Some may disagree, but there is a difference between auto-hit on 3 and auto-hit on 4. In one case, stability is higher, and in the other, it is lower. Therefore, when implementing a system with an emphasis on stability, the first option is better, especially since the mechanics of ghosts are familiar to many.
Although the chance is 30%, not 50%, so the situation is different. Then I suggest this: after 6 misses in a row, the seventh hit is automatic, and after a hit, the next one is an automatic miss. This is balanced and almost doesn't change the 30% chance. Plus, this is the most stable of the possible options.
Simple calculation: 6 auto-misses in a row have a probability of about 12% (0.7^6), in this case, the probability of the 7th hit increases from 30 to 100%, i.e., +70% in 12% of cases. On the other hand, the chance of a simple hit is 30%, after which the chance of hitting on the next attempt decreases from 30 to 0, i.e., by 30%. In total -30% in 30% of cases. In the end, it's about zero.
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