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Intermediate strategy for Jacks or Better video poker
Last update: July 25, 2006
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.
Four of a kind, straight flush, royal flush
4 to a royal flush
Three of a kind, straight, flush, full house
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)
AKQJ unsuited
2 suited high cards
4 to an inside straight with 3 high cards
3 to a straight flush (high cards-gaps=-1)
KQJ unsuited
QJ unsuited
JT suited
KQ, KJ unsuited
QT suited
AK, AQ, AJ unsuited
KT 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.