The Wizard of Odds

Jacks or Better Simple

Last Update: Sep 24, 2001

The following strategy is my "simple strategy" for jacks or better video poker. Using the strategy on a fullpay machine will result in an expected return of 99.46%.Compared to the optimal strategy return of 99.54%, mistakes in the simple strategy will cost 0.08%, or one total bet every 1178 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.

 

  1. Four of a kind, straight flush, royal flush
  2. 4 to a royal flush
  3. Three of a kind, straight, flush, full house
  4. 4 to a straight flush
  5. Two pair
  6. High pair
  7. 3 to a royal flush
  8. 4 to a flush
  9. Low pair
  10. 4 to an outside straight
  11. 2 suited high cards
  12. 3 to a straight flush
  13. 2 unsuited high cards (if more than 2 then pick the lowest 2)
  14. Suited 10/J, 10/Q, or 10/K
  15. One high card
  16. Discard everything

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 andJ,Q,K,A also count as inside straights because they are at an extreme end.

Example: Suppose you have the following hand.

The top three plays are (1) keep the low pair, (2) keep the 4 to a flush, and (3) keep the 2 suited high cards. The4 to a flush is listed highest and is thus the best play, so discard the 3 of hearts.

 

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
Simple Optimal Simple Optimal
Royal flush 800 0.000025 0.000025 0.020076 0.019807
Straight flush 50 0.000111 0.000109 0.005552 0.005465
Four of a kind 25 0.002363 0.002363 0.059067 0.059064
Full house 9 0.011517 0.011512 0.103657 0.10361
Flush 6 0.011087 0.011015 0.066521 0.066087
Straight 4 0.010637 0.011229 0.042547 0.044917
Three of a kind 3 0.074543 0.074449 0.223629 0.223346
Two pair 2 0.129552 0.129279 0.259104 0.258558
Pair 1 0.214437 0.214585 0.214437 0.214585
Nothing 0 0.545729 0.545435 0 0
Total 1 1 0.99459 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 2540016 97.732016%
.01% to .99% 5808 0.223474%
1% to 1.99% 12084 0.464955%
2% to 2.99% 6336 0.24379%
3% to 3.99% 7320 0.281651%
4% to 4.99% 11976 0.4608%
5% to 5.99% 11868 0.456644%
6% to 6.99% 1260 0.048481%
7% to 7.99% 216 0.008311%
8% to 8.99% 0 0%
9% to 9.99% 0 0%
10% to 10.99% 0 0%
11% to 11.99% 768 0.02955%
12% to 12.99% 36 0.001385%
13% to 13.99% 216 0.008311%
14% to 14.99% 840 0.032321%
15% to 15.99% 216 0.008311%
Total 2598960 100%

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Strategies

Full-Pay Jacks or Better:

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