The gamble is true odds and in this format, we expect to get an extra bonus for taking a bankers gamble (Michaels game had massive value), so comparing this bankers gamble to others would show it to be terrible value, but as a 1 off proposition, it has no value, not bad or good.

I'd say that the kind of person who wants to take that gamble is someone where £5k is absolutely perfectly enough money and everything else is a bonus or where £10k is not enough money so why not gamble.

Sally is the former. Someone who had got so much out of the experience, that she was prepared to walk away with less money and a smile on her face.

...a banana of course!!!!

Perfectly reasonable - a 'distortion' of conventional expected utility theory, sure, but everyone who goes to casinos or buys lottery tickets are displaying such distortion in the first place. In fact, given the profit that lottery and casino operators have to make, those gambles have a negative expected value!

The majority of people are prepared to take small-stakes (for values pertaining to their own financial situation) negative-expectation gambles, but become (often strongly) risk-averse at larger stakes.

Lesson of the day - the majority of the public do not behave consistently in accordance with conventional expected utility theory. But economists have realised that for decades, hence alternative explanations like prospect theory which seem to fit better. Certainly in this case, the gamble was seen as no-lose, which made the difference. Me, I'd never see a gamble as no-lose, but that's me...

I agree with everything you say, but one thing that you haven't accounted for is the thrill of a gamble. I love to gamble. I even take on many gambles where I know that I am a slight underdog. This may seem like I am getting no value at all, but if the thrill of a flutter is something that you enjoy, then it makes sense that someone would take these gambles.

The lottery is a prime example. I know that for my £1, the true value of the ticket is probably barely over 50p, but I don't mind that loss, because as I check my numbers, there is that tiny bit of hope which easily makes up for the loss. If I'm lucky enough to get the first 3 numbers, which happened to me once, then the the experience is fully worth it. The feeling that you are on for a possible (although highly unlikely) £3million+ win is unbelievable!

Now I wouldn't have taken the bankers gamble. £10k is enough for me in that situation and I'm not going to gamble at those stakes. For someone where the money is not as important though (Sally), I can see exactly why you'd take that gamble. There is no mathematical benefit, but if you are at a safe situation where the drop doesn't bother you, the value comes from the thrill of the gamble, not from Maths.

That's KP all over; he only gambles if it's on a stable board...and when I say stable, I mean stable!

I'm not disagreeing with you, Dan, but it's also worth pointing out that there was also no mathematical drawback to taking Sally's gamble. Whereas playing the lottery, the odds are most definitely stacked against you.

That's the reason why I found it strange that people were saying here that Sally's gamble was 'irrational'.

Yeah, I agree with that. I might have been a bit unclear. What I was trying to say is that there was NO value in the bet as a numbers thing (not positive or negative). The thing that tipped her over the edge to take the gamble would have been the buzz of a good gamble, hence giving her a reason to take the BG. I suspect she would have taken the BG even if she would have dealt at £10,500, which would probably drive you insane KP, ha ha ha.

The lottery argument was just an argument that even negative gain bets like the lottery are not worthless due to the added value you get by the thrill of thinking it just could be you..... I guess I was just trying to say that to a gambler, the fact you are gambling is worth something to them, it's not just a numbers thing, it's a thrill thing. I've put £200 on black at roulette, knowing that the value of this bet is really only £197.29 (get half back if it hits zero). Another case for why certain bets, even ones that make no mathematical sense is fine if it is a one off. The thrill of waiting for the number to come in is well worth the £2.71 loss.

I really like this site, it's really interesting to see how people approach the game and as i said to people on the show, it is the simplest game in the world, but it has a degree of complexity beneath it's skin that makes it so interesting. Utility curves (thanks for that KP), risk/reward/ psychology.......

Yes, I found that ridiculous as well, to suggest that taking a gamble which is offering you true odds is 'irrational' is bizarre. Buying a lottery ticket can at least be justified as being irrational because firstly the odds of winning the jackpot are astronomical, and you only get £10 for matching 3 numbers rather than the £58 true odds value.

Very true - EV- gambles (as opposed to EV=0 gambles) are much more clearly irrational. EV=0 gambles are only 'clearly irrational' if one assumes a utility function with a constant negative second derivative. To a first approximation, this is true, but in practice that second derivative can approximate zero, to the point where 'the thrill of the chase' offers enough utility in itself to make up the difference.

I guess that's where I differ - I don't gain utility from 'the thrill of the chase'. Clare apparently did, and it's quite conceivable that the part of the utility curve between £5k and £15k is linear enough that anything close to the mean can be turned down. Add the utility of the gamble and we're in different territory altogether!

do you mean sally????!!!! i still havent played!!! hehehe

KP's definitely in love, I reckon...