's transmission was detected.
Furthermore, the Trisolarians presumably only had a rough direction or they would have noticed the transmission lined up with Sol immediately - they would have wanted their fleet away from Trisolaris for the potential hundreds of years it could have taken their sophons to sweep the search zone, rather than risk a disaster destroying their civilisation in the meantime. They likely planned to use sophons as scouts, but obviously had no need to as they ended up launching when they already knew to go to Earth.

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As per the principles of cosmic sociology, more technologically advanced races do exist and they might be able to detect the sophons, and since they contain sensitive intelligence (they're computers with at least basic knowledge of their creators and if hacked would be a major security breach) and they're quantum entangled (the connection could be traced) and which would endanger Trisolaris if captured.

The Trisolarians most likely didn't dare to use them to scout out and spy upon these more powerful races like the Singers.

The only way around this is to make sophons without any intel in them and have them scout planets and rendez-vous in a certain location to be approached by another entangled sophon if its sure the first one wasn't compromised. But that still doesn't completely eliminate the risk.

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