Lottery algorithm - PHP - math seems good, but is the function valid? -


i want make custom lottery extraction motivate users participate in online experiment. rules are:

  • 10% 10$
  • 1% chance 50$
  • 0.1% chance 500$

the lottery php function gets called once , returns prize (0, 10, 50 or 500). created function below, , after 70 000 trials statistics are:

  • 9.11% 10$
  • .91% 50$
  • .01% 500$

should worried algorithm? there better way create distribution of chances mt_rand ?

function lottery() {   // winnings before extraction   $win=0;    // choose winning number between 1 , 10   $target=mt_rand(1,10);    // make 3 independent extractions, each 1/10 probability   if (mt_rand(1,10) == $target) {     // if first extraction winning number -> prize=10     // probability: 1/10     $win=10;      if (mt_rand(1,10) == $target) {         // if second extraction winning number -> prize=50         // probability: 1/10 * 1/10         $win=50;          if (mt_rand(1,10) == $target) {             // if third extraction winning number -> prize=500             // probability: 1/10 * 1/10 * 1/10             $win=500;         }     }   }   // return prize   return $win; }

thank helping newbie!

you have 4 outcomes given probabilities:

  • 0.1% probability win $500.
  • 1% probability win $500.
  • 10% probability win $500.

the fourth outcome - no win - 100% minus sum of other 3 outcomes, namely 88.9%.

mark gabriel has explained why initial code off: promoting 10% of people have won $10 $50 winners, take them away pool of $10 winner, 9% of people.

pham trung has contributed solution takes winners of higher amounts pool of non-winners far , adjusts probabilities. that's workable solution, easiest solution in opintion call random number generator once.

this solution reflects ticket analogy best: place 10,000 tickets in box. 1,000 tickets 1 1000 win $10. 100 tickets 1001 1100 win $50. ten tickets 1101 1110 win $500. 8890 tickets 1111 on don't win anything:

function lottery() {     var pick = math.floor(10000 * math.random());                // random number in range [0, 10000).      if (pick < 1000) return 10;     if (pick < 1100) return 50;     if (pick < 1110) return 500;      return 0; }

in code, tickets have number written on them. pick one. check whether ticket number eligible $10. if not, check same ticket whether may bet $50 win. there 1 random action involved.

(i've used zero-based random-number function in javascript instead of php's mt_rand, think solution clear.)


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