Mystery Bonus Poker

Mystery Bonus Poker is available at online casinos which use Realtime Gaming software. The game is based on short-pay Jacks or Better except immediately after placing a bet, one of the nine paying hands is randomly selected as the Bonus Hand for that round. Each Bonus Hand has its own paytable, where the selected hand has an increased payout. Therefore, there are nine different strategies - one for each Bonus Hand.

Generally speaking, the closer to the bottom of the paytable the Bonus Hand is, the higher the return of the paytable. For example, when the Bonus Hand is Jacks or Better, the paytable returns 118.0993% with perfect play. Obviously, the probability of any given hand being selected as the Bonus Hand cannot be simply 1 in 9 (if it were, the combined return for the game would be 101.8810%). Instead, each hand is weighted - with the higher-paying Bonus Hand paytables being selected less often than the others.

I believe the true combined overall return for the game is just below 99%. Since I don't know the weighting of when each hand is selected as the Bonus Hand, I played 1,000 hands and recorded the number of times each hand was selected. The following table shows the number of times each hand was selected as the bonus hand, and the combined total average for the game by multiplying each bonus hand's paytable by the frequency with which it was selected, and summing the results.

Hand	Count	Probability	Paytable	Contribution
Royal Flush	110	11.0%	97.1035%	10.6814%
Straight Flush	184	18.4%	96.4482%	17.7465%
Four of a Kind	145	14.5%	97.1932%	14.0930%
Full House	104	10.4%	98.3151%	10.2248%
Flush	182	18.2%	100.0037%	18.2007%
Straight	157	15.7%	97.3424%	15.2828%
Three of a Kind	69	6.9%	103.4644%	7.1390%
Two Pair	35	3.5%	108.9596%	3.8136%
Jacks or Better	14	1.4%	118.0993%	1.6534%
Totals	1,000	100.0%	98.8351%

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];

    bool Flush =

        (S1 == S2) &&
        (S2 == S3) &&
        (S3 == S4) &&
        (S4 == S5);

    if (R1 > R2) { R1 ^= R2; R2 ^= R1; R1 ^= R2; }
    if (R1 > R3) { R1 ^= R3; R3 ^= R1; R1 ^= R3; }
    if (R1 > R4) { R1 ^= R4; R4 ^= R1; R1 ^= R4; }
    if (R1 > R5) { R1 ^= R5; R5 ^= R1; R1 ^= R5; }
    if (R2 > R3) { R2 ^= R3; R3 ^= R2; R2 ^= R3; }
    if (R2 > R4) { R2 ^= R4; R4 ^= R2; R2 ^= R4; }
    if (R2 > R5) { R2 ^= R5; R5 ^= R2; R2 ^= R5; }
    if (R3 > R4) { R3 ^= R4; R4 ^= R3; R3 ^= R4; }
    if (R3 > R5) { R3 ^= R5; R5 ^= R3; R3 ^= R5; }
    if (R4 > R5) { R4 ^= R5; R5 ^= R4; R4 ^= R5; }

    if (Flush)
    {

        if (R1 == 8)
        {
            Hand = 9;           // 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))))
        {
            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 >= 9)) || 
                 ((R2 == R3) && (R2 >= 9)) || 
                 ((R3 == R4) && (R3 >= 9)) || 
                 ((R4 == R5) && (R4 >= 9)))
        {
            Hand = 1;           // Jacks or Better
        }
    }

    return Hand;
}