Update: This document does not cover FGH clip, which at the time had not been done in realtime but has now been done by Linkdeadx2 and saves a huge amount of time. Here is a document explaining the new routing options to be considered: http://tinyurl.com/fghcliproutes. The change is not huge, because the only thing special about FGH clip is that it requires picking up an additional backup flower each time you do it, but that does have some effect on the route, and is very complex to analyze all possibilities.

Many 96 exit runners assume that the standard route through Forest of Illusion in 96 exit (listed at e.g. http://deanyd.net/smw/index.php?title=96_Exit_Route) is optimal in terms of overworld travel, but it isn’t. The optimal overworld movement through the forest should walk the path between FoI1 and FoI2 only once, but the standard choice (used by all current high-level runners) traverses this path 3 times. This diagram shows the number of times each path is walked in the forest. The left is for the optimal path, while the right is the current route. (Note that I am not considering routes which use the SW4 warp star or otherwise exit and then re-enter the Forest such as Waz's 95 no cape route. Such routes are harder to analyze because you must consider both additional overworld paths and new possible strats and I cannot prove that none of them are faster but it seems very unlikely.)

This loses 174 frames/2.9s (based on  overworld timing done by Dotsarecool; see http://imgur.com/GRDmXkY). This is one of only two (update: actually 3; the route in Chocolate Island loses 3 frames of overworld time compared to the fastest possible overworld route) places that I know of where the current 96 route is overworld-suboptimal; the other is in Star World and I have found a way to eliminate that (see https://youtu.be/ai91QGFn82Q) though it has not yet been adopted by most RTA runners. (Technically VoB is also overworld-suboptimal but there are many reasons to ignore this, most obviously that we would need to play Front Door instead of Back Door which loses way too much time.) At first glance, the suboptimal overworld here looks like a very easy timesave. However the standard route also crucially gets Yoshi for both exits in FoI2 for clips, which are a large enough timesave to be necessary for any serious route. Hence we need to factor that into our analysis.

Taking a step back, there are actually 6 ways to traverse the Forest with optimal overworld movement (I’m fairly sure I didn’t miss any but if I did tell me). I've listed all 6 here, grouped suggestively.

For FoI1-4, the a exit means the goal tape exit and b means the key exit. FGHa is the exit without the moon (which goes to FoI4) and FGHb is the one with the moon (which goes to FoI1). Exits with Yoshi are green and bold, and FoI2 exits are blue and italics. A few of these routes will be familiar to people who have run other categories. Route 2 is the current WR route in 95 no cape, and route 4 is the WR route for Lunar Dragon and was used in early 96 exit runs before FoI2 clips were found (see e.g. GameCube04’s 2005 run). In addition, route 3 (without any FoI2 clips) was used in both of the 96 exit TASes by VIPer7 and by Fabian prior to the current TAS. (The current TAS does a suboptimal route which walks between FGH and FoI4 2 extra times, losing the same amount of time on the overworld as the standard RTA 96 route. I suspect they would have been better off doing route 3 as well but I have not done the comparisons.)

Routes 4-6 all have the same problem. There is no chance to get a second Yoshi between FoI2b and FoI2a. Hence the only way we will be able to do clips for both exits is to keep the same Yoshi through FoI2b. While you save time on the overworld, you lose time in FoI2b and BSP. Route 6 is particularly bad, but routes 4 and 5 are almost workable. You save a bit of time in FoI1b by flying and by skipping Yoshi. In order to compare these, I made TASes of the 3 levels with what are (I think) the fastest current RTA strats. The end result is that routes 4 and 5 are slower than the standard route by about 3s. The exact number will depend on what strats you compare but if decently fast strats are picked for both the standard route always comes out at least a little bit ahead. The difference is close enough though that if you do not do the block grab in FoI2, then you’d save 5s (realistically a bit more if you’re not doing extremely fast FoI1b strats) switching to route 4 or 5 over the standard route, which may be a small timesave for less advanced runners who do the clip but don’t do the block grab. Another way to say the same thing is that the block grab saves 8 seconds, and the current route does a suboptimal overworld path to get that 8s timesave. The so-called “easy clip” strat which is sometimes recommended to new runners actually loses time for the normal exit and roughly breaks even for the secret exit compared to swimming without Yoshi, but similarly for people who want to use this strat, switching routes to one of these is technically faster.

Route 3 is a bit interesting. It does give a chance to get a second Yoshi, but you need to grab the Yoshi in FoI3 instead of FoI1. The FoI3 Yoshi grab has not been optimized seriously in a realtime setting, but it seems inevitable that it will be slower than the FoI1 grab with the fastest setup we have right now (namely the fast Yoshi + earthquake grab). Note that the current 96 exit TAS does get a Yoshi in FoI3 though, but that strat seems impossible for a human. If we did have an optimized FoI3 Yoshi grab comparisons would be possible, but without one I'll ignore this route and focus on the remaining 2 routes. (update: I came up with this: https://youtu.be/74MdRY1uctQ, which would make this route about 1.5s slower than routes 1 and 2.)

In both routes 1 and 2, we can get Yoshi in both exits of FoI1 and dump him in FoI2 just as on the standard route. The main issue (also present in routes 3 and 6) is that we must keep one of the Yoshis through both exits of FoI4 and FSA, which is sure to lose some time unless we can trigger a glitched ending in FoI4a somehow (I don’t think any glitched ending is known for FSA or FoI4b). And a glitched ending of FoI4a seems unrealistic right now; the current wings strat is far too slow and the Reznor spawn is probably too hard. The best shot would be a small timesave with a goaltape item swap (which seems somewhat possible as it is easy to accidentally get the goal in Yoshi's mouth) but this is a big risk and the timesave isn’t huge. So we’ll put this possibility aside and assume we can only save time with movement optimization. If you do all 3 exits with just p-speed, you lose (approximately) 1.41s in FoI4b, 0.50s in FSA, and 1.57s in FoI4a, compared to cape-only strats for each with perfect flight speed. Including the overworld timesave, you have lost a net 0.58s, and these routes are (only slightly) slower than the standard route. Keep in mind though that this assumes perfect flight speeds; if you generally lose more than this in these 3 levels from suboptimal flight speeds then this route would be faster.

But p-speed is not the fastest possible speed on Yoshi with cape. With Yoshifly you can get 51 speed (the same as with cape flight). The levels are still not as fast as with just cape because initiating a Yoshifly costs time and you need a block to do it, but they're much faster than just using p-speed. With my Yoshifly strats, instead, you lose only (approximately) 0.68s, 0.15s, and 0.23s, respectively (almost half of the total time-loss vs cape is due to the pipe animation in FoI4b). Counting the overworld timesave, routes 1 and 2 above are FASTER than the standard route by about 1.83s. I doubt this is a huge surprise to anyone who has thought seriously about the route in FoI; my main contribution is just finding how to actually Yoshifly these levels.

Side Note: If you are wondering whether it is possible to find a route which loses time over the optimal overworld route, but saves time over the standard route, and does not require Yoshifly anywhere, the answer is no. It is easy to prove with basic graph theory but it isn’t worth sidetracking the discussion to show. Assuming you aren’t willing to Yoshifly FoI4 or FSA, the standard route really is the fastest possible route.

To prove that this is humanly possible, I have done ILs of all 3 exits under these conditions. These are meant as demonstrations and can be improved slightly. If these levels were done this well in an RTA you'd come out 1.67s ahead of the standard route done with perfect flight speeds, with an additional 0.17s possible to save with better execution of the same strats.

FoI4b: https://youtu.be/4sHu3ZsIZUI 

FSA: https://youtu.be/aksJTha_MOI

FoI4a: https://youtu.be/teGYBXNeS8E 

Note also that it is not necessary to do all 3 Yoshiflys to save time with this route. In fact FoI4a Yoshifly alone puts you over 0.5s ahead, and FoI4b Yoshifly is slightly better than breaking even. FSA Yoshifly alone doesn’t break even sadly. Based on this, it is possible to come up with easier strats which only require one shorter, relatively easy Yoshifly in FoI4a: https://youtu.be/WjQTgz_1yTQ. These save considerably less time, but if you executed them as well as in that video (all 3 of which were essentially perfect) you would be 0.12s ahead of the standard route with perfect execution. In addition, there is much less cape-flying in this route so flight speeds are less of an issue; hence the actual timesave will on average be higher. I would still consider these strats not to be worth the small timesave you get from them, but they’re much more realistic for an RTA. Actually FoI4b and FSA here are both easier to do with Yoshi (flight speed is not an issue, FSA p-speed is a much bigger window, and the pipe entry in FoI4b is much easier with a shell), and while FoI4a is significantly harder than cape-only, it’s still easier than VD3 raft skip which is commonly done by high-level runners (albeit for a much larger timesave). There are many cons to these strats which probably still outweigh the pros (most notably, the second Lakitu in FoI4a can rarely throw a spiny at a bad time and there’s little you can do to react), but certainly a human could realistically do this route with these strats in RTAs right now if they really wanted to.

At this point, we can definitively say that the optimal human theory route for the Forest is either route 1 or 2 above rather than the standard route. And as a consequence of that, the human theory route now has optimal overworld movement. With new strats, that may still change, but for now there is no more time to be saved on the overworld in world 5. There are still some points where the optimal human-theory route is still not clear or debatable though, particularly World 2, where 3 competing routes exist and each has advantages over the other 2 (6 if you include the placement of the exit leading to TSA but this likely does not matter in terms of speed, only consistency). Altogether there are 24 routes possible depending on your choices in W2, the placement of C7 (almost completely irrelevant both in terms of consistency and speed), and which of the 2 optimal Forest routes you take. SW3 late is not possible on the human theory route because you can not do SW3 wings after SW2 secret exit, but if we exclude SW3 wings then 48 routes are possible. The only overworld timeloss remaining in the “human theory” route is 3 frames in Chocolate Island and 42 in Valley of Bowser, both of which are probably impossible to remove due to much larger losses in levels.

This is all theoretical and has no immediate practical impact. The strats here are still too hard or inconsistent to be useful for 96 RTAs, and the easier strats save so little time it’s hard to justify the added RNG and difficulty. Unlike the Star World reroute and strat change that I proposed previously, I can’t seriously recommend these strats as a time saving measure for even the best current RTA runners. However we can imagine that a much better player than anyone today, who is willing to lose a lot of attempts for this small timesave, would pick such a route. They would be better off adding other Yoshiflys to their route before these 3, because these 3 together save 0.58s less than what you would expect solely based on the movement in the levels. Other Yoshiflys, like Way Cool, VoB2, CBA (with the easy setup like in https://youtu.be/td0djZfJ9ms, not the TAS setup), etc. give more bang for your buck. But if all of those are already part of the run, and the runner needs to add an additional small timesave, this would be theoretically possible.

There is little practical difference between routes 1 and 2. All the same strats are required for both routes. Other than the strat changes above, the only difference from the normal 96 exit strats is that FF must be done without blue switch blocks, which is a minor inconvenience at worst. Apart from lag reduction via score manipulation (probably not going to be realistic for RTAs any time soon) and backup strats if you mess up (which shouldn't be a major concern of someone on such an aggressive route anyway) I don't think there's any simple reason to prefer one over the other.

When it comes to ordering stages with identical strats and overworld, the “best” route is ultimately a matter of opinion. What follows is my opinion on the best way for the theoretical runner to traverse the forest. They can use the fact that the two routes are identical except level ordering to get some benefit overall. The fastest current strat for FoI1a is keyblock wings by a couple seconds. But attempting this is considered too risky for RTAs because if you miss you must get the secret exit instead and the dupe is not very consistent. For a theoretical runner who is planning to Yoshifly FoI4 and FSA, the only time-loss in getting the secret exit first is the time it takes us to attempt keyblock wings, which is not so much. So if they get keyblock wings on the first attempt of FoI1, they do route 1, and if they miss they switch to route 2 and get a second try at FoI1 wings (this time probably with the p-balloon block unless they're especially crazy). Route 1 would be the intended route, but route 2 is a backup which gives a second try at wings and loses very little time.

I will point out also that this is not so completely theoretical as to be irrelevant. If you really want to add keyblock wings to your route but not Yoshifly in FoI4 and FSA, you can attempt keyblock wings on your first go of FoI1. If you get it, you have saved a bit of time over p-balloon wings and can do the standard route. If you miss you can get the secret exit, do route 2 without Yoshifly in any of the stages, and come out 0.58s behind (plus whatever you lost attempting keyblock wings), but then get a second try at wings in FoI1 (which if successful would still save a fair bit  more time than you lost). Others have suggested similar things in the past (I think I heard Akisto mention this possibility some time ago) but previously it was assumed that route 2 would be much slower than the normal route; actually it loses less than 1 second apart from the wings attempt itself. One does need to learn p-speed Yoshi strats for FoI4 and FSA as well but these are quite reasonable.

In any case my goal mostly to show that the optimal route through FoI is not as clearcut as is generally assumed, which hopefully has been accomplished. The standard route is still the best RTA route for current high-level runners, but for newer runners or for future runners who are much better than anyone today, the best route could look somewhat different even without new glitches being found, simply because of a different choice of strats.