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This strategy was designed to be used for a machine with
the following payoff table (per coin based on maximum coins bet), although
it can be used without much error against any jacks or better machine.
The table also shows the probability of forming each hand, assuming perfect
play, the contribution to the expected return, and the overall expected
return.
|
Jacks or better |
| Hand |
Payoff |
Probability |
Return |
| Royal flush |
800 |
0.000025 |
0.019807 |
| Straight flush |
50 |
0.000109 |
0.005467 |
| Four of a kind |
25 |
0.002363 |
0.059064 |
| Full House |
9 |
0.011512 |
0.103610 |
| Flush |
6 |
0.011014 |
0.066087 |
| Straight |
4 |
0.011230 |
0.044919 |
| Three of a kind |
3 |
0.074449 |
0.223346 |
| Two pair |
2 |
0.129279 |
0.258558 |
| Jacks or better |
1 |
0.214585 |
0.214585 |
| Total |
|
0.454566 |
0.995441 |
To use this strategy look up all reasonable ways to play
a hand and choose the play that is highest on the list. The numbers on
the right represent the average return. These numbers can vary depending
on the discards, those shown are for a typical case. Lets try an example.
If you have a suited ten and jack, an unsuited queen, and two trash cards,
what should you do? Should you keep the suited ten jack, retaining hope
for a flush, straight flush, and royal flush, or keep the jack and queen,
increasing your odds of forming a high pair. The unsuited jack and queen
appear higher on the list than the suited ten and jack, thus keep the
jack and queen. The numbers in parenthesis represent the expected return,
although the number listed is just an example and can vary depending on
the discards. The expected returns are not in order because of the penalty
card problem.
From the numbers on the right the expected return of keeping
the 10 and jack is 0.4968 and that of the jack and queen is 0.4980, thus
keeping the jack and queen is the better play.
While this strategy is 100% accurate (as far as I know) it
is at a cost of being rather long and time consuming to use. Many players
opt to use shorter strategies that only differ in uncommon and/or borderline
plays. I have no problem with this but personally I like to get every
penny I can out of the machine.
- Pat royal flush (800.0000)
- Pat straight flush (50.0000)
- Pat four of a kind (25.0000)
- 4 to a royal flush (18.4894)
- Pat full house (9.0000)
- Pat flush (6.0000)
- 3 of a kind (4.3025)
- Pat straight (4.0000)
- 4 to a straight flush (3.5319)
- Two pair (2.59574)
- High pair (1.5365)
- 3 to a royal flush (1.4995)
- 4 to a flush (1.2766)
- 4 to an outside straight with 3 high cards (0.8723)
- Low pair (0.8237)
- 4 to an outside straight with 2 high cards (0.8085)
- 4 to an outside straight with 1 high cards (0.7447)
- 3 to a straight flush, spread 3, 1 high cards (0.7354)
- 4 to an outside straight with 0 high cards (0.6809)
- 3 to a straight flush, spread 5, 2 high cards (0.6429)
- 3 to a straight flush, spread 4, 1 high card (0.6392)
- 3 to a straight flush, spread 3, 0 high cards (0.6207)
- 2 suited high cards, queen highest (0.6004)
- 4 to an inside straight, 4 high cards (0.5957)
- 2 suited high cards, king highest (0.5821)
- 2 suited high cards, ace highest (0.5678)
- 3 to a straight flush, spread 5, 1 high card (0.5430)
- 4 to an inside straight, 3 high cards (0.5319) A
- 3 to a straight flush, spread 4, 0 high cards (0.5245)
- 2 unsuited high cards queen highest (0.4980)
- 2 to a royal flush, 10 and jack (0.4968) B
- 2 unsuited high cards king highest (0.4862)
- 2 to a royal flush, 10 and king (0.474869) C
- 2 unsuited high cards ace highest (0.474314)
- 4 to an inside straight, 2 high cards (0.4681)
- 2 to a royal flush, 10 and queen (0.4619)
- Jack only (0.4584)
- 3 unsuited high cards ace highest (0.4561)
- Queen only (0.466224)
- King only (0.463802)
- Ace only (0.465102)
- 2 to a royal flush, 10 and ace (0.460561)
- 3 to a straight flush, spread 5, 0 high cards (0.4431)
- 4 to an inside straight, 1 high card (0.4043)
- Garbage, discard everything (0.3597)
- 4 to an inside straight, 0 high cards (0.3404)
Rare Exceptions:
| A
|
3 to a straight flush, spread 5, with 1 high card vs.
4 to an inside straight, with 3 high cards: Normally the 3 to a straight
flush is the better play however if you must discard a straight penalty
card then go for the straight. For example if ace,king,queen,10,9
where the king,10,and 9 are suited. |
| B
|
Suited 10 and jack vs. an unsuited jack and king: If
there is no flush penalty card then keeping the 10 and jack then that
is the better play, otherwise keep the jack and king. |
| C
|
Suited 10, king vs. king only: Normally the suited
ten and king is better than the king alone, however if you must discard
a 9 and a flush penalty card then hold the king only. |
Terms:
- Outside straight : An open ended straight that can be completed
at either end, such as (7,8,9,10).
- Inside straight : A straight with a missing inside card, such
as (6,7,9,10).
- Penalty card : Sometimes one must discard a potentially useful
card. For example if you had an unsuited 10, jack, and queen the ten
would be called a penalty card since you should discard it despite the
fact it could be beneficial if you kept it.
Methodology
To determine the above strategy I created a program can determine
the expected return of the best play of any hand. The way it works is
to consider all 32 ways to play a hand. For every play the program systematically
scores the held cards with every possible set of discards and averages
the results. The play that yields the greatest average is determined to
be the best play and the specific statistics for that play are displayed.
The program can also show the statistics for non-optimal plays. Using
this program, it was then a time consuming task to try numerous borderline
hands and rank them in order of expected return.
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