You can exile Stroke of Luck even if you draw the symbol. The test is still considered a failure, but stroke of luck is exiled. The ability to exile Stroke of Luck is not dependent on the auto-fail not being revealed - only the test being automatically successful.
Automatic Success/Failure: Some card effects make an investigator automatically succeed or automatically fail a skill test. If this occurs, depending on the timing of such an effect, certain steps of the skill test may be skipped in their entirety.
- If it is known that an investigator automatically succeeds or fails at a skill test before Step 3 (“Reveal Chaos Token”) occurs, that step is skipped, along with Step 4. No chaos token(s) are revealed from the chaos bag, and the investigator immediately moves to Step 5. All other steps of the skill test resolve as normal.
- If a chaos token effect causes an investigator to automatically succeed or fail at a skill test, continue with Steps 3 and 4, as normal. - FAQ, v.1.7, March 2020
Commit only to a skill test you are performing.
After revealing chaos tokens for this test, you may choose to exile Stroke of Luck. If you do, this test is automatically successful (unless a token was revealed).
The exile mechanic is an interesting one. Cards with an exile mechanic are extremely expensive near the beginning of a campaign but seem reasonable near the end. If purchasing before the last scenario, any card you purchase has an "exile" effect.
Stroke of Luck came out with the 2nd to last Mythos Pack of this cycle. So what should be the XP value of this skill card? Most skill cards have an XP value of 1 with few exceptions. This card however, is much more powerful than any skill card. No skill card can do better than Stroke of Luck. It's the most powerful skill card in the game. You could have a base skill of 0 and still have a 95% chance of beating a skill check of 10 or more. And as such, it should have a higher cost than other skill cards. But how much more? Double? It's probably worth a bit more than double considering it's Wild and its also saving you from using multiple cards on one skill check. Three times? Depends on the scenario. Will there be those situations where you need a boost of +4 or more? In the last few scenarios it's much more likely.
The conclusion is that Stroke of Luck seems like its very powerful for the final scenario. It only costs 1 more XP than any other skill card and the exile drawback is negated. For the second to last scenario is its breakeven point. I wouldn't recommend purchasing Stroke Of Luck prior to the second to last scenario.
Somewhat comparable to mystics' Seal of the Elder Sign which costs 5 exp. Both practically gives you an autosuccess.
Seal doesnt work as well if your stats are low and you need to put additional resources to succeed (arguably Preston Fairmont and sometimes Calvin Wright) but gives you the benefit of the investigator elder sign.
Stroke of luck also has a small chance of failure but can be used after revealing the token (and always gives +1 skill when commited).
In terms of the value of the elder sign, a lot of survivors have situational abilities that can be hard to quantify. Perhaps it's a moot point since (as far as I can recall) only Agnes Baker can take both cards. In her case, her elder sign just gives lots of stats. You'd be paying 5 exp just for an autosuccess where stroke of luck would only cost 2.
For most other investigators on average, the elder sign also gives you a 1.5 card advantage (like Mandy Thompson Harvey Walters, William Yorick, Silas Marsh, Father Mateo). 1.5 cards is worth about 2 exp (according to Emergency Cache and Lucky!).
So with seal of the elder sign you're paying 3 for the autosuccess and 2 for the side benefits. With stroke of luck, you're paying 2 for selective autosuccess after revealing a token (maybe that's worth 0.5 or 1 exp?).
In most cases you're paying only 2 exp for a around a 4 exp effect is a pretty good value exp wise. I think it might even be worth buying and rebuying for the last 2-3 scenarios of a campaign.