Is there a simpler way than this to calculate a straight in poker?

StackOverflow https://stackoverflow.com/questions/4004856

  •  25-09-2019
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Question

I have an algorithm for calculating whether a player's hand holds a straight in Texas Hold'em. It works fine, but I wonder if there is a simpler way to do it that does not involve array/string conversions, etc.

Here's a simplified version of what I have. Say the player is dealt a hand that is a 52-element array of card values:

var rawHand = [1,0,0,0,0,0,0,0,0,0,0,0,0, //clubs
               0,0,0,0,0,0,0,0,0,0,0,0,0, //diamonds
               0,1,1,0,1,0,0,0,0,0,0,0,0, //hearts
               0,0,0,1,0,0,0,0,1,0,0,0,0];//spades

A 1 represents a card in that value slot. The above hand has a 2-clubs, no diamonds, a 3-hearts, 4-hearts, and 6-hearts, a 5-spades and a 10-spades. Now I look at it to find a straight.

var suits = []; //array to hold representations of each suit

for (var i=0; i<4; i++) {
    var index = i*13;
    // commenting this line as I removed the rest of its use to simplifyy example
    //var hasAce = (rawHand[i+13]);

    //get a "suited" slice of the rawHand, convert it to a string representation
    //of a binary number, then parse the result as an integer and assign it to
    //an element of the "suits" array
    suits[i] = parseInt(rawHand.slice(index,index+13).join(""),2);
}

// OR the suits    
var result = suits[0] | suits[1] | suits[2] | suits[3];

// Store the result in a string for later iteration to determine
// whether straight exists and return the top value of that straight
// if it exists; we will need to determine if there is an ace in the hand
// for purposes of reporting a "low ace" straight (i.e., a "wheel"),
// but that is left out in this example
var resultString = result.toString(2);

//Show the result for the purposes of this example
alert("Result: " + resultString);

The trick here is to OR the various suits so there is just one 2-to-Ace representation. Am I wrong in thinking there must be a simpler way to do this?

Was it helpful?

Solution

Almost all of the work your code does is type conversion. If you just had the hand stored in bit format to begin with(needs > 32 bit type), you could do something like:

var mask = 2^13 - 1; // this will zero out all but the low 13 bits
var suits = (rawHand | rawHand>>13 | rawHand>>26 | rawHand>>39) & mask;

The equivalent using a one line loop would be:

var suits = [];
for(var i=0; i < 13; i++) {
   suits[i] = rawHand[i] || rawHand[i+13] || rawHand[i+26] || rawHand[i+39];
}

This is much shorter and easier to understand.

Converting to and from a bit-wise representation takes more code and CPU time than you save by using the bit-wise OR operator.

OTHER TIPS

Well, a straight must include a 5 or a 10, so you can start by throwing out the hand if it doesn't have one or other:

if (rawHand[3] || rawHand[16] || rawHand[29] || rawHand[42] ||
    rawHand[8] || rawHand[21] || rawHand[34] || rawHand[47]) {
  // do some more checks
} else {
  // not a straight
}

You can use an integer value as a bitfield for the card values, ace gets two spots low and high. Then you compare with bitwise end against the ten possible straights.

Or use a for-loop and check for five consecutive numbers - effectively it's all the same.

This question got me interested. I ended up going way overboard. And wrote a web page to calculate any hand. Its probably not the most efficient but it does work. I did this with just JavaScript (No jQuery). Here is a demo http://jsbin.com/izuto4/2/

Below is the code:

<html>
<head>
<script>
   // var myrawHand = [1,0,0,0,0,0,0,0,0,0,0,0,0, //clubs
   // 0,0,0,0,0,0,0,0,0,0,0,0,0, //diamonds
   // 0,1,1,0,1,0,0,0,0,0,0,0,0, //hearts
   // 0,0,0,1,0,0,0,0,0,0,0,0,0];//spades

    function getCardsInHand(rawHand) {
        var cardsInHand = new Array();
        var counter = 0;
        for (var i = 0; i < rawHand.length; i ++) {
            if (rawHand[i]) {
                cardsInHand[counter] = i;
                counter ++;
            }
        }
        return cardsInHand;
    }

    function cardsfiltered(rawHand) {
        var cards = getCardsInHand(rawHand)

        var cardsfiltered = new Array();
        for (var j = 0; j < cards.length; j ++){
            cardsfiltered[j] = cards[j] - (parseInt(cards[j] / 13) * 13);
        }
        cardsfiltered.sort();
        return {cards : cards, cardsfiltered : cardsfiltered};
    }

    function whatIsMyHand(rawHand) {
        var cardObject = cardsfiltered(rawHand);
        if (((cardObject.cards[0] == 0 && cardObject.cards[1] == 9)
                || (cardObject.cards[0] == 13 && cardObject.cards[1] == 22)
                || (cardObject.cards[0] == 26 && cardObject.cards[1] == 35)
                || (cardObject.cards[0] == 39 && cardObject.cards[1] == 48))
                && cardObject.cards[4] == cardObject.cards[3] + 1 &&
                cardObject.cards[3] == cardObject.cards[2] + 1 &&
                cardObject.cards[2] == cardObject.cards[1] + 1) {
            return "Royal Flush";
        }
        else if (cardObject.cards[4] == cardObject.cards[3] + 1 &&
                cardObject.cards[3] == cardObject.cards[2] + 1 &&
                cardObject.cards[2] == cardObject.cards[1] + 1 &&
                cardObject.cards[1] == cardObject.cards[0] + 1) {
            return "Straight Flush";
        }
        else if ((cardObject.cardsfiltered[1] == cardObject.cardsfiltered[2]
                && cardObject.cardsfiltered[2] == cardObject.cardsfiltered[3])
                && (cardObject.cardsfiltered[0] == cardObject.cardsfiltered[1]
                || cardObject.cardsfiltered[3] == cardObject.cardsfiltered[4])) {
            return "Four of a Kind";
        }
        else if ((cardObject.cardsfiltered[0] == cardObject.cardsfiltered[1]
                && cardObject.cardsfiltered[1] == cardObject.cardsfiltered[2]
                && cardObject.cardsfiltered[3] == cardObject.cardsfiltered[4])
                || (cardObject.cardsfiltered[0] == cardObject.cardsfiltered[1]
                && cardObject.cardsfiltered[2] == cardObject.cardsfiltered[3]
                && cardObject.cardsfiltered[3] == cardObject.cardsfiltered[4])) {
            return "Full House";
        }
        else if (parseInt(cardObject.cards[0] / 13) == parseInt(cardObject.cards[1] / 13)
                && parseInt(cardObject.cards[0] / 13) == parseInt(cardObject.cards[2] / 13)
                && parseInt(cardObject.cards[0] / 13) == parseInt(cardObject.cards[3] / 13)
                && parseInt(cardObject.cards[0] / 13) == parseInt(cardObject.cards[4] / 13)) {
            return "Flush";
        }
        else if ((cardObject.cardsfiltered[4] == cardObject.cardsfiltered[3] + 1
                && cardObject.cardsfiltered[3] == cardObject.cardsfiltered[2] + 1
                && cardObject.cardsfiltered[2] == cardObject.cardsfiltered[1] + 1
                && cardObject.cardsfiltered[1] == cardObject.cardsfiltered[0] + 1)
                || (cardObject.cardsfiltered[0] == 0
                && cardObject.cardsfiltered[1] == 10
                && cardObject.cardsfiltered[2] == 11
                && cardObject.cardsfiltered[3] == 12
                && cardObject.cardsfiltered[4] == 9)) {
            return "Straight";
        }
        else if ((cardObject.cardsfiltered[0] == cardObject.cardsfiltered[1]
                && cardObject.cardsfiltered[1] == cardObject.cardsfiltered[2])
                || (cardObject.cardsfiltered[1] == cardObject.cardsfiltered[2]
                && cardObject.cardsfiltered[2] == cardObject.cardsfiltered[3])
                || (cardObject.cardsfiltered[2] == cardObject.cardsfiltered[3]
                && cardObject.cardsfiltered[3] == cardObject.cardsfiltered[4])) {
            return "Three of a Kind";
        }
        else if ((cardObject.cardsfiltered[0] == cardObject.cardsfiltered[1]
                && (cardObject.cardsfiltered[2] == cardObject.cardsfiltered[3]
                || cardObject.cardsfiltered[3] == cardObject.cardsfiltered[4]))
                || (cardObject.cardsfiltered[1] == cardObject.cardsfiltered[2]
                && cardObject.cardsfiltered[3] == cardObject.cardsfiltered[4])) {
            return "Two Pair"
        }
        else if (cardObject.cardsfiltered[0] == cardObject.cardsfiltered[1]
                || cardObject.cardsfiltered[1] == cardObject.cardsfiltered[2]
                || cardObject.cardsfiltered[2] == cardObject.cardsfiltered[3]
                || cardObject.cardsfiltered[3] == cardObject.cardsfiltered[4]) {
            return "Pair";
        }
        else {
            return "High Card";
        }
    }
    var CardCheckCount = 0;
    function MaxCardCheck(element) {
        if (element.checked) {
            if (CardCheckCount < 5) {
                CardCheckCount++;
                return true;
            }
        }
        else {
            CardCheckCount--;
            return true;
        }
        element.checked = !element.checked;
        alert("You can only pick 5 cards.");
        return false;
    }

    function calculateHand() {
        var checkboxes = document.getElementsByTagName("input");
        var myrawHand = new Array();
        for (var i = 0, element; element = checkboxes[i]; i++) {
          myrawHand[parseInt(element.name)] = element.checked ? element.value : 0;
        }
        alert(whatIsMyHand(myrawHand));
    }
</script>
</head>
<body>
<table>
    <thead>
        <tr>
            <td>&nbsp;A</td>
            <td>&nbsp;2</td>
            <td>&nbsp;3</td>
            <td>&nbsp;4</td>
            <td>&nbsp;5</td>
            <td>&nbsp;6</td>
            <td>&nbsp;7</td>
            <td>&nbsp;8</td>
            <td>&nbsp;9</td>
            <td>10</td>
            <td>&nbsp;J</td>
            <td>&nbsp;Q</td>
            <td>&nbsp;K</td>
            <td>&nbsp;</td>
        </tr>
    </thead>
    <tbody>
        <tr>
            <td><input name="0" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="1" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="2" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="3" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="4" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="5" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="6" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="7" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="8" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="9" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="10" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="11" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="12" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td>Clubs</td>
        </tr>
        <tr>
            <td><input name="13" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="14" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="15" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="16" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="17" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="18" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="19" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="20" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="21" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="22" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="23" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="24" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="25" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td>Diamonds</td>
        </tr>
        <tr>
            <td><input name="26" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="27" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="28" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="29" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="30" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="31" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="32" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="33" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="34" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="35" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="36" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="37" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="38" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td>Hearts</td>
        </tr>
        <tr>
            <td><input name="39" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="40" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="41" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="42" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="43" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="44" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="45" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="46" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="47" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="48" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="49" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="50" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td><input name="51" type="checkbox" value="1" onclick="MaxCardCheck(this);"/></td>
            <td>Spades</td>
        </tr>
    </tbody>
</table>
<button onclick="calculateHand()">Calculate Hand</button>
</body>
</html>

No, that's about as simple as it gets. I looked into poker hand evaluation a while ago, and I think the fastest way uses an approach like yours. See the first result in this site. It uses bitwise operations to compute hands.

EDIT: By first result, I mean "Pokersource Poker-Eval Evaluator".

Why not sort the cards by rank, and then check that each rank is one more than the previous. "ranks" is an array of length 5 with ACE = 1, 2 = 2, ... J = 11, Q = 12, K = 13. I think this is more simple than the other methods presented here.

function isStraight( ranks) {
  ranks.sort();
  return (ranks[0] + 1 == ranks[1] || (ranks[0] == 1 && ranks[4] == 13)) &&
         (ranks[1] + 1 == ranks[2]) &&
         (ranks[2] + 1 == ranks[3]) &&
         (ranks[3] + 1 == ranks[4]);
}

You can use SpecialK's 7-card and 5-card evaluators posted here and ask it to rank hands. If the rank that is returned is between 5854 and 5863 (both inclusive) or between 7453 and 7462 (both inclusive) then your hand, be it of 5 or 7 cards, respectively is or contains a straight.

Note the Ace of Spades is denoted by 0, the Ace of Hearts by 1, through to the Two of Clubs which is represented by 51. The algorithm will "add" up your cards and look up the rank in a small table, taking up 9MB of RAM. It will also do a lot more, but hey...

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