I've changed things around slightly...

The offer pattern is now 3-3-3-3-2

The banker will now always offer 90% of the mean.

The maximum prize is now considerably less. But there are more prizes in the 1000s to compensate.

The new board:

£10
£100
£200
£500
£1,000
£2,000
£3,000
£4,000
£5,000
£6,000
£8,000
£10,000
£15,000
£20,000
£40,000
£70,000

You have box 16 once more.

3 boxes.

Interesting that the offer generosity has now been taken completely out of the equation.

Same system as before despite the new pattern. 8, 2, 4.

The idea of fixing the offers is to make the whole thing a bit more mathematical. On the show there's situations where EV wise it makes sense to go on, but the fact the banker won't offer you what it perhaps deserves changes it slightly. Also, the amounts here are lower. Offering near the mean with a £1/£250k finish is absurd. It's slightly less absurd with £70k. Anyway...

Round One - Board One

8: £100
2: £5,000
4: £1,000

Good start on that one!

Banker's offer:

£12,300

Round One - Board Two

8: £200
2: £4,000
4: £20,000

Not quite as good, but still good.

Banker's offer:

£11,000

The best thing about that is that there's six separate amounts I've taken out, and only one is big. 1/5 chance I have £40k+ now.

NO DEAL. 6, 10, 12.

Round Two - Board One

6: £200
10: £15,000
12: £20,000

Leaving...

£10
£500
£2,000
£3,000
£4,000
£6,000
£8,000
£10,000
£40,000
£70,000

Banker's offer:

£12,800

Round Two - Board Two

6: £70,000
10: £100
12: £40,000

oops

Leaving...

£10
£500
£1,000
£2,000
£3,000
£5,000
£6,000
£8,000
£10,000
£15,000

Banker's offer:

£4,500

Interesting spot here... dealing obviously makes a profit on the box. But with guaranteed offers is there value in hoping the £40k/£70k stick around...

Right. Odds time!

There are nine boxes on the wings. Two of them are known to be bad. I'm picking three.

P (dodging both for an entire round) = (7/9)*(6/8)*(5/7) = 210/506 = ~40%, which is not much more than the chance of losing £70k which is clearly going to send the offer down.

More to the point the gamble is EV=0 with fixed generosity even if one assumes no skew in the odds. We do have skew in the odds.

DEAL.

13, 14, 15.

And yet again a second offer deal in this format! It hasn't provided an OPW yet. It will do this time if damage is done...

Round Three - Board One

13: £4,000
14: £500
15: £70,000 - yes!

Is the damage enough though?

£10
£2,000
£3,000
£6,000
£8,000
£10,000
£40,000

Banker's offer would've been:

£8,900

So a bit of a drop...

Round Three - Board Two

13: £1,000
14: £5,000
15: £15,000

Leaving...

£10
£500
£2,000
£3,000
£6,000
£8,000
£10,000

Banker's offer would've been:

£2,400

So, it goes without saying that the £40k needs to be hit in the next box round. 3 boxes.

Can't decide if this one is a deal or not... I guess it is because we know £40k is there to be hit. So we're selecting 3 from 5 really. If it gets left though the offer goes up. And even if it goes there's a chance we have about what we're no dealing in the box...

11, 7, and 9 are those three...

Round Four - Board One

11: £10
7: £8,000
9: £10,000

Leaving...

£2,000
£3,000
£6,000
£40,000

Banker's offer would've been:

£11,500

So slightly less than what you dealt...

Round Four - Board Two

11: £10 - Our first case of having a value in the same box on both boards... so the potential to get to 2-box and not know the box does exist
7: £500
9: £3,000

Leaving...

£2,000
£6,000
£8,000
£10,000

Banker's offer would've been:

£5,900


2 boxes for the final round...

5 and 3...

Round Five - Board One

5: £40,000
3: £3,000

Leaving £2,000 and £6,000

Banker's offer would've been:

£3,600

Round Five - Board Two

5: £8,000
3: £2,000

Leaving £6,000 and £10,000

Banker's offer would've been:

£7,200


So I think that makes that an OPW on the 2nd offer

And so do I I didn't so much expect an OPW as figure it was a plain old EV- gamble...

Yeah. I think it was the correct deal. It was obviously bigger than your box. So the only way of a higher offer really was to keep £70k/£40k til the end. But because of how close the values on the board are the chance of a total collapse on both boards was quite low. Mathematically I think it was quite close.

Bit of a shame it was all decided by round 2 really. To be offered more than is possibly in your box is quite unlikely by that point I'm guessing...