Last Updated: August 25, 2013

Mississippi Stud

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Introduction

Mississippi Stud is a poker-based table game by ShuffleMaster. It can be played in several Mississippi casinos, as well as a few other states. Here in Las Vegas, it can be played at the Paris. The game is simple to play. Wins are based only on the player's final five card hand. The skill is in deciding how much to raise, or fold, as the cards are revealed.

Rules

  1. Player makes ante wager.
  2. Dealer gives each player two cards face down, and three community cards face down. Player may examine his own cards.
  3. Player may fold or make a "3rd Street" bet, of one to three times the ante.
  4. First community card is turned over.
  5. Player may fold or make a "4th Street" bet, of one to three times the ante.
  6. Second community card is turned over.
  7. Player may fold or make a "5th Street" bet, of one to three times the ante.
  8. Third community card is turned over.
  9. All wagers paid according to the following pay table.

Mississippi Stud Pay Table

Hand Pays
Royal Flush 500 to 1
Straight Flush 100 to 1
Four of a Kind 40 to 1
Full House 10 to 1
Flush 6 to 1
Straight 4 to 1
Three of a Kind 3 to 1
Two Pairs 2 to 1
Pair of Jacks or Better 1 to 1
Pair of 6s thru 10s Push
All other Loss

Strategy

The following strategy was created by Joseph Kisenwether, with permission to publish here. I can verify that this strategy is indeed optimal.

Card Values

  • High = J to A
  • Mid = 6 to 10
  • Low = 2 to 5

2 Cards

  1. Raise 3x with any pair.
  2. Raise 1x with at least one high card.
  3. Raise 1x with two mid cards.
  4. Raise 1x with 6/5 suited.
  5. Fold all others.

3 Cards

  1. Raise 3x with any made hand (mid pair or higher).
  2. Raise 3x with royal flush draw.
  3. Raise 3x with straight flush draw, with no gaps, 567 or higher.
  4. Raise 3x with straight flush draw, with one gap, and at least one high card.
  5. Raise 3x with straight flush draw, with two gaps, and at least two high cards.
  6. Raise 1x with any other three suited cards.
  7. Raise 1x with a low pair.
  8. Raise 1x with two or three high cards.
  9. Raise 1x with three mid cards.
  10. Raise 1x with one high card and one mid card.
  11. Raise 1x with a straight draw, with no gaps, 456 or higher.
  12. Raise 1x with a straight draw, with one gap, and two mid cards.
  13. Fold all others.

4 Cards

  1. Raise 3x with any made hand (mid pair or higher).
  2. Raise 3x with any four to a flush.
  3. Raise 3x with four to an outside straight, 8 high or better.
  4. Raise 1x with any other straight draw.
  5. Raise 1x with a low pair.
  6. Raise 1x with at least two high cards.
  7. Raise 1x with one high card and at least two mid cards.
  8. Raise 1x with one high card and two previous 3x raisess.
  9. Raise 1x with three mid cards and at least one previous 3x raise.
  10. Fold all others.

The following graphic version of my strategy was created and used with permission by Ray A.


Click on image for larger version.

Analysis

The following table shows number of combinations, probability, and contribution to the return of every possible hand and sequence of bets.

Mississippi Stud Return Table

3rd St. 4th St. 5th St. Hand Pays Combinations Probability Return
1 1 1 Loser -4 43594056 0.279561 -1.118244
1 1 1 Pair 6-10 0 5078808 0.032569 0
1 1 1 Pair J-A 4 5396544 0.034607 0.138428
1 1 1 Two pair 8 489888 0.003142 0.025133
1 1 1 Three of a kind 12 163296 0.001047 0.012566
1 1 1 Straight 16 216288 0.001387 0.022192
1 1 1 Flush 24 0 0 0
1 1 1 Full house 40 0 0 0
1 1 1 Four of a kind 160 0 0 0
1 1 1 Straight flush 400 0 0 0
1 1 1 Royal flush 2000 0 0 0
1 1 3 Loser -6 1079292 0.006921 -0.041528
1 1 3 Pair 6-10 0 4761396 0.030534 0
1 1 3 Pair J-A 6 5033856 0.032281 0.193687
1 1 3 Two pair 12 1516536 0.009725 0.116703
1 1 3 Three of a kind 18 539832 0.003462 0.062313
1 1 3 Straight 24 130944 0.00084 0.020153
1 1 3 Flush 36 185808 0.001192 0.042896
1 1 3 Full house 60 14040 0.00009 0.005402
1 1 3 Four of a kind 240 1560 0.00001 0.002401
1 1 3 Straight flush 600 672 0.000004 0.002586
1 1 3 Royal flush 3000 0 0 0
1 1 Fold n/a -3 7569216 0.04854 -0.14562
1 3 1 Loser -6 261252 0.001675 -0.010052
1 3 1 Pair 6-10 0 34236 0.00022 0
1 3 1 Pair J-A 6 41760 0.000268 0.001607
1 3 1 Two pair 12 144 0.000001 0.000011
1 3 1 Three of a kind 18 48 0 0.000006
1 3 1 Straight 24 6432 0.000041 0.00099
1 3 1 Flush 36 0 0 0
1 3 1 Full house 60 0 0 0
1 3 1 Four of a kind 240 0 0 0
1 3 1 Straight flush 600 0 0 0
1 3 1 Royal flush 3000 0 0 0
1 3 3 Loser -8 88644 0.000568 -0.004548
1 3 3 Pair 6-10 0 3459060 0.022182 0
1 3 3 Pair J-A 8 4124256 0.026448 0.211585
1 3 3 Two pair 16 1691352 0.010846 0.173541
1 3 3 Three of a kind 24 750168 0.004811 0.115457
1 3 3 Straight 32 7968 0.000051 0.001635
1 3 3 Flush 48 22440 0.000144 0.006907
1 3 3 Full house 80 76248 0.000489 0.039117
1 3 3 Four of a kind 320 8472 0.000054 0.017385
1 3 3 Straight flush 800 720 0.000005 0.003694
1 3 3 Royal flush 4000 240 0.000002 0.006156
1 3 Fold n/a -5 1152 0.000007 -0.000037
1 Fold n/a n/a -2 11966976 0.076742 -0.153484
3 1 1 Loser -6 2027520 0.013002 -0.078013
3 1 1 Pair 6-10 0 0 0 0
3 1 1 Pair J-A 6 0 0 0
3 1 1 Two pair 12 304128 0.00195 0.023404
3 1 1 Three of a kind 18 101376 0.00065 0.011702
3 1 1 Straight 24 0 0 0
3 1 1 Flush 36 0 0 0
3 1 1 Full house 60 0 0 0
3 1 1 Four of a kind 240 0 0 0
3 1 1 Straight flush 600 0 0 0
3 1 1 Royal flush 3000 0 0 0
3 1 3 Loser -8 0 0 0
3 1 3 Pair 6-10 0 0 0 0
3 1 3 Pair J-A 8 0 0 0
3 1 3 Two pair 16 152064 0.000975 0.015603
3 1 3 Three of a kind 24 101376 0.00065 0.015603
3 1 3 Straight 32 0 0 0
3 1 3 Flush 48 0 0 0
3 1 3 Full house 80 20736 0.000133 0.010638
3 1 3 Four of a kind 320 2304 0.000015 0.004728
3 1 3 Straight flush 800 0 0 0
3 1 3 Royal flush 4000 0 0 0
3 1 Fold n/a -5 0 0 0
3 3 1 Loser -8 0 0 0
3 3 1 Pair 6-10 0 0 0 0
3 3 1 Pair J-A 8 0 0 0
3 3 1 Two pair 16 0 0 0
3 3 1 Three of a kind 24 0 0 0
3 3 1 Straight 32 0 0 0
3 3 1 Flush 48 0 0 0
3 3 1 Full house 80 0 0 0
3 3 1 Four of a kind 320 0 0 0
3 3 1 Straight flush 800 0 0 0
3 3 1 Royal flush 4000 0 0 0
3 3 3 Loser -10 0 0 0
3 3 3 Pair 6-10 0 2534400 0.016253 0
3 3 3 Pair J-A 10 2027520 0.013002 0.130021
3 3 3 Two pair 20 1026432 0.006582 0.131647
3 3 3 Three of a kind 30 785664 0.005038 0.15115
3 3 3 Straight 40 0 0 0
3 3 3 Flush 60 0 0 0
3 3 3 Full house 100 69120 0.000443 0.044325
3 3 3 Four of a kind 400 20160 0.000129 0.051713
3 3 3 Straight flush 1000 0 0 0
3 3 3 Royal flush 5000 0 0 0
3 3 Fold n/a -7 0 0 0
3 Fold n/a n/a -4 0 0 0
Fold n/a n/a n/a -1 48451200 0.310709 -0.310709
Total 155937600 1 -0.049149

The lower right cell shows a house edge of 4.91%. On average, the player will bet 3.59 units per hand. The ratio of the expected loss to total amount bet, what I call the "element of risk," is 4.91%/3.59 = 1.37%.

The following tables show the expected value of raising one unit and three units on all possible starting hands. The player should make the play with the higher expected value. If both are less than -1, then the player should fold.

Unsuited Hands — Expected Values

Higher
Card
Lower
Card
Raise 1X Raise 3X
3 2 -1.716327 -3.333061
4 2 -1.716327 -3.333061
5 2 -1.716327 -3.333061
6 2 -1.389592 -2.67898
7 2 -1.389592 -2.705918
8 2 -1.389592 -2.705918
9 2 -1.389592 -2.705918
10 2 -1.389592 -2.705918
J 2 -0.901429 -1.810408
Q 2 -0.901429 -1.810408
K 2 -0.901429 -1.810408
A 2 -0.901429 -1.722245
4 3 -1.716327 -3.262041
5 3 -1.716327 -3.262041
6 3 -1.389592 -2.587551
7 3 -1.389592 -2.653673
8 3 -1.389592 -2.705918
9 3 -1.389592 -2.705918
10 3 -1.389592 -2.705918
J 3 -0.901429 -1.810408
Q 3 -0.901429 -1.810408
K 3 -0.901429 -1.810408
A 3 -0.901429 -1.722245
5 4 -1.710204 -3.186122
6 4 -1.370952 -2.492857
7 4 -1.377075 -2.55898
8 4 -1.389592 -2.63
9 4 -1.389592 -2.705918
10 4 -1.389592 -2.705918
J 4 -0.901429 -1.810408
Q 4 -0.901429 -1.810408
K 4 -0.901429 -1.810408
A 4 -0.901429 -1.722245
6 5 -1.336122 -2.394354
7 5 -1.342245 -2.460476
8 5 -1.360748 -2.531497
9 5 -1.389592 -2.607959
10 5 -1.389592 -2.705918
J 5 -0.901429 -1.810408
Q 5 -0.901429 -1.810408
K 5 -0.901429 -1.810408
A 5 -0.901429 -1.722245
7 6 -0.78517 -1.51932
8 6 -0.81619 -1.610748
9 6 -0.85102 -1.705986
10 6 -0.893469 -1.806122
J 6 -0.357959 -0.927755
Q 6 -0.357959 -0.927755
K 6 -0.357959 -0.927755
A 6 -0.357959 -0.927755
8 7 -0.748707 -1.510612
9 7 -0.783537 -1.60585
10 7 -0.825986 -1.705986
J 7 -0.292653 -0.829796
Q 7 -0.357959 -0.927755
K 7 -0.357959 -0.927755
A 7 -0.357959 -0.927755
9 8 -0.714422 -1.504082
10 8 -0.756871 -1.604218
J 8 -0.223537 -0.728027
Q 8 -0.292653 -0.829796
K 8 -0.357959 -0.927755
A 8 -0.357959 -0.927755
10 9 -0.686122 -1.500816
J 9 -0.152789 -0.624626
Q 9 -0.221905 -0.726395
K 9 -0.292653 -0.829796
A 9 -0.357959 -0.927755
J 10 -0.080408 -0.519592
Q 10 -0.149524 -0.621361
K 10 -0.220272 -0.724762
A 10 -0.292653 -0.829796
Q J 0.581905 0.374558
K J 0.511156 0.271156
A J 0.438776 0.166122
K Q 0.511156 0.271156
A Q 0.438776 0.166122
A K 0.438776 0.166122

Suited Hands — Expected Values

Higher
Card
Lower
Card
Raise 1X Raise 3X
3 2 -1.478367 -2.884286
4 2 -1.478367 -2.884286
5 2 -1.478367 -2.884286
6 2 -1.133265 -2.243571
7 2 -1.173367 -2.322041
8 2 -1.173367 -2.322041
9 2 -1.173367 -2.322041
10 2 -1.173367 -2.322041
J 2 -0.633265 -1.406939
Q 2 -0.633265 -1.406939
K 2 -0.633265 -1.406939
A 2 -0.591327 -1.279796
4 3 -1.435816 -2.770306
5 3 -1.435816 -2.770306
6 3 -1.090102 -2.113367
7 3 -1.132041 -2.222755
8 3 -1.173367 -2.322041
9 3 -1.173367 -2.322041
10 3 -1.173367 -2.322041
J 3 -0.633265 -1.406939
Q 3 -0.633265 -1.406939
K 3 -0.633265 -1.406939
A 3 -0.591327 -1.279796
5 4 -1.388061 -2.651735
6 4 -1.032347 -1.980102
7 4 -1.078878 -2.08949
8 4 -1.130816 -2.203469
9 4 -1.173367 -2.322041
10 4 -1.173367 -2.322041
J 4 -0.633265 -1.406939
Q 4 -0.633265 -1.406939
K 4 -0.633265 -1.406939
A 4 -0.591327 -1.279796
6 5 -0.960000 -1.841224
7 5 -1.006531 -1.950612
8 5 -1.064694 -2.066633
9 5 -1.129592 -2.185714
10 5 -1.173367 -2.322041
J 5 -0.633265 -1.406939
Q 5 -0.633265 -1.406939
K 5 -0.633265 -1.406939
A 5 -0.591327 -1.279796
7 6 -0.385306 -0.953810
8 6 -0.453469 -1.086054
9 6 -0.529082 -1.225578
10 6 -0.605714 -1.364898
J 6 -0.068367 -0.519082
Q 6 -0.068367 -0.519082
K 6 -0.068367 -0.519082
A 6 -0.068367 -0.519082
8 7 -0.351531 -0.941463
9 7 -0.427143 -1.080986
10 7 -0.509082 -1.225578
J 7 0.026224 -0.382755
Q 7 -0.068367 -0.519082
K 7 -0.068367 -0.519082
A 7 -0.068367 -0.519082
9 8 -0.319626 -0.930986
10 8 -0.401565 -1.075578
J 8 0.135578 -0.231667
Q 8 0.028707 -0.380272
K 8 -0.068367 -0.519082
A 8 -0.068367 -0.519082
10 9 -0.291769 -0.924048
J 9 0.249252 -0.076259
Q 9 0.140986 -0.226259
K 9 0.031190 -0.377789
A 9 -0.068367 -0.519082
J 10 0.527721 0.284762
Q 10 0.419456 0.134762
K 10 0.30966 -0.016769
A 10 0.196939 -0.171224
Q J 1.170816 1.149388
K J 1.057143 0.99398
A J 0.941939 0.837041
K Q 1.057143 0.99398
A Q 0.941939 0.837041
A K 0.941939 0.837041

Pairs — Expected Values

Higher
Card
Lower
Card
Raise 1X Raise 3X
2 2 1.929796 2.177959
3 3 1.929796 2.177959
4 4 1.929796 2.177959
5 5 1.929796 2.177959
6 6 6.739592 8.424490
7 7 6.739592 8.42449
8 8 6.739592 8.424490
9 9 6.739592 8.424490
10 10 6.739592 8.424490
J J 12.486531 15.608163
Q Q 12.486531 15.608163
K K 12.486531 15.608163
A A 12.486531 15.608163

Barona Pay Table

I have an unconfirmed report that the Barona casino in San Diego pays 5 to 1 on a straight, instead of the usual 4. Under optimal Barona strategy the house edge is 3.7591%. Using the basic strategy for the standard pay table in the Barona game results in a house edge of 3.7906%. So, the cost of errors using the standard strategy in the Barona game is 0.0315%.

Acknowledgements

ShuffleMaster, for providing me with their math report by Elliot Frome. I have some minor disagreements with the report, but it was helpful in my analysis.

Joseph Kisenwether, for providing the strategy posted here, and for correcting an earlier mistake in my analysis.

  • ShuffleMaster: Information on Mississippi Stud from the game owners. Includes a link where the game is offered.
  • discountgambling.net: Outstanding page on collusion in Mississippi Stud. According to this site, the player can have a 1.5%+ edge with knowledge of the other player's cards.
  • Game demo that teaches optimal strategy.
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