In my opinion many online casinos are too stingy when setting the odds on their games. They think they will make more money that way but I believe they are misguided, because when players lose too quickly it's not fun, and those players might not come back.
Bodog is one of the few casinos that understands this. They offer generous odds to let you play longer and get you a better chance of winning. Among their generous offerings are Full-Pay Jacks or Better returning 99.54%, six other video poker games paying over 99%, single-zero roulette, two blackjack variants with a house edge under 0.2%, and my favorite, Pick 'em Poker, returning 99.95%!
Kudos to Bodog for not being afraid to give their players a good gamble.(Visit Bodog)
Try free Jacks or Better at Bodog. One click and you're in:
No popups, no download, no registration, no B.S., just the game.
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.
In the unlikely event the player receives a royal flush with maximum coins bet on all hands then each 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 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 much 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.
9/6/5 Double Bonus
So far the best pay table I have seen for this game is 9/6/5 Double Bonus. I have seen this game and pay table at the $1 level at the Texas Station and the 25 cents, 50 cents, and $1 level at the Plaza. Without the Chase the Royal feature the expected return is 0.978062. The probability of a qualifying pair to switch is 0.097464. The expected value per coin of a jack-king pair is 1.446068. The average expected value of 3 to a royal in chase the royal mode is 1.635714. Overall the player gives up 0.140939 in expected value by giving up the jack-king pairs but gets back 0.159423 in chase the royal mode. The player also gets 0.001847 in expected value from the bonus for having a royal flush on every hand. This is very unlikely to happen unless the player is dealt a pat royal flush and this figure ignores the probability of drawing to a royal flush on every hand (this probability varies depending on the number of hands played, but for the record in 3-play mode only it add another 0.000004 in expected value). The overall return for 9/6/5 Double Bonus is 0.998393.
The following table shows each final hand, the associated probability, and the contribution to the total return. Note that the straight and flush is divided according to whether in or out of chase the royal mode.
Chase the Royal - 9/6/5 Double Bonus
Hand
Combinations
Probability
Pays
Return
Royal flush
2139982231
0.000107
800
0.085886
Straight flush
2991445683
0.00015
50
0.007504
4 aces
4466814888
0.000224
160
0.035854
4 2-4
10457017608
0.000525
80
0.041968
4 5-K
26908257060
0.00135
50
0.067496
Full house
194768013060
0.009771
9
0.087939
Flush
71870403110
0.003606
12
0.043267
Flush
221014834488
0.011088
6
0.066527
Straight
37174346436
0.001865
10
0.018649
Straight
309160021656
0.01551
5
0.077549
3 of a kind
1269268986975
0.063676
3
0.191028
Two pair
2147253122420
0.107722
1
0.107722
Jacks or better
3292146162945
0.165159
1
0.165159
Nothing
12343611108640
0.619248
0
0
Total
19933230517200
1
0
0.996548
Royal flush bonus
0
0
0
0.001847
grand total
0
0
0
0.998395
Other Games
The following list shows the expected return with optimal strategy of other Chase the Royal games and pay tables.
Chase the Royal Return Table
Game
Pay table
Return
Bonus Poker Deluxe
7,5
0.976727
Bonus Poker Deluxe
6,5
0.968803
Double Bonus
9,6,5
0.998395
Double Bonus
9,6,4
0.984086
Double Bonus
7,5,4
0.953376
Double Double Bonus
8,5
0.989186
Double Double Bonus
7,5
0.979436
Double Double Bonus
6,5
0.969877
Jacks or Better
6,5
0.966689
Triple Double Bonus
8,5
0.99141
Triple Double Bonus
7,5
0.981893
Triple Double Bonus
6,5
0.97238
Links
Where to play Chase the Royal. This IGT list is a somewhat out of date but a good place to start looking.
Chase the Royal