1: The board has sufficient value to play on, with any-£250k, £15k-£20k being good 2-boxes, and even low-{£15k|£20k} still offers a chance of recovery. £15k + 1 prop averages £20k, and I consider that as slightly worse than the £20k offer.

2: £15k + 2 props averages £10,166. The average of the four low amounts is £1,312, and the 40% chance of winning more after no dealing would need to bring an offer of at least £23,500 to equal the average of the former.

I would say the intrinsic value of £15k + 2 props is around £8-9k. That's close to deal territory, but that 1/3 chance of dropping to £499 (higher than the 1/5 chance when playing on), makes a No Deal slightly higher value for me, even though you drop 60% of the time compared with 33%. The £75k can be a big threat if pursued, as a No Deal at 2-box rewards even higher on average, and a Deal may also be good if the Banker weakens.

It's a personal thing, and would depend on the day. £6,000 wouldn't have been dealt, even on a bad day.

3: There's not a huge amount of difference between £3,050 + 1 prop and £5,050 in value. Purely because I would be happy with £3k, I would choose the former above the latter for the extra money on average. In a gambling mood, I would No Deal, but the 2-box offer might be tricky to decline.

4: One to open is tempting. Would be silly to risk the money though; Orry had a blue, £50k and £100k, was offered £30k, and we know what happened there. £26,000 + 2 props isn't as good, though, but is better than the risk of negative EV through dealing a less-generous offer.

5: £40,000, no question. Banker's Gamble is next, simply because £52,000 isn't as mathematically generous, though stomaching a ~£50,000 loss would be painful. £52,000, if I suddenly had a moment of insanity, and then came to my senses!

1. The prop offer has an EV the same (minus a quid) as the fixed offer, so I'm taking the fixed offer if anything. It's a marginal call, but unless I hit the 10% disaster scenario, I'm getting a two-box offer of at least £6k given Banker convention these days, and I'm quite happy to risk 10% disaster chances when the offer's this far from the mean.

2. This was inspired by Damien's fantastically comedic five-box offer. This time, the prop offer has a much higher EV - over £10,000 - so I'm definitely not taking the sure thing. 2/3 chance of £15k and 1/3 chance of holiday money, or 2/5 chance of £20-26k and 3/5 chance of slightly better holiday money? £20k targetists might be more tempted by the latter. I'm not a £20k targetist, and the EV of the latter is at most slightly higher and possibly lower. I'm taking the higher probability of success.

3. The prop EV is only slightly higher so not going for that, and with a 60% disaster scenario I'm taking the sure thing at half the mean here. This board was inspired by Sarah-Jane in September 2006, my symbolic 'last commentary' at Bother's Bar before I went to university, and I would have Dealt £5k on that £50k/blues final five and still would.

4. The prop EV is lower, so it's £49,995 or one box to open. We're not far off the mean here, and precedent from the twist game with a similar situation is that you're only going to be getting less generous offers unless you hit the fiver, so I'm gone while I can, and not letting the psychology of the offer affect me.

5. The prop EV is lower (by £1k) if you don't take the Banker's Gamble, so if you take the prop offer, you have to take the Gamble if offered. The decision is hence between a 2/3 chance of an unknown two-box offer and a 1/3 chance of £2k (No Deal, and I'm not risking a 1/3 chance of £2k), a sure £40,000, or if you take the prop offer with a view to the gamble... let's go through this.

1/3 chance of £250k going. It's now £26k or £52k from here - overall, a 1/6 chance of each.
2/3 chance an orange goes. One prop leaves you with £26k - overall, a 1/3 chance of that. The other sparks the gamble - leaving, in all, a 1/6 chance of £250k and, for calculation's sake, a 1/6 chance of £2k.

Hence your total probabilities are: 1/2 chance of £26k, 1/6 chance of £2k, 1/6 chance of £52k, 1/6 chance of £250k. Does that trump £40k? EV is about £60k, there's a 5/6 chance of winning at least £26k, yes it does. I'm risking a 1/6 chance of £2k, but not a 1/3 chance.