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  1. PO
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    <p>Here you go.</p> <p>I place this code into the public domain.</p> <pre><code># Function to make an array of 'width' zeros function makerow($width){ $row=array(); for($x=0;$x&lt;$width;$x++){ $row[$x]=0; } return $row; } # Function to make a width*height matrix function makematrix($width,$height){ $matrix=array(); for($y=0;$y&lt;$height;$y++){ $matrix[$y]=array(); for($x=0;$x&lt;$width;$x++){ $matrix[$y][$x]=0; } } return $matrix; } # Adds one matrix to another function matrixadd(&amp;$matrixdest,&amp;$matrixsrc){ for($i=0;$i&lt;count($matrixdest);$i++){ for($j=0;$j&lt;count($matrixdest[$i]);$j++){ $matrixdest[$i][$j]+=$matrixsrc[$i][$j]; } } } # Multiplies a matrix by a scalar function matrixmultiply(&amp;$matrix,$scalar){ for($i=0;$i&lt;count($matrix);$i++){ for($j=0;$j&lt;count($matrix[$i]);$j++){ $matrix[$i][$j]*=$scalar; } } } # Calculates the equity of each place. Rows indicate players; # columns indicate places (0 is 1st place, 1 is second, and so on) # The parameter 'places' is optional. If not given, uses the # number of stacks. function equitymatrix(&amp;$stacks, $places=-1){ if($places==-1){ # replace places with the stack count $places=count($stacks); } if(count($stacks)&lt;=1){ return array(array(1)); } $totalStacks=0; for($i=0;$i&lt;count($stacks);$i++){ $totalStacks+=$stacks[$i]; } # Optimize for case where there is only one place if($places==1){ $matrix=makematrix(1,count($stacks)); for($i=0;$i&lt;count($stacks);$i++){ $matrix[$i][0]=$stacks[$i]*1.0/$totalStacks; } return $matrix; } # Optimize for case where there are two places if($places==2){ $matrix=makematrix(2,count($stacks)); for($i=0;$i&lt;count($stacks);$i++){ $matrix[$i][0]=$stacks[$i]*1.0/$totalStacks; } for($i=0;$i&lt;count($stacks);$i++){ for($j=0;$j&lt;count($stacks);$j++){ if($i!=$j){ $matrix[$i][1]+=$matrix[$j][0]*($stacks[$i]*1.0/($totalStacks-$stacks[$j])); } } } return $matrix; } # Calculate the probabilities of each player getting first place $probabilities=array(); for($i=0;$i&lt;count($stacks);$i++){ $probabilities[$i]=$stacks[$i]*1.0/$totalStacks; } #echo(count($stacks)." ".$places."\n"); $subequities=array(); for($i=0;$i&lt;count($stacks);$i++){ $substacks=array(); # Assume that player i would be in first place # Create a new array with i's stack removed for($j=0;$j&lt;count($stacks);$j++){ if($j!=$i){ array_push($substacks,$stacks[$j]); } } # Find the subequity of the remaining players $subequities[$i]=equitymatrix($substacks, min($places,count($substacks))); for($j=0;$j&lt;count($subequities[$i]);$j++){ array_unshift($subequities[$i][$j],0); } # Add player i back $newrow=makerow($places); $newrow[0]=1; array_splice($subequities[$i],$i,0,array($newrow)); } $equities=makematrix($places,count($stacks)); for($i=0;$i&lt;count($stacks);$i++){ # Multiply the probabilities matrixmultiply($subequities[$i],$probabilities[$i]); # Add the subequity matrixadd($equities,$subequities[$i]); } return $equities; } </code></pre> <p>Example:</p> <pre><code>$mystacks=array(10,40,30,20); print_r(equitymatrix($mystacks)); </code></pre> <hr> <p>As to the use of matrices:</p> <p>In PHP, a matrix can be represented as an array of arrays. You can see that in the function <code>makematrix</code>, which returns an array of length <code>height</code>, with each element being an array of <code>width</code> zeros. Your problem uses the following matrix operations, both of which are simple:</p> <ul> <li>Adding two matrices (<code>matrixadd</code>). Here, just add the elements of one matrix to the corresponding elements of the other matrix.</li> <li>Multiplying a matrix by a single number (a scalar) (<code>matrixmultiply</code>) simply involves multiplying each element of the matrix by that number.</li> </ul>
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    1. POHow to translate this Math Formula in Haskell or Python? (Was translated in PHP)
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    1. USPeter O.
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    1. COIf it works - phenominal. Great job!
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    2. COYou are my idol! :)
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    3. COI've analyzed your code and it's awsome! :) The only problem is in the math algorithm itself: too slow. Is it possible to speed up the code by calculating only a determined number of equity on places? I mean: in a scenario where there are 6 players, the code above would calculate the equity of every player on each place till the 6th place. If we need only their equity on 1st and 2nd place can we skip the remanent code, can't we? It would be useful to have something like print_r(equitymatrix($mystacks,2)); Where the number stays for the places we wanna calculate the equity on.
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