Three Card Poker tournaments have become a mainstay of several casinos on the Vegas Strip and in Laughlin.  Entry into these tournaments is usually awarded to players who win large hands during normal casino play, although more and more casinos have been offering “buy-ins” for interested patrons.  These tournaments are simple to play and offer potentially huge payouts.

How It Works

Tournament play consists of one or more “rounds” where each player starts with a predetermined sum of money.  Each round entails a fixed number of hands of standard three card poker. After each round, the floorperson counts the chip value in each player’s possession.  When a tournament has more than one round, each player’s final score is determined by adding their individual round totals.

Final Round

The six highest-scoring players face off in a final round.  Once a player reaches the final round, their previous ranking is discarded - the #1 and the #6 player have an equal chance of winning the grand prize.  The chip total determines the ranking of the final six and the prizes.  Most large (100-200 player) tournaments award money to all six finalists.

Strategy

We’ll get to the “why” later and summarize optimum tournament strategy here:

1. Call on any Queen/Six/Four or higher.  Fold otherwise.

This is classic Three Card Poker strategy and does not change because of the tournament.

2. 2.Place equal bets on the Ante and Pair Plus.
   

Betting heavy on the Ante provides a lower overall payout (see “How To Bet”).  Betting heavy on the Pair Plus is even worse since 74.4% of hands lose money on the Pair Plus bet.

3. 3.Keep bets low enough to survive the entire round.
   

This means no more than your bankroll divided by the number of hands per round, divided by three.  For a standard $3,000/20-hand round, this works out to $50 Ante, $50 Pair Plus.

4. 4.Don’t buy “bonus rounds”.
   

This is a sucker bet designed to increase the casino’s take.  It doubles your entry fee and provides almost no increase in your odds of winning.

5. 5.Bet consistently.
   

This allows you to place the maximum safe bets without having to scale back after losing a larger bet.

Now on to the details.....

How To Play

Casinos use different pay tables for Three Card Poker.  The Wizard of Odds has an excellent analysis of the standard game here.  What’s important to remember is that the tournament format does not affect the basic call/fold strategy.

That means you should call any Queen/Six/Four or greater, and fold otherwise, just as you would during normal Three Card Poker.

So Is There Any Way To Improve My Chances?

Absolutely!  The call/fold decision is only a small part of the game.  No less important is the choice of betting amounts.  The money used in these tournaments is not “real money”; it is only used as an indicator to determine player ranking.  The player doesn’t provide the betting money directly.  The effective tournament player works to maximize this money regardless of risk, since any “money” lost does not represent an actual financial loss for the player.

How To Bet

To get into the final round and have any hope of winning money in a tournament, you must maximize the most likely outcome of a given round.  There are too many variations on the types of tournaments out there to investigate every possibility.  Nevertheless, a computer analysis of one type of tournament popular on the Strip lends insight as to how they operate.

The tournament is a standard three round tournament where each player is given $3,000 in chips at the start of each round.  Rounds consist of 20 hands each, and the player’s total is the best two out of three rounds.  A computer analysis of all possible outcomes of the 20 hands using fixed bets is presented below:

        Ante & PP Wager        Most Probable Outcome

                                (Best two of three)

      -----------------------------------------------

         $25 - $25                     $5,650

         $50 - $50                     $5,300

        $100 - $100                    $4,600

        $150 - $150                    $4,200

As you can see, the most probable payout steadily decreases as the wager increases.  This is not surprising since statistically, every hand loses money (3.37% on the Ante wager, 5.57% on the Pair Plus wager).

But doesn’t this mean I should bet the minimum?

Not necessarily.  A minimum $25/$25 bet is excellent strategy, but in order to get into the final round, the player needs significantly better than “most probable” payouts.  There is a large element of luck to the tournament, and even the optimum betting requires lots of luck to make it when the player pool is large.

To account for this, I analyzed the probability of scoring high enough to get into the final round.  In a standard tournament, this requires a score 2.58 standard deviations above the peak.  Results below come from a computer simulation of a standard tournament using historical winning totals from previous tournaments.

        Ante & PP Wager        Odds of making the final round

      -----------------------------------------------

         $25 - $25                     20.24%

         $50 - $50                     21.06%

        $100 - $100                    13.08%

        $150 - $150                     7.22%

Taking this into account, the $50/$50 wager is slightly more advantageous than the $25/$25 wager.  High resolution interpolation shows the peak wager to be at $36.53 with a success probability of 21.83%.  Standard tournaments require betting in multiples of $25.

What about very large bets?

Some players mistakenly believe that placing large bets makes sense because if they get a lucky hand, they’ll make huge gains and outperform conservative betters.  This is a common fallacy, like the Martingale strategy, based on “hunches” and “intuition” but without valid mathematical support.  On average, betting more means losing more.

Computer analysis (above) shows that your chances of making enough money to enter the final round drop off quickly once your wager climbs above $50.  There are two reasons high betting doesn’t work.

1. Large hands don’t happen often enough

The odds of getting a high hand are simply too low for a typical tournament.  A player has only a 0.217% chance of getting a straight flush on any given hand.  In a full tournament, there is an 87.77% chance that you’ll never see a single straight flush.  Even if you’re lucky enough to hit a straight flush and win 45 bets on that hand, you’ll spend 120 bets to get there.    The player making smaller wagers does not depend on an unlikely straight flush.

2. Large bets means fewer hands

An often overlooked element of large betting is that you can run out your money before the end of each round.  It is no coincidence that the optimal $50 bet guarantees that you’ll have money to play all 20 hands no matter what.

Imagine betting large and going broke on the 13th hand, only to watch another player get your straight flush on the 14th hand.  You can’t win if you can’t play.

The table below shows the chances of running out of money before the final hand in a standard 20-hand tournament round:

        Ante & PP Wager        Odds of running out of money

      -----------------------------------------------

         $50 - $50                      0.00%

        $150 - $150                    16.18%

        $250 - $250                    43.67%

        $350 - $350                    59.26%

These odds may seem large, but think about it.  Betting $250 on each, you could lose $750 per hand.  Losing the first four hands in a row would wipe out a $3,000 bankroll, leaving 16 of the 20 hands unplayable.  Even a $150 wager gives roughly a 1 in 6 chance of going broke early.

What about large ante or pair plus bets?

The key to success in a tournament is to make the most effective use of the limited money and hands available in each round.  The nominal $50/$50 wager risks $150 on each hand.  Computer analysis of similar risk using even, ante-heavy, and pair-plus heavy wagers appears below:

        Ante & PP Wager        Odds of making the final round

      -----------------------------------------------

         $50 - $50                     21.06%

        $100 - $25                     14.67%

         $25 - $100                    11.32%

The ante-heavy wager is significantly less promising than the $50/$50 bet because an ante can only win when backed by an equal call bet.  Thus the $100 ante/$25 pair plus wager risks $225 on every betting hand.  Even a fold entails a larger ($125) loss.

The disadvantage of the ante-heavy bet is tempered by the possible $100 wins resulting from the dealer not qualifying.  This is not so with heavy pair plus betting.  The call/fold decision has little effect, and a pair plus bet needn’t be doubled.  Nevertheless,74.4% of all hands will throw away the pair plus wager.  That is, exactly 74.4% of all hands will lose money, even if you beat the dealer!

Beware the Bonus Round

More and more casinos have grabbed onto the “Bonus Round” to entice players into spending more money on the same tournament.  It works by offering players a chance to play an extra tournament round in exchange for a non-trivial sum of money.  In some cases, this can be as much as the entire tournament entry fee!  Worst of all, this money is typically not added to the prize pool.

The Bonus Round is a sucker bet, which is why the casinos offer it.

An extra round will improve your overall odds of winning, but the improvement is almost undetectable.  I ran 100 million simulated tournaments to determine how much advantage the Bonus Round provides:

        Number of Rounds      Odds of making the final round

      -----------------------------------------------

              3                        21.06%

              4                        22.68%

This simulation assumes the other players didn’t play the bonus round.  The extra round adds only 1.61% to your chances of making the final round.

In order to improve your overall score, the extra round must be one of the top two rounds.  The odds are exactly 50% that the extra round will be in the bottom (or top) two, so 50% of all players can expect no score increase whatsoever from an extra round.

If your total score is improved by the extra round, the improvement must still make the difference between being in the top six and not.  If your previous score is so high or so low that an extra round won’t move you from the bottom to the top six, then the bonus round makes no difference.

For example, suppose your three round score is huge (~$7,500).  You’ve probably already made it into the final round.  Increasing your score to $8,000 makes no difference.

On the same note, if your three round score is low (~$1,500), raising it to $2,500 won’t make the difference either.

Only a tiny minority of players have a chance of moving into the final round by buying a bonus round.  Casinos force players to make the bonus round decision before the completion of the tournament.  At this early stage, there is no way to know if the bonus round could have any chance of helping.

Stay away from the bonus round; its not worth it.

Beware the Gambler’s Fallacy

For those considering betting strategies other than flat betting (the same bet for each hand), check out this warning against the Martingale betting system.  Cheating aside, there is no way to know that one hand is more likely to win than any other, so there is no basis for betting more or less on any given hand.  Choose a betting level and stick with it.

Copyright (C) 2006 Wild Woolly’s Poker Tournaments.  All rights reserved.

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