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anything else means you die in a few turns or waste dice (7d6 gives you a 98% chance of success per roll, 6d6=~90%), 5d6=~70%)

It has admittedly been a little while since I played Jenga, but I would estimate that a good number of the pulls I've made (especially in the later stages of the game) were well below 70% chance of success. 5 is definitely the lowest I'd go in terms of "reasonable chance", though; it drops off pretty harshly below that. A range of 14-20 reasonably successful pulls sounds about right to me.

One method that I would probably use to mitigate the risk of death would be borrowed from the grand-daddy of Jenga-based horror games, Dread. You give the player the choice of whether or not to pull. If they pull without fail, their story is slightly more positive. If they don't pull, they don't succeed at what they try to do, but at least they know they're not dying.

Basically, it feels more arbitrary, but somehow also more my fault. 

Interesting! Personally, I would say that if I tip over a Jenga tower, it feels a lot more like my fault than if the dice I rolled ended up being low. That's not to dismiss your point of view: just saying that I don't share it.

 what if there were multiple things at stake that you distribute dice between?
Alternatively, multiple layers of failure (e.g. someone posted an idea in the idea thread about a journalist on the case of a serial killer, who kills again every time the tower falls).

I am all for adding more options for dice results! For your first case, I could see something like, rather than having a single goal at 16, you could do two separate goals at 9 and 9, or whichever distribution is more appropriate for the situation. Towerfalls that aren't gameovers are fun as well, and depending on the concept, they can definitely be a good fit.

A range of 14-20 reasonably successful pulls sounds about right to me.

Ah, 14 is the highest you can reasonably get, with pretty much the best strategy. 20 is what you can get if you succeed with every 5d6 roll, but if you roll 5d6 more than once then you're more likely dead than alive. Any mix of 7, 6, and 5d6 is worse than just 7d6—you get the possibility of some more rolls/turns in the future, but you're much less likely to get there.

It's very unforgiving—deviate from the strategy and you die quick or cut your game short by wasting dice. The problem then is either people go with the best strategy for part or all the game (so they have less/no choice) or they gamble and fail quick (so they don't play for long enough to have many choices). Most people aren't gonna figure out a strategy, so they'll go with option 2.

Interesting! Personally, I would say that if I tip over a Jenga tower, it feels a lot more like my fault than if the dice I rolled ended up being low. That's not to dismiss your point of view: just saying that I don't share it.

Yeah, 'more' was the wrong word—but it still has a single clear point of responsibility (making a single bad gamble) where jenga's drawn-out.

Well said on all points. (I would say that Jenga still has a single point of responsibility, but I digress.)  I've adapted this take on the system for my second submission, which is a lot more flexible when it comes to target numbers and failing a roll. Basically, we've got variable targets, multiple targets per prompt (on many, but not all) prompts, and failing to meet the prompt just means a less favorable outcome, rather than certain death. While I'm sure that each individual target number can still be optimized for, if one wants to play the spreadsheet game, the larger variance should mean that most of the problems we've discussed can be avoided.