I don’t play poker or gamble in any form. However I would imagine that rather than being taken to the cleaners the small chip player can always just get up and walk away....
Thats a smart move I think (though as most poker players say, they are not gamblers, they're seeking to minimise the risk).
But yes, a small chip player would play very differently. In many ways it's a much easier spot to play. Infrequent, very aggressive play but crucially where you are not bluffing. You do have to start by recognising your position at the table though.
I imagine it's a similar rule in business. If you are negotiating a takeover as a smaller partner, there's leverage with the bigger company, so you have to think differently about things. You probably won't get as much as they do in the negotiation, but proportionately you can exert more from the negotiation.
Essentially, trying to play it out as if you're Churchill and it's imminent WW2 again wouldn't be the framework I'd give to the negotiations. I would also want to avoid the "all in" (a poker term) scenario of a no deal on the basis that it would harm Europe (which it would) when they know, and have made clear it would damage us more. If they are aware of that, you have sort of lost the leverage you had.
