Sunday 5 June 2011

The Diceman Goes to Wembley

Ready to go in a two-player game
 

No sponsors on these shirts!
 "Wembley" was one of my treasured board games as a child, although my current Gibson’s copy has been cobbled together from a couple of car-boot-sale purchases after my original Ariel copy long since fell apart.  The artwork, and the choice of the 32 named teams in the game, varied over the years as the game was reissued, but the game mechanics were unchanged.  Spare cards and stickers were supplied so you could always add your favourite team into the mix.  West Brom, with their cup record up to the 70s, were safely installed in the top group.  A good and complete Wembley set will probably set you back about £50 on eBay these days, but there are quite a few spares around too.


On an educational note, I find it interesting that players of the target audience (ages 10-14 I imagine) are expected to be able to calculate the 2:1 ratios of amounts like £4500 for the gate money distribution without further help.  Slightly more arithmetic was needed for second replays – and all before the days of pocket calculators of course.  The probability calculations are not necessary for the game, as intuition and experience could be sufficient, but should be within the capabilities of a good key stage 3 pupil (Years 7-9 in the English school system).  Someday I might write about the cognitive benefits of traditional board games (as opposed to the first-person shoot ‘em-ups and the manipulative frenzy of the driving sims and platform games).

How It Works

Each player “owns” a random selection of teams and the objective is to be the owner of the team that wins the FA Cup.  Along the way, a player has to make decisions:
  •           When to purchase “star” players (demand exceeds supply) and whether to risk them in the matches (because you lose them if you lose the match).  The star players in effect belong to the owner rather than any particular team.  They are worth one goal in each game – if playing.
  •           Whether to try to get lower league teams through to the later rounds (for big cash bonuses to buy more star players), or to rely on the dice to carry one of the “big eight” through.
  •           Occasionally, a chance arises to manipulate results or the draw if two of your own teams are drawn against each other.
  •           The matches are decided with six dice (home and away for the three team categories) that weight the odds in favour of the First Division while allowing for the chance of a giant-killing.  Though the dice give a reasonable representation of home advantage and a big team wins the cup more often than not, the individual match scores are faintly ridiculous even by standards of the 60s and 70s!

Moments of Nostalgia

-          Second (or third, fourth ...) replays on neutral grounds - no penalty shootouts in sight
-          First, Second, Third and Fourth Divisions
-          Newport on the board, and Orient rather than Leyton Orient
-          A star goalie for £5k and a striker for £40k inclusive of hair transplant


Gratuitous Geeky Dice Tables

A lower division team such as Rochdale would have the blue die at home.  If drawn against Manchester United of Div One, the visitors would have the orange die.  Here’s the outcome table.

Rochdale v Manchester United

If neither owner chooses to play star players, the odds are as shown in the first table.


0
1
2
3
3
4
0
0-0
0-1
0-2
0-3
0-3
0-4
0
0-0
0-1
0-2
0-3
0-3
0-4
1
1-0
1-1
1-2
1-3
1-3
1-4
2
2-0
2-1
2-2
2-3
2-3
2-4
4
4-0
4-1
4-2
4-3
4-3
4-4
5
5-0
5-1
5-2
5-3
5-3
5-4

Rochdale win 14 times out of 36 on average, or 39%.  The Draw occurs 5 out of 36 times, or 14%.  Man Utd win 17 times out of 36, or 47%.


Let’s imagine that Rochdale’s owner decides to risk a star goalkeeper.


0
1
2
3
3
4
0+1
1-0
1-1
1-2
1-3
1-3
1-4
0+1
1-0
1-1
1-2
1-3
1-3
1-4
1+1
2-0
2-1
2-2
2-3
2-3
2-4
2+1
3-0
3-1
3-2
3-3
3-3
3-4
4+1
5-0
5-1
5-2
5-3
5-3
5-4
5+1
6-0
6-1
6-2
6-3
6-3
6-4

The probabilities now change to: Rochdale win 53% / Draw 14% / Man Utd win 28% which would mean a 67% chance of Rochdale not losing.


The Man Utd owner now has to decide whether to risk one star player (which would cancel out the opposing one and restore the original odds) or, for example, to throw two on to the table.


0+2
1+2
2+2
3+2
3+2
4+2
0+1
1-2
1-3
1-4
1-5
1-5
1-6
0+1
1-2
1-3
1-4
1-5
1-5
1-6
1+1
2-2
2-3
2-4
2-5
2-5
2-6
2+1
3-2
3-3
3-4
3-5
3-5
3-6
4+1
5-2
5-3
5-4
5-5
5-5
5-6
5+1
6-2
6-3
6-4
6-5
6-5
6-6

This would give Rochdale win 25% / Draw 14% and Man Utd win 61%.  This is similar but not quite the same as would have happened if the Rochdale owner had played no stars and the Man Utd owner had played one, which would be:


0+1
1+1
2+1
3+1
3+1
4+1
0
0-1
0-2
0-3
0-4
0-4
0-5
0
0-1
0-2
0-3
0-4
0-4
0-5
1
1-1
1-2
1-3
1-4
1-4
1-5
2
2-1
2-2
2-3
2-4
2-4
2-5
4
4-1
4-2
4-3
4-4
4-4
4-5
5
5-1
5-2
5-3
5-4
5-4
5-5

This also has Rochdale win 25%, Draw 14% and Man Utd win 61%.

I will leave the other calculations to you!


Die
Colour
Numbers on Die
Div 1 (H)
Red
0 1 2 3 4 4
Div 1 (A)
Orange
0 1 2 3 3 4
Div 2 (H)
Green
0 1 2 2 3 4
Div 2 (A)
Yellow
0 1 1 2 3 4
Div 3 / 4 (H)
Blue
0 0 1 2 4 5
Div 3 / 4 (A)
White
0 0 1 1 4 5

So here is a little competition.  No prize except Kudos and a retweet – send your answer to @GrahamYapp on Twitter.  What would be the chances of Brighton (Division Two) and their two star players, shockingly losing at home to a starless Bournemouth side (Div 3 / 4).

Meanwhile, let’s play …



In the final, West Bromwich beat Birmingham 4-0.  Just like when I played as a kid :)

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