Obviously, if your loved one needs an operation or the mob is threatening to cut your hands off and you need exactly £15000, then you’re not going to risk going for more.
But assuming that you don’t have such an urgent need, and you’re reasonably knowledgeable would you ever quit at the 16K mark? I wouldn’t, even if I lost all my lifelines and it was a straight 1 in 4 chance. I figure like the fact you occasionally lose 10 coin tosses in a row, you’ll occasionally get 2-3 questions you find tricky stuffed into the first 10; it makes the last set no more likely to be difficult than normal. £16000 is nice, but ven if you assume you have 0% chance of answering the £125,000 question you only need a 50% or better chance on the £64000 to break even in EV. Besises which, you’re never likely to get such a good oppurtunity for serious money again, why waste it on chump change?
*using Pounds as I live in the UK. Dollars would be an even easier decision.