Following on from this post...

http://www.haloscan.com/comments...9122005/ #144869

...yesterday, I thought I'd share with you the probabilities that I'd worked out. These are the ones that I personally find most useful when following the game.


NUMBERS OF COMBINATIONS POSSIBLE AT START OF GAME
(22C5 = 26334, so 26334 possible combinations overall)

Choosing 3 of top 3 amounts: 171 combinations (0.6%)
2 of top 3: 2907 combinations (11.0%)
1 of top 3: 11628 combinations (44.2%)
0 of top 3: 11628 combinations (44.2%)

2 of top 2: 1140 combinations (4.3%)
1 of top 2: 9690 combinations (36.8%)
0 of top 2: 15504 combinations (58.9%)


NUMBERS OF COMBINATIONS WHEN 17 BOXES REMAIN
(17C3 = 680, so 680 possible combinations overall)

3 of top 3: 1 combination (0.1%)
2 of top 3: 42 combinations (6.2%)
1 of top 3: 273 combinations (40.1%)
0 of top 3: 364 combinations (53.5%)

2 of top 2: 15 combinations (2.2%)
1 of top 2: 210 combinations (30.9%)
0 of top 2: 455 combinations (66.9%)


NUMBERS OF COMBINATIONS WHEN 14 BOXES REMAIN
(14C3 = 364, so 364 possible combinations overall)

3 of top 3: 1 combination (0.3%)
2 of top 3: 33 combinations (9.1%)
1 of top 3: 165 combinations (45.3%)
0 of top 3: 165 combinations (45.3%)

2 of top 2: 12 combinations (3.3%)
1 of top 2: 132 combinations (36.3%)
0 of top 2: 220 combinations (60.4%)


NUMBERS OF COMBINATIONS WHEN 11 BOXES REMAIN
(11C3 = 165, so 165 possible combinations overall)

3 of top 3: 1 combination (0.6%)
2 of top 3: 24 combinations (14.5%)
1 of top 3: 84 combinations (50.9%)
0 of top 3: 56 combinations (33.9%)

2 of top 2: 9 combinations (5.5%)
1 of top 2: 72 combinations (43.6%)
0 of top 2: 84 combinations (50.9%)


NUMBERS OF COMBINATIONS WHEN 8 BOXES REMAIN
(8C3 = 56, so 56 possible combinations overall)

3 of top 3: 1 combination (1.8%)
2 of top 3: 15 combinations (26.8%)
1 of top 3: 30 combinations (53.6%)
0 of top 3: 10 combinations (17.9%)

2 of top 2: 6 combinations (10.7%)
1 of top 2: 30 combinations (53.6%)
0 of top 2: 20 combinations (35.7%)


NUMBERS OF COMBINATIONS WHEN 5 BOXES REMAIN
(5C3 = 10, so 10 possible combinations overall)

3 of top 3: 1 combination (10%)
2 of top 3: 6 combinations (60%)
1 of top 3: 3 combinations (30%)
0 of top 3: 0 combinations (0%)

2 of top 2: 3 combinations (30%)
1 of top 2: 6 combinations (60%)
0 of top 2: 1 combination (10%)


Please feel free to correct any errors...
Mister Al | 12.20.05 - 1:41 pm | #

Excellent. I can't see any errors though I might not be looking hard enough...
KP | Homepage | 12.20.05 - 2:02 pm | #

Oh, and as a response to the first part of this post...

http://www.haloscan.com/comments...9122005/ #144877

...here's some freshly calculated probabilities regarding the top five amounts' longevity.

WHEN 17 BOXES REMAIN
(22C17 = 26334 possible combinations)

5 of top 5 remain: 6188 combinations (23.5%)
4 of top 5 remain: 11900 combinations (45.2%)
3 of top 5 remain: 6800 combinations (25.8%)
2 of top 5 remain: 1360 combinations (5.2%)
1 of top 5 remain: 85 combinations (0.3%)
0 of top 5 remain: 1 combination (less than 0.1%)


WHEN 14 BOXES REMAIN
(22C14 = 319770 possible combinations)

5 remain: 24310 combinations (7.6%)
4 remain: 97240 combinations (30.4%)
3 remain: 123760 combinations (38.7%)
2 remain: 61880 combinations (19.4%)
1 remain: 11900 combinations (3.7%)
0 remain: 680 combinations (0.2%)


WHEN 11 BOXES REMAIN
(22C11 = 705432 possible combinations)

5 remain: 12376 combinations (1.8%)
4 remain: 97240 combinations (13.8%)
3 remain: 243100 combinations (34.5%)
2 remain: 243100 combinations (34.5%)
1 remain: 97240 combinations (13.8%)
0 remain: 12376 combinations (1.8%)


WHEN 8 BOXES REMAIN
(22C8 = 319770 possible combinations)

5 remain: 680 combinations (0.2%)
4 remain: 11900 combinations (3.7%)
3 remain: 61880 combinations (19.4%)
2 remain: 123760 combinations (38.7%)
1 remain: 97240 combinations (30.4%)
0 remain: 24310 combinations (7.6%)


WHEN 5 BOXES REMAIN:
(22C5 = 26334 possible combinations)

5 remain: 1 combination (less than 0.1%)
4 remain: 85 combinations (0.3%)
3 remain: 1360 combinations (5.2%)
2 remain: 6800 combinations (25.8%)
1 remain: 11900 combinations (45.2%)
0 remain: 6188 combinations (23.5%)


Again, corrections to any errors are most welcome.
Mister Al | 12.20.05 - 2:43 pm | #

I'm off now, watching in a room without the Internet today unfortunately.

I predict a riot... oh sorry, a big win.
KP | Homepage | 12.20.05 - 4:19 pm | #

Bit busy at moment but will try and do some commentary again.
Simon | 12.20.05 - 4:21 pm | #

Today's player is Mary-ann - carrying box 10.
Simon | 12.20.05 - 4:21 pm | #

Mary-ann Thorpe. Married with 3 kids.
Simon | 12.20.05 - 4:22 pm | #

I'll provide backup for box opening, then. And my usual analysis. Player is Mary-Ann today.
Gizensha | Homepage | 12.20.05 - 4:23 pm | #

She's going in numerical order!

Opened 2,1,3,4,5
HF | 12.20.05 - 4:28 pm | #

Box 2 - Lee - £250k. (that was after "We want an increadable opening round.")

Box 1 - Chris - £750. That's better. She's going for horizontal symmatry at the moment, it seems.

Box 3 - Louise, with her 'unbroadcastable' comments. £100

Box 4 - Jill (spelt Gill if I'm reading the nametag right) - 10p

Box 5 - Jenna ("It's a good box" 'You think so' "Yes *crosses fingers*") - £50,000.

Not a good opening round, all things considered.
Gizensha | Homepage | 12.20.05 - 4:29 pm | #

FD is £5,633
Absolute Balance is -14
Significant Balance is at 7/18; -4

Board's probably worth about £4000. The offer was a little over £2000, no deal.
Gizensha | Homepage | 12.20.05 - 4:30 pm | #

Thanks - my comp decided to crash.
Simon | 12.20.05 - 4:32 pm | #

Clive - 18 - £15,000
Andy - 8 - £1,000
Micheal C - 9 - Break coming up. This time on the word 'heartbreak'.
Gizensha | Homepage | 12.20.05 - 4:32 pm | #

I'm a little busy hosting online games at moment too.
Simon | 12.20.05 - 4:32 pm | #

(above figures were slightly inaccurate due to me forgetting to remove the 10p, sorry)

FD at £6363 (pretty number ^^, though not in the context of the game)
Absolute Balance at -10
Significant Balance at 2/5; -3

Assuming on target is defined as 50% chance of this many of the top 5 boxes or more having been eliminated by this stage, then if she avoids any of the top five she's on target at this point. Though that's more important in terms of 'ahead of expectations', I'd think.
Gizensha | Homepage | 12.20.05 - 4:36 pm | #

Micheal - 9 - £250.

We're on track for the top five stuff.

3/7 (6/14); -3 is now the significant balance. FD is at £7,113. Absolute Balance is -7

Board's worth about £6500 probably.
Offer is at £5300, more than double.

On this board it's almost worth it but not quite. Audience goes into a frenzy of 'No Deals'.
Gizensha | Homepage | 12.20.05 - 4:39 pm | #

The expected for this stage No Deal comes.
Gizensha | Homepage | 12.20.05 - 4:40 pm | #

(speed round) Box 13 - July - £10
Box 7 - Pat - £20k
Box 11 - Nick - £3000.
Gizensha | Homepage | 12.20.05 - 4:41 pm | #

Significant Balance at 5/11; -3
Absolute Balance at -9
FD at £7,959.

She tries to open a box before the banker rings. "If he thinks your dippy, his confidence could be building."

Offer of £14k.

...Dear hell.
Gizensha | Homepage | 12.20.05 - 4:43 pm | #

There's got to be another deal in this board I reckon.
Simon | 12.20.05 - 4:44 pm | #

NO DEAL!!!!!!!!
Simon | 12.20.05 - 4:45 pm | #

Another speed round

Box 21 (Dave) £1 - Will have at least 2 5 figure amounts left now

Box 19 (Max) £10,000 - Noel thinks its the £100K at first
Simon | 12.20.05 - 4:47 pm | #

Box 21 - Dave - £1
Max "I have no feelings" - Box 19 - £10k (Noel thought it was £100k, and jumped)
Jenni - 6 - Break by the sounds of it. Yeah, he said break.
Gizensha | Homepage | 12.20.05 - 4:48 pm | #

Box 16 (Jenny) - Another tenuous break link !!!!!!!!
Simon | 12.20.05 - 4:48 pm | #

And we're back
Simon | 12.20.05 - 4:52 pm | #

Significant Balance, 5/9; -1
Absolute Balance -5
FD £9,568.

And we're back.
Gizensha | Homepage | 12.20.05 - 4:53 pm | #

With a £5 box.
Simon | 12.20.05 - 4:54 pm | #

Offer of £18,000.
Simon | 12.20.05 - 4:55 pm | #

Only 1 in 56 chance of taking out all 3 big amounts in this round.
Simon | 12.20.05 - 4:56 pm | #

Noel tells Mary not to stare at the board when she's thinking about whether to deal.
Simon | 12.20.05 - 4:56 pm | #

I'm guessing at 4.50 we are going to get a deal here.

DEAL it is.
Simon | 12.20.05 - 4:57 pm | #

Box six - Jenni - £5.

We're at expectations for the bottom five, and better than expectations for top five. I think.

Sig Balance is now 5/8; +0 (good)
Absolute Balance at +2
FD £12,048.

Offer at £18k. Still above what the boards worth, not as much above expectations as the £14k was, however.

I'd deal without a doubt now.

However, there is probably another deal here on this board, Though it should be noted that either the £100k or the £75k is likely to disappear.

And she deals.
Gizensha | Homepage | 12.20.05 - 4:57 pm | #

She has continued her advice throughout her stay for others to deal.
Simon | 12.20.05 - 4:58 pm | #

Prove out

Box 17 (Irene) 1p OUCH

Box 22 (Simon) £500

Box 16 (Gavin) £100,000

Deal would have been £23,000
Simon | 12.20.05 - 4:59 pm | #

Prove out - Irene, missed the box number. "It feels warm." - 1p
Box 22 - Simon - £500
Box 16 - Gavin - £100k. As expected, one but not both of the top two goes, and one of the top three goes.

Offer would have gone up to £23k. That's only £10 less than the mean.
Gizensha | Homepage | 12.20.05 - 5:00 pm | #

FD would have been £11,600 ish.

Next box 50p
Box 20 (Michael) £5,000

Next box can't be £50 - and it is box 14 with £35,000

£50 / £75,000 decision at end with an offer of £37,000.
Simon | 12.20.05 - 5:01 pm | #

Missed the first box, but it was obviously the 50p
Michael - £5k
Terry - 14 - £35k

Offer of £37k.
Gizensha | Homepage | 12.20.05 - 5:01 pm | #

Noel gets Mary's daughter to open the box to reveal......

£50 !!!!!!!!!!!!!
Simon | 12.20.05 - 5:02 pm | #

Like yesterday a good result but a deal too early.
Simon | 12.20.05 - 5:03 pm | #

Irrelevent bit - Box 3 picked to reveal £1,000 which goes to Tracy Burrels in Mansfield.
Simon | 12.20.05 - 5:04 pm | #

Her daughter opens the box. £50.

...Though that isn't good for the overall banker vs player war, due to the taken deal being just about less than half the highest offer.
Gizensha | Homepage | 12.20.05 - 5:04 pm | #

Best result on a Tuesday so far, incidently. In fact, the first result above £10,100.

We're still not quite as good as the first week, but if the week continues as it started we'll only be about £66.67 below it.
Gizensha | Homepage | 12.20.05 - 5:06 pm | #

Technical Banker win, but only just (51-49)...

and the US DoND started out pretty well...11.6million viewers and won it's timeslot. Let's see how the rest of the week goes...
David | 12.20.05 - 5:38 pm | #

As with yesterday yells into the office to put Deal on went unanswered to ensure that I did some work. Even though there was no work to be done.
NJ | Homepage | 12.20.05 - 5:42 pm | #

Thanks guys.
Brig Bother | Homepage | 12.20.05 - 7:31 pm | #