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The situation here is an 8/5 Jacks or Better progressive with the royal at
$3000. Normally, we do not break up a high pair for a 3-card royal, but the
return on the pair of Kings is 7.6827 and the return on the 3-card royal is
14.3617. Go for it!
Video Poker Review #5
This is a continuation of our discussion of the optimal play for hands received at a 9/6 "Jacks or Better" video
poker game. The figure shown is the average return for making that play if five coins have been wagered.
The hand which gives the highest return is the proper play.
How would you play these?
Hand #1:

Hold J, Q: 2.4961
Hold J, Q, A: 2.2803
So, don't hold an Ace "kicker".
Hand #2:

Hold 3 spades: 6.6836
Hold 8, 9, 10, J: 3.7234
The 3-card Royal gives a better return than the straight.
Hand #3:

Hold 9, 10, J, Q: 4.0426
Hold J, Q: 3.0339
But, the straight is better than a 2-card Royal.
Hand #4:

Hold J, Q: 2.5492
Hold 3 clubs: 2.2202
There's no future in drawing to a 3-card flush here.
Hand #5:

Hold J, Q: 3.0019
Hold J, Q, K, A: 2.9787
That's a close call, but you need all the edge you can get.
Hand #6:

Discard all: 1.7907
Hold 5, 6, 8, 9: 1.7021
If the Straight paid more, we'd go for it. But at only 20 for 5,
it's a "dump".
Hand #7:

Hold 4 diamonds: 92.7660
Just wanted to show you the value of a 4-card Royal. (I never
hit them, either.)
Hand #8:

Hold J, Q: 2.4900
Hold 10, Q: 2.3928
The 10 in the 2-card Royal drags down the value of that play
since the possibility of a high-pair "push" is reduced.
Hand #9:

Hold J, Q, K: 7.3404
Hold 4 diamonds: 6.7021
This particular Royal draw is the best to have, so ignore the
flush.
Hand #10:

Hold 4 spades: 5.7447
Hold 3, 4, 5: 2.8400
Don't let the 3-card Straight Flush tempt you here.
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