Today's 3 box reminded me of Callum's game, where with 2 blues and the £100,000 left the Banker offered £15,000 with the stipulation that the offer would be £40,000 if a blue was found. So with a 3 box of £50, £500, and £100,000, what would be the minimum the Banker would guarantee for finding a blue that would tempt you to on one more box?

I think it would have to start with a 3. If we take box 23 out of the equation, that makes the EV over 20k which is probably enough for me to go out of my comfort zone in 1 box games at 3-box.

It's likely the Banker would offer the Governor if the £100k stays. If he said that the offer would be higher than that (£27/£28k) then I might have pushed on.
Anything starting with a 3 and I'd have gone for it.

At £14,000 with those three boxes remaining, no 'guarantee' would force me on. I think that concept in and of itself is rather silly. Finding a blue isn't guaranteed, therefore that magical offer is also no guarantee whatsoever. It's a conditional promise - 'if' this happens, I'll give you 'that'. Well, there's every likelihood that 'this' isn't going to happen - and you've got £14,000, here, now! If you don't take £14,000 and you find the £100,000, hold on, where's that 'guaranteed' offer? Oh, bugger, now you don't even have the £14,000...and he's taken you for a complete mug, and he's won. And more importantly, you're still poor, when you had a gilt-edged chance to change that when you were offered £14,000.

It's a stonewall deal for me. No conditional offer of any sort is going to change my mind on that.

I would press my luck... I'd want at least £30,666.24...

35,001

I'd have dealt that £14,000 offer in a heartbeat. In fact, I'd have dealt at that point, regardless.

There is no specific amount of money that would force me on. If I get an offer that's good enough for me, I'm gone. I don't care for statistics; I just want to guarantee myself some cash.