Royal Draw

Last update: November 8, 2006

Royal Draw is a video poker variation by Bally I noticd at the Suncoast in Las Vegas on November 7, 2006. The rules are the same as conventional video poker except the player plays the Royal Draw bonus with any four of a kind, in addition to his regular four of a kind win. The bonus round is like another hand of video poker except with a 13-card deck, one each of the 13 cards of a suit chosen by the player. The pay table in the bonus round is the same as the base game, based on the same number of coins bet as the initiating game. Comparing the "9/6" Royal Draw game to "9/6" Jacks or Better, the former will have 3.317 times as many royals.

Proper strategy in the bonus round is to go for the royal, with the exception to always keep a pat straight flush. Following optimal strategy, the return table of the bonus round is as follows.

Royal Draw Bonus Round Return Table
Hand	Payoff	Combinations	Probability	Return
Royal flush	800	436939	0.024745	19.796025
Straight flush	50	282877	0.01602	0.801004
Flush	6	16937830	0.959235	5.755409
Total		17657646	1	26.352438

The lower right cell shows the bonus has an average value of 26.352438 times the amount bet. Adding that to the value of a four of a kind (50) results in an average win of 76.352438 for a four of a kind. The following is the pay table for the "9/6" game I noticed at the Suncoast, substituting the average value for a four of a kind.

Royal Draw "9/6" Pay Table
Hand	Payoff	Combinations	Probability	Return
Royal flush	800	473481924	0.000024	0.019003
Straight Flush	50	2172269688	0.000109	0.005449
Four of a Kind + Bonus	76.352438	47014134108	0.002359	0.180083
Full House	9	228947750892	0.011486	0.103372
Flush	6	221544090528	0.011114	0.066686
Straight	4	255600824868	0.012823	0.051291
Three of a kind	3	1476003456204	0.074047	0.222142
Two pair	1	2558163543084	0.128337	0.128337
Pair	1	4214845162188	0.211448	0.211448
Nonpaying hand	0	10928465803716	0.548254	0
Total		19933230517200	1	0.987811

Here is the "9/6" pay table, breaking down the possible Royal Draw bonus events. Combinations are to 15 significant digits (a constraint I hate in Excel).

Royal Draw "9/6" Pay Table
Hand	Payoff	Combinations	Probability	Return
Royal flush	800	8,360,576,201,390,900	0.000024	0.019003
Straight Flush	50	38,357,169,167,234,400	0.000109	0.005449
Four of a kind + royal flush	850	20,542,308,743,015,400	0.000058	0.049609
Four of a kind + straight flush	100	13,299,217,214,068,700	0.000038	0.003778
Four of a kind + flush	56	796,317,411,118,506,000	0.002262	0.126696
Full House	9	4,042,678,337,747,120,000	0.011486	0.103372
Flush	6	3,911,947,123,935,380,000	0.011114	0.066686
Straight	4	4,513,308,882,827,140,000	0.012823	0.051291
Three of a kind	3	26,062,746,524,426,700,000	0.074047	0.222142
Two pair	1	45,171,146,253,883,000,000	0.128337	0.128337
Pair	1	74,424,243,818,728,300,000	0.211448	0.211448
Nonpaying hand	0	192,970,980,485,123,000,000	0.548254	0
Total		351,973,928,109,115,000,000	1	0.987811

The rest are hypothetical pay tables, which may or may not ever exist in a real casino.

Royal Draw "7/5" Pay Table
Hand	Payoff	Combinations	Probability	Return
Royal flush	800	491854620	0.000025	0.01974
Straight Flush	50	2154468204	0.000108	0.005404
Four of a Kind + Bonus	76.352438	47005734660	0.002358	0.180051
Full House	7	228890267460	0.011483	0.08038
Flush	5	216500514576	0.010861	0.054306
Straight	4	260261261016	0.013057	0.052227
Three of a kind	3	1475241247320	0.074009	0.222027
Two pair	1	2556431280000	0.12825	0.12825
Pair	1	4216659716952	0.211539	0.211539
Nonpaying hand	0	10929594172392	0.54831	0
Total		19933230517200	1	0.953925

Royal Draw "8/5" Pay Table
Hand	Payoff	Combinations	Probability	Return
Royal flush	800	491854620	0.000025	0.01974
Straight Flush	50	2154468204	0.000108	0.005404
Four of a Kind + Bonus	76.352438	47005734660	0.002358	0.180051
Full House	8	228890267460	0.011483	0.091863
Flush	5	216500514576	0.010861	0.054306
Straight	4	260261261016	0.013057	0.052227
Three of a kind	3	1475241247320	0.074009	0.222027
Two pair	1	2556431280000	0.12825	0.12825
Pair	1	4216659716952	0.211539	0.211539
Nonpaying hand	0	10929594172392	0.54831	0
Total		19933230517200	1	0.965408

Royal Draw "9/5" Pay Table
Hand	Payoff	Combinations	Probability	Return
Royal flush	800	491856684	0.000025	0.01974
Straight Flush	50	2153793276	0.000108	0.005403
Four of a Kind + Bonus	76.352438	47005841988	0.002358	0.180052
Full House	9	228890861892	0.011483	0.103346
Flush	5	216486883920	0.010861	0.054303
Straight	4	260255023608	0.013056	0.052225
Three of a kind	3	1475246648808	0.074009	0.222028
Two pair	1	2556440400816	0.12825	0.12825
Pair	1	4216746386376	0.211544	0.211544
Nonpaying hand	0	10929512819832	0.548306	0
Total		19933230517200	1	0.976891

Royal Draw "8/6" Pay Table
Hand	Payoff	Combinations	Probability	Return
Royal flush	800	473481924	0.000024	0.019003
Straight Flush	50	2172269688	0.000109	0.005449
Four of a Kind + Bonus	76.352438	47014134108	0.002359	0.180083
Full House	8	228947750892	0.011486	0.091886
Flush	6	221544090528	0.011114	0.066686
Straight	4	255600824868	0.012823	0.051291
Three of a kind	3	1476003456204	0.074047	0.222142
Two pair	1	2558163543084	0.128337	0.128337
Pair	1	4214845162188	0.211448	0.211448
Nonpaying hand	0	10928465803716	0.548254	0
Total		19933230517200	1	0.976325

Royal Draw "10/6" Pay Table
Hand	Payoff	Combinations	Probability	Return
Royal flush	800	473734764	0.000024	0.019013
Straight Flush	50	2173028208	0.000109	0.005451
Four of a Kind + Bonus	76.352438	47036533668	0.00236	0.180169
Full House	10	229024825812	0.01149	0.114896
Flush	6	221668234968	0.011121	0.066723
Straight	4	254739744708	0.01278	0.051119
Three of a kind	3	1476869429076	0.074091	0.222272
Two pair	1	2559283090740	0.128393	0.128393
Pair	1	4211166789108	0.211264	0.211264
Nonpaying hand	0	10930795106148	0.54837	0
Total		19933230517200	1	0.9993