Yet more on Take It or Leave It

I don't just write about Take It or Leave It. In fact, judging from the last month I don't write at all. Ahem. End game scenario. 3 safes left and hence 2 questions left. You know that whatever will come up 5th is wrong (you hastily took an answer, during the ad break you realised you made a terrible mistake), but on this 4th question you do not have a clue. Time to bail out, or plough on to try and increase your odds when you open a safe? The contestants knew there was some maths they could apply to this decision, didn't know what the maths were, and ploughed on. It was a mistake. But why? To stop now gives a 1/3 chance of winning the money. Play on here, and 1/2 of the time it's instant lose. The other 1/2 of the time you then have to stop and take a 1/2 on the safes. So you are only 1/4 by playing on. Not a major drop, but still a mistake. So how sure would you have to be to play on? Simply, anying that when multiplied by 1/2 is greater than 1/3. As 1/3 divided by 1/2 is 2/3, you just need to be over 67% sure of your answer to make playing on right. All this was useless, though, as the players would have picked the wrong safe anyway.