This appendix presents my analysis of Chase the Royal video poker. The rules for Chase the Royal are as follows:
The game is based on conventional video poker. The player may choose among four different video poker variations and either 3-play, 5-play, or 10-play.
If the player is dealt a pair of jacks, queens, or kings and made a max coin bet then the player may exchange the high pair for 3 cards to a royal flush. This Chase the Royal option does not apply if the pair is part of a higher hand (for example a two pair) or if the player also has 4 cards to a straight or royal flush.
The 3 cards to a royal shall be chosen at random from among the 40 possible (4 suits by 10 ways to choose 3 ranks out of 5). The player may see the specific three cards before deciding to switch.
If the player opts to chase the royal then the other two cards will be dealt immediatly from the remaining 49 cards in the deck.
As an incentive to chase the royal a straight shall pay 10 and a flush shall pay 12 in chase the royal mode.
A dealt royal shall pay 2000, as opposed to the usual 800 per coin bet based.
Strategy
As in conventional video poker, the player should seek out the best pay table possible and play proper strategy. If the player has the opportunity to chase the royal, then the player should always do so.
Overall, the player will get 4.39 as many royal flushes as conventional video poker, at the expense of fewer low paying hands. The standard deviation is very high at 9.15 (for 9/6/5 double bonus), compared to the normal 5.55 for the same game. This game is well suited for the player who puts an emphasis on excitement, over bankroll preservation.
Jacks or Better
Chase the Royal — 6/5 Jacks or Better
Hand
Pays
Probability
Return
Dealt Royal Flush
2000
0.000002
0.003078
Royal Flush
800
0.000106
0.084992
Straight flush
50
0.000149
0.007472
Four of a kind
25
0.002092
0.05229
Full house
6
0.010519
0.063113
Flush
12
0.003606
0.043267
Flush
5
0.010911
0.054556
Straight
10
0.001865
0.018649
Straight
4
0.011283
0.045134
3 of a kind
3
0.06403
0.192091
2 pair
2
0.115907
0.231814
Pair
1
0.170233
0.170233
Nothing
0
0.609297
0
Total
1
0.966689
Triple Bonus
Chase the Royal — 8/5 Triple Bonus
Hand
Pays
Probability
Return
Dealt Royal Flush
2000
0.000002
0.003078
Royal flush
800
0.000108
0.086187
Straight flush
50
0.000148
0.00742
4 aces + 2-4
800
0.000071
0.056458
4 2-4 + A-4
400
0.000173
0.069043
4 aces + 5-K
160
0.00015
0.023953
4 2-4 + 5-K
80
0.00032
0.025622
4 5-K
50
0.001348
0.067387
Full house
8
0.009521
0.076164
Flush
12
0.003606
0.043267
Flush
5
0.011
0.054999
Straight
10
0.001865
0.018649
Straight
4
0.013745
0.054981
3 of a kind
2
0.064745
0.129491
Two pair
1
0.108976
0.108976
Jacks or better
1
0.165734
0.165734
Nothing
0
0.61849
0
Total
1
0.99141
Double Double Bonus
Chase the Royal — 8/5 Double Double Bonus
Hand
Pays
Probability
Return
Dealt Royal Flush
2000
0.000002
0.003078
Royal flush
800
0.000106
0.085045
Straight flush
50
0.000148
0.007422
4 aces + 2-4
400
0.000062
0.024632
4 2-4 + A-4
160
0.000143
0.022911
4 aces + 5-K
160
0.000173
0.027752
4 2-4 + 5-K
80
0.000384
0.030754
4 5-K
50
0.001362
0.068089
Full house
8
0.009876
0.079006
Flush
12
0.003606
0.043267
Flush
5
0.010985
0.054926
Straight
10
0.001865
0.018649
Straight
4
0.012951
0.051804
3 of a kind
3
0.064935
0.194806
Two pair
1
0.109796
0.109796
Jacks or better
1
0.167249
0.167249
Nothing
0
0.616357
0
Total
1
0.989186
Bonus Poker Deluxe
Chase the Royal — 6/5 Bonus Poker Deluxe
Hand
Pays
Probability
Return
Dealt Royal Flush
2000
0.000002
0.003078
Royal flush
800
0.000106
0.084818
Straight flush
50
0.00015
0.007476
4 of a kind
80
0.00222
0.177599
Full house
6
0.007228
0.043368
Flush
12
0.003606
0.043267
Flush
5
0.010861
0.054306
Straight
10
0.001865
0.018649
Straight
4
0.013057
0.052227
3 of a kind
3
0.067824
0.203471
2 pair
1
0.095637
0.095637
Pair
1
0.184907
0.184907
Nothing
0
0.612539
0
Total
1
0.968803
7/5/4 Double Bonus
Chase the Royal — 7/5/4 Double Bonus
Hand
Pays
Probability
Return
Dealt Royal Flush
2000
0.000002
0.003078
Royal flush
800
0.000106
0.085072
Straight flush
50
0.00015
0.00749
4 aces
160
0.000224
0.035842
4 2-4
80
0.000527
0.042161
4 5-K
50
0.001363
0.06815
Full house
7
0.009844
0.068905
Flush
12
0.003606
0.043267
Flush
5
0.010919
0.054593
Straight
10
0.001865
0.018649
Straight
4
0.013101
0.052404
3 of a kind
3
0.064577
0.193732
Two pair
1
0.109409
0.109409
Jacks or better
1
0.170623
0.170623
Nothing
0
0.613686
0
Total
1
0.953376
Other Games
The following list shows the expected return with optimal strategy of other Chase the Royal games and pay tables.
