Cash game 6 handed and everyone is deep and the cut off raises all pocket pairs, all Broadway, suited connectors and all ace x suited. Roughly what kind of pot odds will we want to call here with a hand like 67s? Just a general approximation or rule of thumb. What fraction of the total flop pot should be our risk investment.

if you/opponents are 400bb deep call.

Edit: what fraction of the total flop pot (before any flop betting occurs) should be our risk investment

Fold.

What position are you in, and how big was the raise?

Assuming 100bb+ deep, if you're on the button you can call or 3-bet.
If you're in the SB, you should almost always fold.
If you're in the BB, you should almost always call.

If you have <30bb, it's probably only playable in the BB.

I don't think it's particularly useful to calculate a specific pot odds number. You just want to have a stack size that enables you to make some moves post-flop. If you're deep you'll be able to see the river quite often and realize your equity or make a semi-bluff or two. If you're shallow (in the BB) you can check-raise jam (or donk-shove) draws on the flop. If you have a trickier stack like 25-35bb, the hand won't play so well.

thanks for that. Answered it very comprehensively as always.