I would expect an equation to take into account your overall stack, and the relative value of your hand contrasted to his SEMI-random holdings ...

Its pretty clear what to do when you have a good hand (one you would bet with confidence in most situations)

When faced with marginal raising or calling situations, my strat against this kind of guy would be this:

Bet an amount representative of the strength (rarity) of your hand. Therefore you are self-hedging your bets.

Take it up to 4-bets on riv with any decent pair, on a board of moderate danger.

Take it to six bets on low two pair.

Take it to eight bets on high two pair...

ETC...

lower your number of bets when there are flush and str draws out there... but basically you KNOW this guy is betting with nothing, and the chance of ruin if he happens to hit big is just a part of poker.

Playing against someone pushing a lot of money in will always increase variance, but it will be to your advantage when they do it this recklessly. You could go broke, because he can, like anyone, hit a hand....

I can only do a little bit in the way of a formula, but I'm sure that your assessment of how much to skew his "random" holdings is the most important factor..

At the river, look at the number of cards in the deck that would beat you.. Lets say he is 20% more likely than random to be holding these cards... you'd have to observe his fold rates to get more accurate on this skew.

Wager so that you only risk 1 / (your percentage to lose) percent of your stack.

Use whole number percentage under the reciprocal:

for example: at the river with 45 unseen cards.. you count 6 alone and 8 held in combination that would beat you.

I'd make that 8/45 or so... 17.7% which skewed 20% upwards ends up at 21.25%.

plug this whole number percent into my little fraud formula here:

1/25.25 = .03

Don't risk more than 3% of the stack (overall tolerance of loss) which you are willing to expose on this venture...

It's pretty crummy, and this clearly shows that I'm a theory and not a praxis guy when it comes to the math/logic world.... but I think it provides a guide (or at least the way of thinking) that could be fine tuned to make sure you are making solid EV decisions for the odds you are getting. Betting more when it is likely you are ahead, and much less on risky ventures, while making sure to keep it in proportion to your overall stack sounds like the overall strategy of a winner.

I leave you with this thought:
No matter what, the more you try to press your marginal advantages, the higher your variance will be. You'll make more money in the long run pressing marginal edges, but this guy is only going to be around for the short term, and could take you for a big one and then split. So hedge.

Cheers
and I hope u find donks like this all the time...