Sequential Royal Flush Games

Games which feature a payline for a Sequential Royal Flush require additional handling in order to analyze them accurately. Each hand actually needs to be analyzed twice: once under the assumption that the hand was dealt with cards that are not in sequential position, and again under the assumption that the cards were dealt in sequential position.

In some cases, the value of the second analysis is greater than the value of the first analysis. When this happens, the two plays need to be weighted according to how often the cards held could be dealt in sequential position. The following table illustrates these numbers. Note that each number has already been multiplied by a weighting factor so that the number of possibilities for each number of cards held adds up to 120 (which corresponds to the number of ways to arrange the 5 cards):

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.

Sequential Royal Flush Analyzers

I have Sequential Royal Flush analyzers for the following games: