Joker Poker (Aces or Better Sequential Royal Flush)

This version of Joker Poker (Aces or Better) includes an added payline with a large prize for a Sequential Royal Flush. Under the "Options" tab above you can select whether a Sequential Royal Flush is TJQKA, AKQJT, or both.

Deck Simplification

Hand Scoring Code

int GetHandType(int C1, int C2, int C3, int C4, int C5)
{
    int Hand = 0;

    int R1 = Rank[C1],
        R2 = Rank[C2],
        R3 = Rank[C3],
        R4 = Rank[C4],
        R5 = Rank[C5];

    int S1 = Suit[C1],
        S2 = Suit[C2],
        S3 = Suit[C3],
        S4 = Suit[C4],
        S5 = Suit[C5];

    if (R1 > R2) { R1 ^= R2; R2 ^= R1; R1 ^= R2; S1 ^= S2; S2 ^= S1; S1 ^= S2; }
    if (R1 > R3) { R1 ^= R3; R3 ^= R1; R1 ^= R3; S1 ^= S3; S3 ^= S1; S1 ^= S3; }
    if (R1 > R4) { R1 ^= R4; R4 ^= R1; R1 ^= R4; S1 ^= S4; S4 ^= S1; S1 ^= S4; }
    if (R1 > R5) { R1 ^= R5; R5 ^= R1; R1 ^= R5; S1 ^= S5; S5 ^= S1; S1 ^= S5; }
    if (R2 > R3) { R2 ^= R3; R3 ^= R2; R2 ^= R3; S2 ^= S3; S3 ^= S2; S2 ^= S3; }
    if (R2 > R4) { R2 ^= R4; R4 ^= R2; R2 ^= R4; S2 ^= S4; S4 ^= S2; S2 ^= S4; }
    if (R2 > R5) { R2 ^= R5; R5 ^= R2; R2 ^= R5; S2 ^= S5; S5 ^= S2; S2 ^= S5; }
    if (R3 > R4) { R3 ^= R4; R4 ^= R3; R3 ^= R4; S3 ^= S4; S4 ^= S3; S3 ^= S4; }
    if (R3 > R5) { R3 ^= R5; R5 ^= R3; R3 ^= R5; S3 ^= S5; S5 ^= S3; S3 ^= S5; }
    if (R4 > R5) { R4 ^= R5; R5 ^= R4; R4 ^= R5; S4 ^= S5; S5 ^= S4; S4 ^= S5; }

    bool Flush =

        (S1 == S2) &&
        (S2 == S3) &&
        (S3 == S4) &&
       ((S4 == S5) ||
        (R5 == 13));

    if (R5 == 13)
    {
        if (Flush)
        {
            if (R1 >= 8)
            {
                Hand = 9;           // Wild Royal Flush
            }
            else if (((R4 - R1) <= 4) || ((R4 == 12) && (R3 <= 3)))
            {
                Hand = 8;           // Straight Flush
            }
            else
            {
                Hand = 5;           // Flush
            }
        }
        else
        {
            if ((R1 == R2) && (R2 == R3) && (R3 == R4))
            {
                Hand = 10;          // Five of a Kind
            }
            else if ((R2 == R3) && ((R1 == R2) || (R3 == R4)))
            {
                Hand = 7;           // Four of a Kind
            }
            else if ((R1 == R2) && (R3 == R4))
            {
                Hand = 6;           // Full House
            }
            else if ((((R4 - R1) <= 4) || ((R4 == 12) && (R3 <= 3))) &&
                            (R1 != R2) && (R2 != R3) && (R3 != R4))
            {
                Hand = 4;           // Straight
            }
            else if ((R1 == R2) || (R2 == R3) || (R3 == R4))
            {
                Hand = 3;           // Three of a Kind
            }
            else if (R4 >= 12)
            {
                Hand = 1;           // Aces or Better
            }
        }
    }

    else
    {

        if (Flush)
        {

            if (R1 == 8)
            {
                Hand = 11;          // Natural Royal Flush
            }

            else if ((R1 == (R2 - 1)) &&
                 (R2 == (R3 - 1)) &&
                 (R3 == (R4 - 1)) &&
                ((R4 == (R5 - 1)) || ((R1 == 0) && (R5 == 12))))
            {
                Hand = 8;           // Straight Flush
            }

            else
            {
                Hand = 5;           // Flush
            }
        }

        else
        {
            if ((R2 == R3) && (R3 == R4) && ((R1 == R2) || (R4 == R5)))
            {
                Hand = 7;           // Four of a Kind
            }

            else if ((R1 == R2) && (R4 == R5) && ((R2 == R3) || (R3 == R4)))
            {
                Hand = 6;           // Full House
            }

            else if ((R1 == (R2 - 1)) &&
                     (R2 == (R3 - 1)) &&
                     (R3 == (R4 - 1)) &&
                    ((R4 == (R5 - 1)) || ((R1 == 0) && (R5 == 12))) && (R5 != 13))
            {
                Hand = 4;           // Straight
            }

            else if (((R1 == R2) && (R2 == R3)) ||
                 ((R2 == R3) && (R3 == R4)) ||
                 ((R3 == R4) && (R4 == R5)))
            {
                Hand = 3;           // Three of a Kind
            }

            else if (((R1 == R2) && (R3 == R4)) ||
                 ((R1 == R2) && (R4 == R5)) ||
                 ((R2 == R3) && (R4 == R5)))
            {
                Hand = 2;           // Two Pair
            }
            else if (((R1 == R2) && (R1 >= 12)) ||
                     ((R2 == R3) && (R2 >= 12)) ||
                     ((R3 == R4) && (R3 >= 12)) ||
                     ((R4 == R5) && (R4 >= 12)))
            {
                Hand = 1;           // Pair of Aces
            }
        }
    }

    return Hand;
}

Sequential Royal Flush

Because this game features a Sequential Royal Flush, some adjustments are necessary to accurately analyze the game. All 32 ways to play each hand need to be analyzed twice: once under the assumption that the cards held were dealt in Sequential order, and then again under the assumption that the cards were dealt in a Non-Sequential order.

There are a distinct number of ways each number of held cards can result in a Sequential Royal Flush, based on whether or not they were dealt sequentially. The following table illustrates these numbers:

Number of Cards Held	Weight Factor
	One-Way Sequentials				Two-Way Sequentials
	Non-Sequential Deal		Sequential Deal		Non-Sequential Deal		Sequential Deal
	Non-Seq.	Sequential	Non-Seq.	Sequential	Non-Seq.	Sequential	Non-Seq.	Sequential
5	120	0	0	120	120	0	0	120
4	120	0	0	120	120	0	0	120
3	120	0	60	60	120	0	60	60
2	120	0	100	20	120	0	100	20
1 (A,K,J,T)	120	0	115	5	120	0	115	5
1 (Queen)	120	0	115	5	120	0	110	10
0	119	1	119	1	118	2	118	2

The number of Royal Flush hands that occur in each way to play are split into Sequential Royal Flushes and Non-Sequential Royal Flushes, by multiplying the number of Royal Flushes by the appropriate weighting factor shown above. All non-Royal Flush hands are simply multiplied by 120.

After computing the average value of all 32 ways to play each hand for both types of deals, the best Sequential-deal result is compared to the best Non-Sequential result to see if it is greater. If so, it means that it is better to go for the Sequential Royal Flush for that particular hand. When this is the case, the Sequential average value and Non-Sequential average values are both weighted according to how frequently each type of deal can occur. The following table illustrates the weighting factors that need to be used based on how many cards were held:

Number of Cards Held	Weight Factor
	One-Way Sequentials		Two-Way Sequentials
	Non-Seq.	Sequential	Non-Seq.	Sequential
5	119	1	119	1
4	119	1	119	1
3	118	2	118	2
2	114	6	114	6
1 (A,K,J,T)	96	24	72	48
1 (Queen)	96	24	96	24
0	120		120

When the average value of the best play is the same for both types of deals, it is simply multiplied by 120 since the order of the cards did not make a difference.

Finally, the total number of permutations for the entire game is the same as the regular version, multiplied by 14,400 (120 × 120 = 14,400). The first 120 is for the number of ways that the five cards can be arranged on the deal (5 × 4 × 3 × 2 × 1), and the other 120 is for the number of ways the five cards can be arranged on the draw.