As you leave a bar in the early hours you are approached by a shifty character who offers you the following deal. If you first pay him $100 you can choose a number and he will roll a die, this die here. If it lands with your chosen number up he will pay you $1,000. If it lands with any other number up, well, it’s goodbye to him and to your $100. Of course you worry a bit about whether the deal really is as described, even though he throws the die a few times and it doesn’t seem loaded, and you have a quick glimpse of ten $100 bills in his hand. On the other hand, it’s a good deal. You are being offered a one in six chance of $1,000, which you take to be worth one hundred and sixty seven, for only one hundred. And yet, a vague worry flashes through your mind, elusive enough that you cannot quite state it, but strong enough to make you decline the deal.