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  • Football league predictions - 2005-06 season
    Sunday 19 February 2006 at 23 53 01 GMT Monday 20 February 2006 at 23 53 11 GMT Tuesday 21 February 2006 at 23 53 01 GMT Wednesday 22 February 2006 at 23 53 04 GMT Thursday 23 February 2006 at 23 53 22 GMT Friday 24 February 2006 at 23 53 02 GMT Saturday 25 February 2006 at 23 53 39 GMT Sunday 26 February 2006 at 23 53 13 GMT Monday 27 February 2006 at 23 53 08 GMT Sunday 5 March 2006 at 00 47 24 GMT Sunday 5 March 2006 at 23 53 05 GMT Monday 6 March 2006 at 23 53 27 GMT Tuesday 7 March 2006 at 23 53 18 GMT Wednesday 8 March 2006 at 23 53 09 GMT Thursday 9 March 2006 at 23 53 13 GMT Friday 10 March 2006 at 23 53 04 GMT Saturday 11 March 2006 at 23 53 10 GMT Sunday 12 March 2006 at 23 54 23 GMT Monday 13 March 2006 at 23 53 25 GMT Tuesday 14 March 2006 at 23 53 27 GMT Wednesday 15 March 2006 at 23 53 16 GMT Thursday 16 March 2006 at 23 53 21 GMT Friday 17 March 2006 at 23 53 15 GMT Saturday 18 March 2006 at 23 53 11 GMT Sunday 19 March 2006 at 23 53 34 GMT Monday 20 March 2006 at 23 53 17 GMT Tuesday 21 March 2006 at 23 53 14 GMT Wednesday 22 March 2006 at 23 53 19 GMT Thursday 23 March 2006 at 23 53 14 GMT Friday 24 March 2006 at 23 53 21 GMT Sunday 26 March 2006 at 00 58 02 GMT Sunday 26 March 2006 at 23 56 43 GMT Monday 27 March 2006 at 23 56 35 GMT Tuesday 28 March

    Original URL path: http://www.archduke.org/footballpreds/2005-06.html (2016-04-27)
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  • final states to a minimum If after n moves the number of possible final states is s n then the average branching factor is the limit of the n th root of s n Take the example of b There are three sorts of trees that can arise in the course of the game There is the two ply tree b which we ll call B There is the one ply tree which comes from playing the left move from B We ll call this 1 And there is the one ply tree which comes from playing the right move from B We ll call this 2 The initial state of the game is BBBBBBBBB S s strategy will be to force P to play in a 1 if one exists otherwise force P to play in the first new B never letting P play in a 2 So after one move P can arrive at 1BBBBBBBB or 2BBBBBBBB After two moves P can arrive at BBBBBBBB 21BBBBBBB or 22BBBBBBB and after three moves the list is 1BBBBBBB 2BBBBBBB 2 BBBBBBB 221BBBBBB 222BBBBBB You can get the formula for s n the number of reachable states after n moves by considering what happens after the first move If the first move is to 2BBBBBBBB then the number of states reachable after n moves will be s n 1 because the 2 is never played in and so can be ignored So this state is like the initial state but there are only n 1 moves remaining If the first move is to 1BBBBBBBB then the number of states reachable after n moves will be s n 2 because the 1 is always played in next move which absorbs a move and after that you get back to a state like the initial state but with only n 2 moves left to play So s n s n 1 s n 2 and s n is the n th Fibonacci number which means the limit of the n th root of s n is 1 sqrt 5 2 1 618 The idea is that this will also work to some extent when you mix trees of different types not just take copies of one type of tree If the branching factors of trees are b 1 b 2 b 3 b 4 where b 1 b 2 b 3 then the number of states reachable after n moves should be somewhere between b 1 n and b 1 b 2 b 3 b n As you might expect there is a less cumbersome way to calculate these average branching factors We can go more or less directly to the defining polynomial The procedure is as follows Take an n ply tree Label all the level n i e bottom level nodes with the number 1 Label each level n 1 node with the expression min b sum of labels of children Label each level n 2 node with the expression min

    Original URL path: http://www.archduke.org/eternity/method/lbf.html (2016-04-27)
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  • Let
    S given we re allowed to do some computation of the form 1 We ll end up with S between 0 and S 0 Now we ll describe the modifications to the above formula but first let s talk instead in terms of the more convenient log likelihood L L å B Î B é ë å S Î S B log P B R S å X Î A B S B log 1 P B R X ù û 2 What sort of size are the numbers We mainly used k 24 and n is likely to be at least 60 Say n 60 The typical number of solutions will vary according to how good the pieces and regions are but let s aim very roughly at a few hundred solutions per B Î B There are 60 24 4 10 16 elements of A B choices of 24 pieces so P R X will be very small of the order 10 14 and so we can replace log 1 P B R X with P B R X and A B S B with A B in 2 Actually this is not really an approximation we re just changing to a model where the number of solutions to R X has Poisson distribution with parameter P R X which happens to be a very similar model because P R X is so small Now the formula for L looks like L å B Î B é ë æ è å S Î S B logP B R S ö ø å X Î A B P B R X ù û Let n B S B the number of solutions in B The trouble with using the above L is that n B will vary a lot Some B might have n B 0 others n B 5 and a few B might have n B 100000 because it is hard to accurately control how many solutions you get when you add a lot of pieces This L will be dominated by the terms arising from B for which n B is particularly large It will turn out that we may as well not have bothered exhausting 99 9 of the regions because the p i and m j will end up being geared almost entirely towards minimising the terms in L arising from B for which n B is very large So most of our data will be ignored and the model will spend all of its effort trying to explain the B for which n B is very large and the values it gets for p i and m j will be pretty useless When we chose lots of different B we were trying to make a uniform sample from the very large space of all possible B In effect with the above L we are weighting each sample point according to n B but this is bad because the results associated with a given

    Original URL path: http://www.archduke.org/eternity/method/model.html (2016-04-27)
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  • Pieces
    piece set cannot be displayed here You may like to look at the solution page since pictures of our solution contain all the pieces permission has been obtained from Mr

    Original URL path: http://www.archduke.org/eternity/talk/slide1.html (2016-04-27)
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  • Board
    Picture of the Eternity board Postscript pdf

    Original URL path: http://www.archduke.org/eternity/talk/slide2.html (2016-04-27)
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  • stuff › Lost Password
    stuff Please enter your username or email address You will receive a link to create a new password via email Username or E mail Log in Back to stuff

    Original URL path: http://www.archduke.org/stuff/wp-login.php?action=lostpassword (2016-04-27)
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  • Football league predictions
    55 76 2 97 49 00 0 00 21 00 0 00 0 00 0 00 0 00 0 00 0 00 Brighton 46 47 10 15 16 6 50 9 52 47 00 0 00 10 00 0 00 0 00 0 00 0 00 0 00 0 00 Millwall 46 41 34 3 38 36 77 5 10 41 00 0 00 34 00 0 00 0 00 0 00 0 00 100 00R 0 00 Wigan 46 39 25 17 69 3 45 16 06 39 00 0 00 25 00 0 00 0 00 0 00 0 00 100 00R 0 00 Blackpool 46 26 55 12 34 7 99 15 04 26 00 0 00 55 00 0 00 0 00 0 00 0 00 100 00R 100 00 League 1 Latest match accounted for Sunday 3 May 2015 Barnsley 5 0 Rochdale Check up to date Current Luck Expected Percentage chance Team Pld Pts GD Points pts GD Points sd pts GD Top1 Top2 Top6 2 3 6 Bot4 Bot1 Bristol City 46 99 58 9 91 83 71 17 68 99 00 0 00 58 00 100 00 100 00 100 00 100 00P 0 00 0 00 MK Dons 46 91 57 2 61 59 41 17 50 91 00 0 00 57 00 0 00 100 00 100 00 100 00P 0 00 0 00 Preston 46 89 39 5 16 68 91 8 50 89 00 0 00 39 00 0 00 0 00 100 00 39 37P 0 00 0 00 Swindon 46 79 19 4 37 66 02 1 96 79 00 0 00 19 00 0 00 0 00 100 00 24 11P 0 00 0 00 Sheff Utd 46 71 13 0 62 47 68 0 62 71 00 0 00 13 00 0 00 0 00 100 00 21 73P 0 00 0 00 Chesterfield 46 69 13 1 47 55 71 6 65 69 00 0 00 13 00 0 00 0 00 100 00 14 79P 0 00 0 00 Bradford 46 65 0 3 96 65 04 2 69 65 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 Rochdale 46 63 6 0 72 52 98 8 23 63 00 0 00 6 00 0 00 0 00 0 00 0 00 0 00 0 00 Peterborough 46 63 3 3 79 35 91 8 35 63 00 0 00 3 00 0 00 0 00 0 00 0 00 0 00 0 00 Fleetwood Town 46 63 3 7 26 76 27 7 26 63 00 0 00 3 00 0 00 0 00 0 00 0 00 0 00 0 00 Barnsley 46 62 1 4 70 33 07 4 07 62 00 0 00 1 00 0 00 0 00 0 00 0 00 0 00 0 00 Gillingham 46 62 1 2 67 60 51 5 59 62 00 0 00 1 00 0 00 0 00 0 00 0 00 0 00 0 00 Doncaster 46 61 4 2 29 41 81 4 21 61 00 0 00 4 00 0 00 0 00 0 00 0 00 0 00 0 00 Walsall 46 59 4 2 46 40 72 2 28 59 00 0 00 4 00 0 00 0 00 0 00 0 00 0 00 0 00 Oldham 46 57 13 1 85 57 80 1 19 57 00 0 00 13 00 0 00 0 00 0 00 0 00 0 00 0 00 Scunthorpe 46 56 13 0 13 51 14 0 70 56 00 0 00 13 00 0 00 0 00 0 00 0 00 0 00 0 00 Coventry 46 55 11 4 66 32 62 5 57 55 00 0 00 11 00 0 00 0 00 0 00 0 00 0 00 0 00 Port Vale 46 54 10 2 22 42 13 0 90 54 00 0 00 10 00 0 00 0 00 0 00 0 00 0 00 0 00 Colchester 46 52 19 1 80 43 78 4 06 52 00 0 00 19 00 0 00 0 00 0 00 0 00 0 00 0 00 Crewe 46 52 32 6 17 74 17 4 98 52 00 0 00 32 00 0 00 0 00 0 00 0 00 0 00 0 00 Notts County 46 50 18 5 03 31 52 5 93 50 00 0 00 18 00 0 00 0 00 0 00 0 00 100 00R 0 00 Crawley Town 46 50 26 1 31 45 59 7 59 50 00 0 00 26 00 0 00 0 00 0 00 0 00 100 00R 0 00 Leyton Orient 46 49 10 16 85 5 44 13 71 49 00 0 00 10 00 0 00 0 00 0 00 0 00 100 00R 0 00 Yeovil 46 40 39 6 97 24 77 14 93 40 00 0 00 39 00 0 00 0 00 0 00 0 00 100 00R 100 00 League 2 Latest match accounted for Saturday 2 May 2015 AFC Wimbledon 1 1 Cheltenham Check up to date Current Luck Expected Percentage chance Team Pld Pts GD Points pts GD Points sd pts GD Top1 Top3 Top7 3 4 7 Bot2 Bot1 Burton Albion 46 94 30 18 30 96 43 11 45 94 00 0 00 30 00 100 00 100 00 100 00 100 00P 0 00 0 00 Shrewsbury 46 89 36 5 22 69 12 6 51 89 00 0 00 36 00 0 00 100 00 100 00 100 00P 0 00 0 00 Bury 46 85 20 11 02 85 91 3 87 85 00 0 00 20 00 0 00 100 00 100 00 100 00P 0 00 0 00 Wycombe 46 84 22 13 32 90 20 10 52 84 00 0 00 22 00

    Original URL path: http://www.archduke.org/footballpreds/pred20150625-210001.html (2016-04-27)
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  • Football league predictions
    54 65 2 59 49 00 0 00 21 00 0 00 0 00 0 00 0 00 0 00 0 00 Brighton 46 47 10 15 31 6 16 9 71 47 00 0 00 10 00 0 00 0 00 0 00 0 00 0 00 0 00 Millwall 46 41 34 3 38 36 80 5 08 41 00 0 00 34 00 0 00 0 00 0 00 0 00 100 00R 0 00 Wigan 46 39 25 17 57 3 59 15 95 39 00 0 00 25 00 0 00 0 00 0 00 0 00 100 00R 0 00 Blackpool 46 26 55 12 39 8 00 15 05 26 00 0 00 55 00 0 00 0 00 0 00 0 00 100 00R 100 00 League 1 Latest match accounted for Sunday 3 May 2015 Barnsley 5 0 Rochdale Check up to date Current Luck Expected Percentage chance Team Pld Pts GD Points pts GD Points sd pts GD Top1 Top2 Top6 2 3 6 Bot4 Bot1 Bristol City 46 99 58 10 22 84 02 18 19 99 00 0 00 58 00 100 00 100 00 100 00 100 00P 0 00 0 00 MK Dons 46 91 57 2 45 58 90 17 26 91 00 0 00 57 00 0 00 100 00 100 00 100 00P 0 00 0 00 Preston 46 89 39 5 03 68 42 8 28 89 00 0 00 39 00 0 00 0 00 100 00 39 88P 0 00 0 00 Swindon 46 79 19 4 13 65 34 1 63 79 00 0 00 19 00 0 00 0 00 100 00 24 18P 0 00 0 00 Sheff Utd 46 71 13 0 74 47 13 0 45 71 00 0 00 13 00 0 00 0 00 100 00 21 27P 0 00 0 00 Chesterfield 46 69 13 1 32 55 06 6 42 69 00 0 00 13 00 0 00 0 00 100 00 14 67P 0 00 0 00 Bradford 46 65 0 4 03 65 51 2 79 65 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 Rochdale 46 63 6 0 65 52 47 8 08 63 00 0 00 6 00 0 00 0 00 0 00 0 00 0 00 0 00 Peterborough 46 63 3 3 89 35 81 8 49 63 00 0 00 3 00 0 00 0 00 0 00 0 00 0 00 0 00 Fleetwood Town 46 63 3 7 37 76 50 7 36 63 00 0 00 3 00 0 00 0 00 0 00 0 00 0 00 0 00 Barnsley 46 62 1 4 30 34 46 3 51 62 00 0 00 1 00 0 00 0 00 0 00 0 00 0 00 0 00 Gillingham 46 62 1 2 83 60 88 5 83 62 00 0 00 1 00 0 00 0 00 0 00 0 00 0 00 0 00 Doncaster 46 61 4 2 50 40 99 4 54 61 00 0 00 4 00 0 00 0 00 0 00 0 00 0 00 0 00 Walsall 46 59 4 2 82 39 44 2 75 59 00 0 00 4 00 0 00 0 00 0 00 0 00 0 00 0 00 Oldham 46 57 13 1 92 58 34 1 13 57 00 0 00 13 00 0 00 0 00 0 00 0 00 0 00 0 00 Scunthorpe 46 56 13 0 29 51 74 0 53 56 00 0 00 13 00 0 00 0 00 0 00 0 00 0 00 0 00 Coventry 46 55 11 4 52 33 41 5 35 55 00 0 00 11 00 0 00 0 00 0 00 0 00 0 00 0 00 Port Vale 46 54 10 2 29 41 68 0 79 54 00 0 00 10 00 0 00 0 00 0 00 0 00 0 00 0 00 Colchester 46 52 19 1 47 44 94 3 51 52 00 0 00 19 00 0 00 0 00 0 00 0 00 0 00 0 00 Crewe 46 52 32 6 10 74 14 5 02 52 00 0 00 32 00 0 00 0 00 0 00 0 00 0 00 0 00 Notts County 46 50 18 5 23 31 01 6 15 50 00 0 00 18 00 0 00 0 00 0 00 0 00 100 00R 0 00 Crawley Town 46 50 26 1 38 45 53 7 64 50 00 0 00 26 00 0 00 0 00 0 00 0 00 100 00R 0 00 Leyton Orient 46 49 10 16 79 5 57 13 62 49 00 0 00 10 00 0 00 0 00 0 00 0 00 100 00R 0 00 Yeovil 46 40 39 6 88 24 61 14 82 40 00 0 00 39 00 0 00 0 00 0 00 0 00 100 00R 100 00 League 2 Latest match accounted for Saturday 2 May 2015 AFC Wimbledon 1 1 Cheltenham Check up to date Current Luck Expected Percentage chance Team Pld Pts GD Points pts GD Points sd pts GD Top1 Top3 Top7 3 4 7 Bot2 Bot1 Burton Albion 46 94 30 18 50 96 44 11 75 94 00 0 00 30 00 100 00 100 00 100 00 100 00P 0 00 0 00 Shrewsbury 46 89 36 5 46 70 08 6 84 89 00 0 00 36 00 0 00 100 00 100 00 100 00P 0 00 0 00 Bury 46 85 20 11 30 86 61 4 35 85 00 0 00 20 00 0 00 100 00 100 00 100 00P 0 00 0 00 Wycombe 46 84 22 13 48 90 56 10 76 84 00 0 00 22 00

    Original URL path: http://www.archduke.org/footballpreds/pred20150624-210001.html (2016-04-27)
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