Jacks or Better Intermediate Strategy
Written July 21, 2008 by Jack Jones
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% |
Better known as “The Wizard of Odds”, Michael Shackleford uses math and computer analysis to determine optimal playing strategy for all casino games. His work can be found on his website, WizardofOdds.com with player strategies and probabilities on most of the casino games. Michael lives in Las Vegas and in his spare time likes to college license plates and gamble.
You can read more about Michael’s work at his website, WizardofOdds.com