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Okay, I'm probably wrong on 100% of all these points, but I'm going to post this.
Mostly because I don't like seeing the same issues raised over and over. Someone correct me if I'm wrong.
How to Egg Roll Properly Versus Captain Olimar
Step One A: Make sure Captain Olimar is in the air.
Step One B: Make sure Captain Olimar is lying on the ground from a missed tech or during a tech roll.
Step Two: Egg Roll, if you wish.
Step Three: You're done.
A Detailed Explanation: You can Egg Roll safely against Captain Olimar when he is in either of the two states mentioned above. While in the air, the only attack that can beat Egg Roll is, from my experience, a direct-on-the-top strike with his down aerial. Other than that, Olimar's feeble attempts to break your Egg Roll will tie, at best. During a tech roll, Olimar is quite vulnerable, although lucky powershields may save him on the getup if the frames line up.
Do not Egg Roll Captain Olimar if he is tech rolling toward an edge.
How to Strike With Dangerous Chinese Delicacies: When you attempt to Egg Roll Captain Olimar in the air, there are a few considerations you have to make. You need to visually confirm that the stage will allow you to do Egg Roll first (is the stage moving, will the stage spawn some obstacles, are there any hazards, etc.). Next, you need to confirm Yoshi's distance from Captain Olimar. You also need to detect how high Olimar is from the ground, how high the Egg Roll hits, Olimar's falling speed, and what you can do if things suddenly go awry. When Captain Olimar is tech rolling, you need to watch for which direction he's rolling in (of course), and
THIS IS VERY IMPORTANT! YOU MUST DETERMINE HOW FAR AWAY FROM THE EDGE HE WILL BE IF HE WERE TO SUCCESSFULLY COMPLETE HIS TECH ROLL. A rule of thumb to go by is that if Captain Olimar is less than two and a half Yoshi body lengths (measured as Yoshi standing upright) away from the edge, YOU
SHOULD NOT ATTEMPT TO EGG ROLL.
Now, with all the confirmations and calculations out of the way, you can commence rolling eggs. Assuming you have landed your first successful hit, there are just a few more calculations you need to make. Olimar has been sent into the air. How far up is he? How much room do you have to turn around? Is it even safe to turn around or should you stop the attack right here? The rule of thumb here is that if you can estimate getting to hit Olimar again between the time when he completely hits the ground and the time when he can space any aerial swing at maximum distance and connect, you are good to go, as this is an optimal circumstance. If you think Captain Olimar may be able to follow up with an aerial, but you know for sure that you can get to him before he hits the ground, proceed with caution. If you have any doubts about getting to Captain Olimar before he hits the ground,
DO NOT FOLLOW THROUGH.
Ways Captain Olimar Can Stop the Gay: Also known as defensive options. First and foremost, when Captain Olimar is in the air and you are eying the Egg Roll, consider his airdodge. This is a win-win, situation for the both of you, as Captain Olimar will not get hit and you will get to reset. Pursuit is highly discouraged at this point unless the Olimar player enjoys retreating short hops out of airdodge landings. This trait is rare, but can be most commonly found in playstyles involving heavy aerial Pikmin throwing when the player feels under pressure. Another defensive option Captain Olimar has is attempting to tie or beat the Egg Roll with aerials (if he is in the air, of course >_>). When Captain Olimar ties with the Egg Roll, Yoshi will come to an immediate and lagless halt while Captain Olimar completes his swing. This is your opportunity to do, quite literally,
whatever you want. Recommendations include jabs, standing grabs (judge the distance intelligently), pivot grabs, up tilts, or simply running away. If Captain Olimar managed to stop the Egg Roll while you are facing away from him, you may want to consider turnaround forward tilts, turnaround down tilts, or running away. In this position, Yoshi is often too far away to perform anything else safely. The final option is the most disadvantageous for Yoshi; the lucky powershield. Lucky powershields occur very close to the body in the cases where it would happen here, so you stand a very low risk of getting grabbed, but suffer a proportionally high risk of getting downsmashed or having Pikmin tossed at you. Even if the attacks tie, you are in a bad spot facing backwards and a considerable distance away, so be smart with your options. If you get powershielded (misjudged Olimar's fallspeed, his height from the ground, or your roll speed, etc.), your first and only priority is to get as far away as you can from him. Period.
How Yoshi Can Use the Gay: The general idea of Egg Roll in this matchup is to perform it in such a way where retaliation from the opponent is minimal and leaves you at absolute minimum risk while putting the enemy into extremely uncomfortable positions with few viable options. One of the most important parts of knowing how to use Egg Roll is knowing when to stop using it. After a successful hit, you will want to keep rolling in the same direction for a distance such that aerial retaliation
will not connect when the enemy comes out of stun. Ideally, you will want to be just outside of maximum range to bait swings and then Egg Roll back into the enemy during the lag on their attack. Enemies will not always blindy swing, however, and should be approached cautiously during your turnaround in the egg. If you choose to stop the Egg Roll at any point,
make sure you are a considerable distance away. If you have doubts about the safe points of a roll sequence on a smaller stage, you can feel free to Egg Roll for one guaranteed hit (or a hit you feel will be guaranteed) and continue rolling in the same direction until you must release to avoid falling off the stage or allowing the enemy too much time to set up. Stopping under platforms is a boon and rolling past spawning obstacles can help as well. In the rare situation that you may be cornered, do not hesitate to consider Egg Roll as a viable GTFO option to escape to the other side of a stage.
I hope this was accurate and helpful. I probably forgot one or two things while I was on the few tangents that I couldn't help but succumb to. If I do remember something I didn't mention, I'll post later. I hope the information was fairly intuitive and that nothing was overly confusing. If you don't like my wording or think that I may have conveyed something incorrectly, please let me know and I will fix it as soon as I can. I would like for this to be a resource for people to stop asking the same questions over and over while others have to constantly answer those questions each time they are brought forth.