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I just came across a blog post. I believe the answer is a correct approximation:

http://tastytradenetwork.squarespace.com/tt/blog/probability-of-touching-both-sides

I modified the question in the post to: What is the combined probability of the stock moving up to touch the short call strike but not touching the short put strike price of the short strangle?

**Same delta values of 0.3 for the call and 0.3 for the put. Assume symmetric random walk.

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If $A$ is the event of touching the higher strike (between now and expiry) and $B$ is the event of touching the lower strike (and $B^c$ is its complement, that is the event of not touching the lower strike), then:

$$P(A\cap B^c) = P(A) - P(A\cap B). $$

They have already estimated POT on the higher (lower) side, $P(A)$ ($P(B)$), to be twice the probability of stock price at expiry to be less than the higher/lower strike, and POT on both sides, $P(A\cap B)\approx P(A)\cdot P(B)$.)

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    $\begingroup$ Strangle is just a package of vanillas that only pay at expiry. Traders probably monitor POT (via estimations above) because (quote from your link) "when a short strike is touched, traders may become nervous ...". You're probably thinking of rebate options, also called touch options (pay $1 if such and such events take place). But even there, the rebate is usually payed at expiry. It can also be payed at touch (hit) time in some cases. Term sheets would have to explicitly state that. $\endgroup$
    – ir7
    Jun 11, 2021 at 16:14

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