Programming: How to find best hold based on strategy?

Quote: JB

Is it for a specific game and paytable which will never change? Or is it for an arbitrary game and paytable, requiring an accurate, generic function?

Is it for a simulation?

Quote: Wizard

I wrote a whole page about it: My Methodology for Video Poker Analysis.

Quote:

ten = 0;
jack = 0;
queen =0;
king = 0;
ace = 0;

spade = 0;
club = 0;
heart = 0;
diamond = 0;

for (i = 0; i < 5; i++) {
if (rank == "T")
ten++;
elseif (rank == "J")
jack++;
....etc

if (suite == "s")
spade++;
elseif (suite == "d")
diamond++;
}

if (spade == 5 or diamond == 5 or heart == 5 or club == 5)
if (ten == 1 and jack == 1 and queen == 1 and king == 1 and ace == 1)
echo "Dealt royal flush!\n";

Quote: RS

That's part of the problem. Right now I'm doing it for a simulation on 9/6 JOB. But I'm hoping to include other paytables/strategies in the future like DW and DDB primarily.

    static Random RNG = new Random();

    static int[] Paytable = { 800, 50, 25, 9, 6, 4, 3, 2, 1, 0 };

    static double[] ProbabilityTable =
    {
        0.0000247582680375947,  // Royal Flush
        0.000109309090371472,   // Straight Flush
        0.00236254568587687,    // Four of a Kind
        0.0115122073362865,     // Full House
        0.0110145109680315,     // Flush
        0.0112293672413438,     // Straight
        0.0744486985711364,     // Three of a Kind
        0.129278902480178,      // Two Pair
        0.214585031125644,      // Jacks or Better
        0.545434669233094       // All Other
    };

    // the probabilities don't quite sum to exactly 1 but are close enough

    //////////////////////////////////////////////////////////////////////

    while (true)
    {
        int outcome = 0;

        double r = RNG.NextDouble();

        for (int x = 0; x < 10; x++)
        {
            double p = ProbabilityTable[x];

            if (r < p)
            {
                outcome = x;
                break;
            }

            r -= p;
        }

        int prize = Paytable[outcome];

        // use the outcome or prize however you need
    }

Quote: JB

The reason I ask is because you don't need to go through much trouble at all for a simulation.

1) Create a static array holding the probability of each outcome when optimal strategy is used.

2) For the simulation itself, repeatedly generate a random double r such that 0 <= r < 1 and determine which outcome it corresponds to. Use the outcome however you need (such as adding its payoff to a running total, etc.)

The following code snippets are in C# but you should be able to adapt the code to whatever language you use:

    static Random RNG = new Random();

    static int[] Paytable = { 800, 50, 25, 9, 6, 4, 3, 2, 1, 0 };

    static double[] ProbabilityTable =
    {
        0.0000247582680375947,  // Royal Flush
        0.000109309090371472,   // Straight Flush
        0.00236254568587687,    // Four of a Kind
        0.0115122073362865,     // Full House
        0.0110145109680315,     // Flush
        0.0112293672413438,     // Straight
        0.0744486985711364,     // Three of a Kind
        0.129278902480178,      // Two Pair
        0.214585031125644,      // Jacks or Better
        0.545434669233094       // All Other
    };

    // the probabilities don't quite sum to exactly 1 but are close enough

    //////////////////////////////////////////////////////////////////////

    while (true)
    {
        int outcome = 0;

        double r = RNG.NextDouble();

        for (int x = 0; x < 10; x++)
        {
            double p = ProbabilityTable[x];

            if (r < p)
            {
                outcome = x;
                break;
            }

            r -= p;
        }

        int prize = Paytable[outcome];

        // use the outcome or prize however you need
    }

This will also let you run many more trials per second than if you actually shuffled a deck, dealt a hand, decoded it, applied optimal strategy, drew replacement cards, and scored the final hand for each trial.

Quote: RS

I already know the best hold. I don't know how to code the best hold strategy, other than hard-coding it.

Quote: RS

JB, I started it in PHP.

Quote: JB

Wow, that's... brave.

Quote: RS

ME, indeed. I hadn't even thought about ordering the cards.

Quote: MathExtremist

First, definitely use C++. If you're on linux, you probably do have some version of the gnu compiler on there, but you probably don't have a proper IDE (which I'd use if you're not an emacs hacker).

As for the ordering, that approach will break games that pay on things like sequential royals or whatnot. Those are rare but it's still an edge case. Actually both techniques I mentioned are order-agnostic so if you really want to be safe for a generic case of "order matters" then you'll need to intentionally check for that. I'm unaware of any other games that involve different pays based on hand ordering though, and I haven't looked at whether the order has an actual impact on the sequential royal strategy (i.e. do you hold an A in the first position more than in the 2nd).

But if you don't care about those, an order-agnostic treatment is definitely less work.