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Simple Jacks or Better Strategy

Written July 21, 2008 by Jack Jones

The following strategy is my “simple strategy” for jacks or better video poker. Using the strategy on a full pay 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.

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
2 suited high cards
3 to a straight flush
2 unsuited high cards (if more than 2 pick then pick lowest 2)
Suited 10/J, 10/Q, or 10/K
One high card
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 and J,Q,K,A also count as inside straights because they are at an extreme end.

Example: Suppose you have the following hand.

3 clubs jack clubs five clubs queen clubs three hearts

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. The 4 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
Hand	Pays	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%

HTML clipboardBetter 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

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