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| Strategies for playing Video Poker |
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Playing Strategy
House Edge
Advice and Comments
Appendices
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Video Poker Appendix 4
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.
StrategyAs 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 few 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 BonusSo 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 |
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 |
|
|
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0.998393 |
Other GamesThe 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 |
LinksWhere
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.
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