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Mississippi Stud

Introduction

Mississippi StudMississippi Stud is a popular poker-based table game by Scientific Games. 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.

Video Tutorial

The Wizard of Odds demonstrates his Mississippi Stud demo game, showing the rules, odds, and strategy for the game.

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

Playing Online For Real Money

Mississippi Stud is not widely available at online casinos but it is available at these brands:

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 = 2 points
  • Mid = 6 to 10 = 1 point
  • Low = 2 to 5 = 0 points

2 Cards

  1. Raise 3x with any pair.
  2. Raise 1x with at least two points.
  3. Raise 1x with 6/5 suited.
  4. 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 at least three points.
  9. Raise 1x with a straight draw, with no gaps, 456 or higher.
  10. Raise 1x with a straight draw, with one gap, and two mid cards.
  11. 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 four points.
  7. Raise 1x with three mid cards and at least one previous 3x raise.
  8. 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%.

Millionaire Progressive

This is a $5 "red light" progressive side bet that pays $1,000,000 for a royal flush in spades, using the player's five-card hand. For all the rules and analysis, please see my page on the Millionaire Progressive.

Golden Nugget Progressive

I saw another progressive jackpot bet at the Golden Nugget in Las Vegas on June 13, 2023. The bet amount is $5 and it pays based on the player's five-card hand. It is a linked progressive with other poker-based games using five cards. Following is the pay table. Wins for a full house or less pay on a "for one" basis.

Golden Nugget Progressive Pay Table

Event Pays
Royal flush Mega jackpot
Straight flush Major jackpot
Four of a kind Minor jackpot
Full house 50
Flush 40
Straight 30
Three of a kind 9

The following table shows my analysis of the Golden Nugget Progressive. It is a linked progressive with the same bet in Ultimate Texas Hold 'Em. The bottom right cell shows the expected value of the three of a kind to full house is 45.85%.

Golden Nugget Progressive Return Table

Event Pays Combinations Probability Return
Royal flush Mega jackpot 4 0.000002 ?
Straight flush Major jackpot 36 0.000014 ?
Four of a kind Minor jackpot 624 0.000240 ?
Full house 50 3744 0.001441 0.072029
Flush 40 5108 0.001965 0.078616
Straight 30 10200 0.003925 0.117739
Three of a kind 9 54912 0.021128 0.190156
All lother 0 2524332 0.971285 0.458540
Total   2598960 1 0.458540

Following are the values of the three progressive jackpots.

  • Royal flush: 0.030782 per $100,000 in Mega jackpot
  • Straight flush: 0.027703 per $10,000 in Major jackpot
  • Four of a kind: 0.048019 per $1,000 in Minor jackpot

Acknowledgements

Scientific Games, 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.

Links

  • 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.