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April 24th, 2007, 08:07 AM   #1
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advanced adds calculating texas hold'em

I'm dutch so I dont know all the proper names for certain calculations, but I'll try to explain myself.

Yesterday I started on a calculation to calculate your odds when playing texas hold'em poker. I was searching the internet and I noticed that you can't exactly calculate your odds.

First of all, lets see how texas hold'em works. You and a certain number of people (usually 9 others) sit at a table. Everyone gets dealt two cards. You can place a bet or fold at this stage. Then you move on to the following stage. Three cards (which were in the deck) are dealt face upwards and another betting/folding round commences. On to the following stage: one card (which were in the deck) is dealt face upwards and another betting and folding round follows. Last stage: the final card is dealt face upwards (which were in the deck) and the last betting/folding round ends that hand.

The calculation I have so far (far from accurate) can only be used after the first three cards (called the flop) has been dealt. You know than what cards you need to have a winning hand. Those cards, of which you dont know whether they are in the deck or in an opponents hand, are called 'outs'. With these 'outs', you can determine the chance you have of hitting such a card.

At http://xeon.ele.tue.nl/~s030517/poker/ you can see a working example of this calculation. Just click the table-button and you see the chances in % for each number of outs.
For the people understanding php-code:
Code:
function calculateOutsOdds($outs,$river=false)
{
  if($river)
    $outcome = (1 - (/*riverodd*/((46 - $outs) / 46)))*100;
  elseif(!$river)
    $outcome = (1 - ((/*turnodd*/((47 - $outs) / 47)) * (/*riverodd*/((46 - $outs) / 46))))*100;

  return $outcome;
}

function buildOutsTable($maxOuts)
{
  $rval = "<table><tr><th># of outs</th><th>Turn or River</th><th>River-fucker</th></tr>\r\n";
  for($i = 1; $i <= $maxOuts; $i++)
  {
    $rval .= "<tr><td>".$i."</td><td>".calculateOutsOdds($i)."</td><td>".calculateOutsOdds($i,true)."</td></tr>\r\n";
  }


  $rval .= "</table>\r\n";

  return $rval;
}
My question is whether there is another way to really calculate the odds... Can you calculate a percentage per winning hand, taking in account what all you opponents can possible have. Is there any other way than simulating yourself true all the possible hands for each opponent (kind of doing a brute-force attack on it)? Because that takes a lot of time ofcourse...
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