Jacks or Better (Grand Virtual Progressive)

This game is the progressive jackpot version of Jacks or Better which is available at online casinos that use Grand Virtual software. To win the jackpot you have to be dealt a Sequential Royal Flush in Spades (both directions count). The strategy is the same regardless of the amount of the jackpot, because there is no strategy involved in the deal portion of a hand.

The odds of winning the jackpot are 1 in 155,937,600. By comparison, the odds of winning the Powerball are 1 in 146,107,962. The base return of the game when the jackpot resets at 25,000 coins is 98.3954%. Every 5,000 coins adds 0.000641% to the long-term return of the game. The break-even point is when the jackpot reaches 12,536,039 coins (2,507,207.8 times the bet). I would say that it is extremely difficult to win the jackpot, which means it would probably grow for a long time before being won. Yet, I doubt the jackpot would ever reach the break-even point before being won. Personally I would recommend avoiding this game unless you feel extremely lucky. If you want to play Jacks or Better at a Grand Virtual casino, you should play their regular version which uses the full-pay paytable that returns 99.5439%.

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;
}

Sequential Spade Royal Flush on the Deal

Because this game has a jackpot for a Sequential Royal Flush in Spades on the deal, some adjustments are necessary to accurately analyze the game. Unlike regular Sequential Royal Flush games, there is no strategy involved because the Sequential Royal Flush must occur on the deal. Therefore, we only need to multiply the number of hands that are possible on the deal by 120, and do not need to do the same for the number of hands possible on the draw.

For the majority of starting hands, the number of permutations is calculated by simply multiplying by 120. When the starting hand is a Royal Flush, there are two weight factors that need to be fiddled with because the Sequential Royal Flush that wins the jackpot must be in Spades. The weight factor applied to this hand from the Deck Simplification is 4 because there are four possible Royal Flush hands, one for each suit. We also need to multiply by 120 to accommodate the number of ways to arrange the five cards. Since there are only 2 ways to be dealt a Sequential Royal Flush, and only 1 of the 4 suits counts for the jackpot, the number of times a jackpot-winning permutation occurs must be weighted by (1 × 2) ÷ (4 × 120), and the number of possible non-jackpot Royal Flush starting hands is weighted by (3 × 118) ÷ (4 × 120).

No other modifications are necessary. The strategy for the game always remains the same regardless of how large the jackpot is.