I take the view that I want to have the option of completing a ride under my own steam. For the tire related problems I carry: spare tubes; a patch kit (constantly refilled with glue and patches); booting material; a set of 50 y.o. metal tire irons; a working frame pump that with a 160 psi capacity and a foldable spare tire. The extra weight is perfect for training. I'll count the grams for the real thing. I did brevets in the past and its self-sufficiency credo means I'm responsible for finishing under my own power.
Flats are a fact of life. I've learned to fix them quickly, preferably with a patch when it happens. Nothing but a solid rubber tire is flat proof. However, a friend of mine discovered that riding one on what passes for NYC pavement will result in frame failure. There are worse things than repairing a flat. I'm not impressed with going 2000 miles without a flat. I had that experience using 290 gram tubulars before the bottle deposit law was passed. I'd still ride tubulars, if I could afford top of the line hand made tubs on my pension.
I started carrying a foldable spare when riding clinchers as soon as foldables first became available. I've needed that spare 5 times in 30 years. Four of those times were in 2009. I had some rotten luck with tires last year. I'm off the armadillos because one of them de-laminated on me after less than 2 weeks use. I was 5 miles from the nearest rail station and 20 odd miles from the nearest open bike shop, when I discovered the cause of that thump-thump-thump.
I'm also leery of high pressure clinchers. I've seen too many of them split open once a couple of carcass threads get torn. I had a couple of 120 pound specialized fail in that manner. The tires I'm currently using are rated at 105 lbs. They ride like Michelin 50's from years past. They are around $20 a piece, no performance but I expect them to last out the year. I used to inflate tubulars to 120 lbs. The theory was that at 120 lbs the tubulars would crush glass and still give a comfortable ride. I believe the clincher manufacturers went to the higher pressures to delude riders that these clinchers were as good as tubulars and to extract excessive amounts of money to further that delusion.
I prefer to start near the rear, if I'm going on an event ride with hundreds or thousands of participants. Let all these speedsters pick up all the glass on the road.