Mississippi Stud Poker Hole-Card Play: Update #1

In this post,  I presented flop-hole-card strategy for Mississippi Stud (MS). At the time, I stated that the most common hole-card to see in MS is the flop card. After watching the game at several casinos, I was not so sure. Then I read a message board post at wizardofvegas, stating:

"Yesterday, I got to play with a Mississippi Stud dealer consistently flashing the river. SCORE!"

This post presents river-hole-card strategy for MS.

First, a quick review of the game. Here are the rules for MS:

1. The player makes an Ante wager.

2. The player is dealt two cards.

3. Three community cards are dealt (flop, turn, river).

4. Player may fold or make a flop bet. The flop bet is either 1x or 3x the Ante.

5. The flop card is exposed.

6. Player may fold or make a turn bet. The turn bet is either 1x or 3x the Ante.

7. The turn card is exposed.

8. Player may fold or make a river bet. The river bet is either 1x or 3x the Ante.

9. The river card is exposed.

10. All wagers are paid according to the given pay table.

Here is the most common pay table:

1. Royal Flush pays 500-to-1.

2. Straight Flush pays 100-to-1.

3. Four of a Kind pays 40-to-1.

4. Full House pays 10-to-1.

5. Flush pays 6-to-1.

6. Straight pays 4-to-1.

7. Three of a Kind pays 3-to-1.

8. Two Pairs pays 2-to-1.

9. Pair of Jacks through Aces pays 1-to-1.

10. Pair of Sixes through Tens is a push.

11. All other hands lose.

The baseline house edge for the river-hole-card game is 104.4668636686%. As far as I know, this is the strongest edge from hole-carding available in any proprietary game (assuming only one hole-card is flashed).  The fact that this edge can be obtained in practice is extraordinary.

In the normal game of MS, the player knows zero cards before making his ante bet, two cards before making the flop bet, three cards before making the turn bet, and four cards before the river bet. In the flop-hole-card game, the player knows the same three cards on his flop and turn bets, and then knows four cards for his river bet. For the river-hole-card game, the player knows three cards before the flop bet, four cards for his turn bet, and all five cards for his river bet.

In presenting river-hole-card strategy, I refer to three groups of cards. The “high cards” are J, Q, K, A. The “mid cards” are 6, 7, 8, 9, T. The “low cards” are 2, 3, 4, 5. Any hand that contains a pair of 6s or higher will be referred to as a “made hand.” Here is river-hole-card strategy for MS:

Pre-flop (knowing the player’s two cards and the river card)

Raise 3x with:

• Any made hand (6-6 or better).

• Any straight flush that is 5/6/7 or higher.

• Any straight flush with 1 gap and 1 or more high cards (e.g. 8/9/J suited).

• Any straight flush with 2 gaps and 2 or more high cards (e.g. 9/J/K suited).

Raise 1x with:

• Any pair 2-2 through 5-5.

• Any straight with 0 gaps that is 3/4/5 or higher.

• Any straight with 1 gap that is 3/4/6 or higher.

• Any straight with 2 gaps that contains an 8 or higher. (not 3/6/7, yes 4/6/8, yes A/2/5).

• Any hand that contains two high cards.

• Any hand that contains one mid-card and one high card.

• The straight flushes 2/3/4, 3/4/5 and 4/5/6.

• Any straight flush with 1 gap and no high cards (e.g. 2/3/5 suited).

• Any straight flush with 2 gaps and at most 1 high card (e.g. 2/3/6 suited, 8/9/Q suited).

• Any other suited hand.

Pre-turn (knowing player’s two cards, flop card and river card)

Raise 3x with:

• Any made hand (6-6 or better).

• Any four to a flush.

• Open-ended straight 5678 or higher.

Raise 1x with:

• Pair 2-2 through 5-5.

• The straights 2/3/4/5, 3/4/5/6 and 4/5/6/7.

• Any gut-shot straight.

• Two or more high cards.

• One high card and three mid cards.

Pre-river (knowing all five cards)

• Fold with a non-paying hand (pair of 5's or less).

• Raise 1x with a pushing hand (pair of 6's through T's).

• Raise 3x with a paying hand (pair of J's or higher).

In computing river-hole-card strategy, I wrote a program that cycled through each possible situation, computed optimal strategy at each street, and dumped the results to a file. In creating the rules above, I assumed that the strategy for river-hole-card play would be similar in structure to that for flop-hole-card play. I then culled the spread sheet for borderline situations to get the strategy.

There is a lot of data to examine. Over 2.5 million situations can arise. If you would like to examine some of this data, the file below contains the first 500,000 situations, downloadable as an Excel spreadsheet.

MSHC_01 (14,3M)

Exposing the river-hole-card in MS is one of the most significant opportunities an AP can find. The following are my suggestions for protecting MS from hole-card play:

• Learn hole-card strategy to be able to identify suspect play.

• Frequently audit hole-card exposure on all proprietary games.

• Frequently re-train and remind dealers of hole-card issues.

• Re-configure tables that have poorly placed Ace/iDEAL shufflers.