Many APs preach that the book “Beyond Counting” by James Grosjean contains everything you need if you just know how to find it.  They say that you must simply “read everything.” Mississippi Stud (MS) is a good example.  The most common hole-card to see in MS is the flop card, yet at first this strategy appears missing from Beyond Counting. After giving hole-card strategy for seeing the turn card, Grosjean states the following about flop-hole-card strategy: “This [turn] strategy is way off for the [flop] game, so you’ll have to work out your own there.” I did. Then I found out that Grosjean did too, 16 pages after his comment.

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

  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 player edge for the flop-hole-card game is 54.8660%. This is a very strong edge. That last sentence was an understatement and opportunities are not rare. Like Three Card Poker, MS is dealt in a fashion that makes exposure of the flop-card a reasonable consequence of sloppy procedure. Using either the Ace shuffler or the iDEAL shuffler, opportunities arise both because of table layout issues and sloppy dealer procedure.

One thing to keep in mind in playing the flop-hole-card game is that the player has knowledge of the same 3 cards for his action on the flop and the turn. It follows that the player will either fold, wager (1x, 1x) or wager (3x, 3x). The player will take the same action on the flop and turn bets. Thus, heading into the river bet, the player will either have folded, have 3 units in action, or have 7 units in action. Because of this, combinations of cards and total wagers will occur that are not covered by basic strategy or the strategy presented by Grosjean for the turn-hole-card game.

In computing flop-hole-card strategy, I first wrote a computer program that output all possible three card starting hands and the flop/turn-bet action the player should make with each. This file had 5525 lines of data. I then attempted to cull rules from this data by going through it one line at a time. Every time a new situation arose, I added that rule. At a certain point through the log file, it was clear that no new rules would arise.  I used the same procedure for river-bet action. This file had 71295 lines of data.

If you would like to examine this data, here it is, given in downloadable Excel spreadsheets. Of course, I welcome corrections/additions to my strategy.

In presenting this 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 my strategy:

Flop-hole-card strategy for Mississippi Stud Poker

Flop/turn-bet

Raise (3x, 3x) with:

  • Any made hand.

  • 567 or higher straight flush.

  • 679 or 689 straight flush.

  • Straight flush with 1 gap and 1 or more high cards (e.g. 9/T/Q suited).

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

Raise (1x, 1x) with:

  • Any low pair.

  • Any straight flush not covered above with 0, 1 or 2 gaps (e.g. 2/4/6 suited).

  • Any straight with 0 gaps and 1 or more high cards (e.g. 9/T/J off-suit).

  • Any straight with 1 gap and 1 or more high cards (e.g. 8/T/J off-suit).

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

  • Any flush hand with 1 or more high cards.

River-bet

Raise 3x with:

  • Any made hand.

  • Four to a flush.

  • Open-ended straight 5678 or higher.

Raise 1x with:

  • Any straight A234 through 4567.

  • Any gut-shot straight.

  • At least two high cards.

  • At least one high card and two mid cards.

  • At least three mid cards.

  • Any low pair.

I have never hole-carded this game. Indeed, this game did not exist when I was last active as an AP in 2005. But I am certain that the player will have to use a lot of cover. Suppose the player has the obviously foldable hand 2/7 off-suit, yet makes a 3x bet knowing that the flop-hole-card is a 7. This is as much of a tell (or more) as folding an Ace in Three Card Poker.

Like many other proprietary games, exposing a hole-card is one of the most significant opportunities an AP can find. Many games have extremely complex strategies. Although the strategy above is tougher than Three Card Poker, it is trivial to learn compared to blackjack card counting.

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.

About the Author
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received his Ph.D. in Mathematics from the University of Arizona in 1983. Eliot has been a Professor of both Mathematics and Computer Science. Eliot retired from academia in 2009. Eliot Jacobson