Video 789bet login Poker Appendix 5
April 15, 2022 | by Crouse Linwood
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.
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 789bet login 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 2139799619 0.000107 800 0.085879
Straight flush 2991354378 0.00015 50 0.007503
4 aces 4466814888 0.000224 160 0.035854
4 2-4 10457017608 0.000525 80 0.041968
4 5-K 26908853040 0.00135 50 0.067497
Full house 194770198320 0.009771 9 0.08794
Flush 71862459498 0.003605 12 0.043262
Flush 221014834488 0.011088 6 0.066527
Straight 37170237671 0.001865 10 0.018647
Straight 309160021656 0.01551 5 0.077549
3 of a kind 1269291897844 0.063677 3 0.191032
Two pair 2147282520349 0.107724 1 0.107724
Jacks or better 3292244905073 0.165164 1 0.165164
Nothing 12343469602767 0.619241 0 0
Total 19933230517200 1 0.996546
royal flush bonus 0.001847
grand total 0.998393
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 0.976726
Bonus Poker Deluxe 6,5 0.968802
Double Bonus 9,6,5 0.998393
Double Bonus 9,6,4 0.984084
Double Bonus 7,5,4 0.953374
Double Double Bonus 8,5 0.989184
Double Double Bonus 7,5 0.979434
Double Double Bonus 6,5 0.969874
Jacks or Better 6,5 0.966687
Triple Double Bonus 8,5 0.991407
Triple Double Bonus 7,5 0.98189
Triple Double Bonus 6,5 0.972376
Where to play Chase the Royal. This IGT list is a somewhat out of date but a good place to start looking.
Practice Chase the Royal for free at videopoker.com.