Perfect 789Bet Strategy for Jacks

789Bet

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 789Bet 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.

Play jacks or better.

Play deuces wild.

Play double bonus.

Play joker poker.