Jacks or Better
The following
strategy is my "intermediate strategy" for jacks or better video
poker. Using the strategy on a full
pay machine will result in an expected return of 99.52%.
Compared to the optimal strategy return of 99.54%, mistakes in the
simple strategy will cost 0.03%, or one total bet every 3805 hands.
To use the strategy look up all viable ways to play an initial
hand on the following list and elect that which is highest on the
list. A "high card" means a jack or higher.
- Full house or better
- 4 to a royal flush
- Straight, three of a kind, or flush
- 4 to a straight flush
- Two pair
- High pair
- 3 to a royal flush
- 4 to a flush
- Low pair
- 4 to an outside straight
- 3 to a straight flush (high cards-gaps>=0)
- 2 suited high cards
- 4 to an inside straight w/ 3-4 high cards
- 3 to a straight flush (high cards-gaps=-1)
- J/Q/K unsuited
- J/Q unsuited
- 10/J suited
- J/K, Q/K unsuited
- 10/Q suited
- J/A, Q/A, K/A unsuited
- 10/K suited
- One high card
- 3 to a straight flush (high cards-gaps=-2)
- Discard everything
Note: The number of high cards in holding 3 to a straight
flush is roughly offset by the number of gaps. When evaluating 3 to
a straight flush subtract the number of gaps from the number of high
cards.
Terms:
High card: A jack, queen, king, or ace. These cards are
retained more often because if paired up they return the original
bet.
Outside straight: An open ended straight that can be
completed at either end, such as the cards 7,8,9,10.
Inside straight: A straight with a missing inside card,
such as the cards 6,7,9,10. In addition A,2,3,4 and J,Q,K,A also
count as inside straights because they are at an extreme end.
Gap: The number of ranks needed to fill in the middle of a
straight flush. For example a 6,7,8 would have 0 gaps, a 6,7,9 would
have 1, and a 6,7,10 would have 2. The following are considered to
have 2 gaps because they are at extreme ends: A,2,3; A,2,4; A,3,4;
J,Q,A; J,K,A; and Q,K,A. The following are considered to have 1 gap
because they are close to an extreme end: 2,3,4 and J,Q,K.
Example: Suppose you have the following hand.
The top two plays are (1) keep the three to a straight flush and
(2) keep two to a royal flush. The number of gaps to the straight
flush is 2 and the number of high cards is also 2. So gaps-high
cards=0. The table shows that 3 to a straight flush, where
gaps-highcards>=0, beats two suited high cards, so go keep the 3
cards to the straight flush.
Comparison to Optimal Strategy
The following table
compares the probability and return of each hand under both the
simple strategy and the optimal strategy.
| Simple Strategy to Optimal Strategy
Comparison |
| Hand |
Pays |
Probability |
Return |
| Interm. |
Optimal |
Interm. |
Optimal |
| Royal flush |
800 |
0.000025 |
0.000025 |
0.020204 |
0.019807 |
| Straight flush |
50 |
0.000114 |
0.000109 |
0.005696 |
0.005465 |
| Four of a kind |
25 |
0.002362 |
0.002363 |
0.059039 |
0.059064 |
| Full house |
9 |
0.011507 |
0.011512 |
0.103565 |
0.10361 |
| Flush |
6 |
0.011171 |
0.011015 |
0.067029 |
0.066087 |
| Straight |
4 |
0.011122 |
0.011229 |
0.04449 |
0.044917 |
| Three of a kind |
3 |
0.074421 |
0.074449 |
0.223263 |
0.223346 |
| Two pair |
2 |
0.129261 |
0.129279 |
0.258523 |
0.258558 |
| Pair |
1 |
0.213368 |
0.214585 |
0.213368 |
0.214585 |
| Nothing |
0 |
0.546648 |
0.545435 |
0 |
0 |
| Total |
|
1 |
1 |
0.995176 |
0.995439 |
The next table is a frequency distribution of the error, or
difference in expected return, between the simple strategy and the
optimal strategy.
| Error Frequency |
| Error |
Number |
Probability |
| 0 |
2576244 |
99.125958% |
| .01% to .99% |
5064 |
0.194847% |
| 1% to 1.99% |
1872 |
0.072029% |
| 2% to 2.99% |
2820 |
0.108505% |
| 3% to 3.99% |
5496 |
0.211469% |
| 4% to 4.99% |
4656 |
0.179149% |
| 5% to 5.99% |
2376 |
0.091421% |
| 6% to 6.99% |
432 |
0.016622% |
| 7% to 7.99% |
0 |
0% |
| 8% to 8.99% |
0 |
0% |
| 9% to 9.99% |
0 |
0% |
| 10% to 10.99% |
0 |
0% |
| 11% to 11.99% |
0 |
0% |
| 12% to 12.99% |
0 |
0% |
| 13% to 13.99% |
0 |
0% |
| 14% to 14.99% |
0 |
0% |
| 15% to 15.99% |
0 |
0% |
| Total |
2598960 |
100% |
Other Video Poker Games and Information
Jacks or
better simple
strategy.
Jacks or better optimal
strategy.
Deuces wild simple
strategy.
Deuces wild optimal
strategy.
Jacks or better quiz.
Go
to the video poker main
page.
Go to optimal strategy for deuces
wild.
Go to expected
return tables for other forms of video poker.
Jacks or better
practice
quiz.
