Royal Draw is a video poker variation by Bally. I noticed it 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
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.
