Pliers-type multitools never come with a corkscrew. I'm pretty sure this is because they have to market to the camo-wearing survival macho crowd and a corkscrew would ruin the image - those guys think wine is for girls or worse yet Euros.
The screwdriver arrangements on a lot of them kind of suck. on a trip I'd be tempted to also take one of those cheap T-handle things that takes standard bits. Yes it's another thing to carry, but sucky screwdrivers really suck.
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