I always want to be able to get back to T2. Even in a sprint, you could be 6mi from the race site (worst case).

I carry a tube, patch kit, tire lever, and micropump. Yes, the pump will be slow, but a flat basically turns a sprint/Oly into a training day anyway. All this easily fits in a water bottle (you could also get a CO2 and a multitool in).

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I always carry a tube, lever and co2 in a little pod. I accept that a flat puts me out of it in a short race but I’m still here to ride my bike and run a bit regardless. And I don’t want to walk my bike back miles.

Of course, the only time I ever flatted in a race it was a double. I changed the rear and rode with a flat front tire, sitting up and pulling back on the pursuit bar like a half-wheelie thing all the 2-3ish miles back.

I carry a tube, lever and CO2 cartridge/chuck taped under my seat with electrical tape. 80mm valve on the tube so I don't have to mess with a valve extender on my race wheels.

Depends on what your goal is. If it is to simply finish the race, take a kit. If it is to podium, every bit of weight makes you slower. I specialize in OLY distance and never take a kit. The vast majority of races I've done have bike support on the course to get you back.

Even for short races I don't fancy walking back to T2. I use the lightest most packable tube I can find, one gas cannister and a tire lever. Normally taped under the saddle.
When I was using a long tail helmet they all fit inside the tail and the weight kept my head position locked in.

Assuming there is a support vehicle, I usually would not take a flat kit.

Nobody is fast at changing flats until they practice a bit. There are many videos online or a lot of bike shops will offer classes.

Standing on the side of the road watching the race go by or hoofing it back to transition in your bike shoes would stink. Bring a minimal flat kit, it's worth the fraction of a second it might cost you due to the weight.

You fix the flat, continue with the race and try and salvage the day by putting up a good run split.

I've flatted once during a race and it didn't cost me any places (it was a 5 hr race)

Here is a pretty good video for doing it quickly...esp note the way she gets the bead back on the rim using her palms as opposed to her thumbs.

https://www.youtube.com/watch?v=mK_ZIlu74YQ

Unpopular I'm sure but I don't carry anything. If i have to fix a flat in an Oly my race is already done so why bother. I'd just hope for some SAG eventually or a kind racer to stop and help

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A single tube/co2/lever fits in my bento on my top tube.

I hang my bike by the back of the saddle. Saddle bag gets in the way of that. Plus, I assume the saddle bag incurs some aero penalty, but I haven't tested it.

I have one of these Lezyne compact bags with a tube, a tire lever, co2 cartridge and inflater. I am still rack my bike on the rear if the saddle because it is so compact. https://ride.lezyne.com/...ts/1-sb-rdcaddy-v104[/url]

Put just enough air into the new tube to keep it from twisting/kinking.

Make sure once you get the tire bead onto the rim, you squeeze it into the center of the rim as the rim has a smaller diameter in the center and it makes getting the rest of the tire bead onto the rim easier.
(Here is a cross section of the rim section...the tire would be on top, the spokes would be coming out of the bottom, and you can see how the rim track has a curve to it)

fix the flat, finish the race.
Race is over when the flat happens but might as well take the rest of the race as a catered training day..
I carry a spare tubular, CO2 cartridge and inflator. There aren't any Oly or sprint courses where that added weight is going to make a difference in race times.