10x is not remotely enough. 15x is not enough.
The full analysis is somewhat complicated, especially for multi-way, but reviewing a simplified HU case should suffice.
Assumptions:
Effective stack is S
Initial pot is P and we'll say it's 0 (assume it's small compared to S and that some or all is raked or toked away).
V has bet B
V is known to have KK+
Stacks always go in on the flop
If we flop 2P+, we will always win (clearly BS, but simplifying to make a point)
If we flop a combo draw, we will have 50% equity (reasonably close approximation)
We'll flop 2P+ 5.7% of the time.
We'll flop a combo draw (FD + pair, OESD, GSSD or OESD + pair) 5.6% of the time.
So 5.7% we flop 2P+ and always win S + P.
5.6% of the time, we win (S + P) * 50% - S * 50% = 50% P.
(Be careful not to confuse EV calculated from the flop with EV calculated from preflop when we're considering calling.)
The rest of the time we give up and fold so 88.7% of the time we lose B
So to break even we need 0.887 * B = 0.057 (S + P) - 0.056 * (50% * P).
With P = 0, and solving for B:
S / B = 0.887 / 0.057 = 15.6
We've assumed V never outflops or outdraws our 2P; we've also assumed he never folds when an overcard (or overcards) flops to his PP (more relevant if he QQ). Those counteract each other to some extent, but we lose our stack when V outdraws us, but only win the bet when he folds, so the net effect is that our assumptions are optimistic.
Clearly in the HU case, 10x isn't even nearly enough. 15x isn't either.
Adding some dead money to the pot obviously helps. You can plug the numbers in above to find out how much. Note that dead money means the person folds pre. If they're in the hand, it's multi-way, which is a much more complicated analysis (that I don't know I can even do).
Some side notes:
If we flop 2P, V will likley have about 25% - 30% equity.
If we flop trips, he'll probably have ~10% equity.
If we flop a boat, he'll have ~9% equity
If we flop quads or a SF, we have pretty close to 100% equity
All of these mean we need more than the above multiplier to make money.
Multi-way is really complicated to analyze; I think it needs a tool that will provide an equity breakdown on the flop for each hand range or a bunch of grunge work to analyze representative flops.
There's a region for small S where we actually call the flop even with a naked flush or OESD draw, but that region features such a small S that it's clear it's not profitable to call pre, even with the slight advantage we gain from correctly calling with FDs and OESDs.
Oh, and 1K. Woot.