It’s both surprising, and not, if you think about it. The way I’ve usually seen it happen is first the rear tire goes flat, then the front one. My theory is that both tires went through the same pile of glass/thorns/metal bits and they both picked up junk. the reason for the flat occurring on the back first is because there’s more weight on that tire, so the offending article works its way through the tread more quickly.
As you mentioned, it is surprising how often you can get multiple flat tires on while riding, particularly on longer sprints. The tip about bringing a patch kit in your bike repair kit can be incredibly helpful if you’ve already had one flat tire. I agree that all you listed seems like an awful lot to carry, but it’s always better to be safe than sorry, isn’t it?

Friction gear systems are a lot simpler to adjust, because the movement of the derailer cable can be modulated as you ride, every time you change the gear- they require less cycle maintenance. Modern index shifting systems are a little more complicated because each ‘click’ must release the exact right amount of cable to allow the derailer to move the correct distance to move the chain from one gear to another. Setting up and adjusting a derailer is not difficult and requires only basic tools, but there is a methodical procedure to follow.
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