Oooo, very nice! I might play one box at a time now, if that's alright with you? 11 next, of course.

Ok...

Round 4 (continued)

-Box 11-
£5

Button or Box?

Definitely looking up now. 1/3 chance of hitting power 5, 1/9 of losing the big one. Might as well continue with Box 4 as planned!

-Box 4-
£1!

This has been an amazing run for the player!

Banker time

NICE!
Especially now that I've got a button in hand, this offer's surely got to be reaching into power 5 territory?

The banker is weeping at this run of fortune. He is in deep trouble... He wonders if this will be enough to tempt you...

BANKER'S OFFER

£34,000

Board:





£10

£100


MYSTERY BOX


£3,000

£10,000


£35,000
£50,000


£250,000

£34k... 8 boxes left in play, 3 are worth more than that. 78% of the mean is rather impressive, though... The offer is definitely being kept afloat by the big one here, obviously. My fallback is 20% of that and then a second at about the level of this offer. Looking at it all up... If I didn't still have three of the power 5 I'd be extremely tempted to take this offer, but as things are right now the odds are too great that I'll be able to improve on it naturally. NO DEAL, thankyou!
Box 2 shall be the next one I open.

Ooh! A bold decision, but indeed justifiable... will it pay off?

-Box 2-
£10!!

Button or Box...?

Oh my god, awesome!
A button offer would undoubtedly be around £40k, so we're looking at 2/7 higher than that now. Somewhat more difficult to justify continuing...
Realistically though, I've got the momentum firmly on my side here. The £35k is still very close to a potential offer so I can likely count it on my side, and even if I were to lose it at this point it would still push the offer up. Not to mention that if I can survive the coinflip and clear out another of the lesser values I'm going to be looking very good... Possibly even good enough to make a potential run for the grand prize? It's a difficult call.
I'd agonise over this for longer, but I can tell my mind's already made up to push to six-box. Box 3, please!

High tension now... can this amazing run continue?

-Box 3-
£3,000

YES!!

Button or box...?

Boxes remaining: 14, 18, 19, 20, 21

You have box 6.

I had my mind made up that if I dropped the £35k or £50k I was hitting the button and bailing out while I still had a fallback to force the Banker to be nice to me. As we are now, though, it's pretty much the same argument all over again with marginally worse odds. If I don't lose the big one things are going to improve, and even if I do there's still a decent chance I've got good money. Even if worst were to come to worst there's only a 4/18 chance my box holds less than ten grand at this point! Every low box that falls is making it harder and harder to justify bailing out, so I think I might actually have to take another box! Number 18, please!

On we go!

-Box 18-
MYSTERY BOX

Well, that avoids a variable that could've won you a blue! Particularly great on this board!

Banker time...

HOH!
Well then, banker. Current mean is £69k, you know. If you want me out of this game before I really make dreams come true, you'd better offer something seriously worthwhile.

The banker says this is the luckiest game he has seen for quite some time! Even without the button, he would have to make a strong offer... But WITH it?!

BANKER'S OFFER

£62,000

Board:
£100
£10,000
£35,000
£50,000
£250,000

DEAL!!!

The offer is 90% of the average and the Banker will likely go down if you find ANY of the Power 5 here. It's not worth the risk.

Sixty-two grand... that's honestly about what I was hoping for. It's about a quarter of the top prize at five-box, which is impressive enough as it is. I would love to get brave with this board and push it all the way, but without the £75k or £100k I'm not entirely sure that can be justified. We're getting out of the range where the fallbacks can realistically still be called that... and of course, there's always the chance my own box has a mere hundred pounds and any further play is going to cause it to all crash down around me. Of course, there's always the argument that this is a ridiculously powerful board, especially when I'm only playing one box at a time... but honestly, though I would love to play another box and go all-out, I don't think I can justify taking the gamble at this point. Thank you Banker, I'm glad we could come to an agreement. It's a done DEAL!

...yeah, I'm just going to post this now before I let my gut talk myself into playing on. Even if I had the big one all along, this is still a great total to retire on. For the proveout, my next boxes would be 19, 14, and 21.

Oh, hey again Ben. Didn't see your post until after I locked in my decision, but that's also a pretty valid point. Though, would it really drop if I hit the £35k next? At this point I'd argue that one's falling into the "lesser value" territory, but it doesn't really matter now anyway.

Ok, it's a mighty DEAL AT £62,000!

Proveout:

-Box 19-
£10,000

WOW! Playing with honesty, would you have pressed the button at this point...?

YES, as you would've had to open two boxes and the Banker would know you were looking to get out of the game if you pressed the button.