# Card Counting the Tie Max Baccarat Side Bets

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A few days back I received an unexpected email from a game developer who asked me to consider two of his new baccarat side bets, Low Tie Max (LTM) and High Tie Max (HTM). These two are part of a collection of side bets collectively called Lucky Max (LM). I believe the developer's intention was to get some publicity for his wagers by having me post favorable card counting results here. The problem is that for one of his side bets it didn't turn out that way.

The Tie bet in baccarat is fairly robust. Though it can be counted (see this post and this post), no self-respecting AP would bother. However, any time the Tie bet is modified, bad things can happen. This is exactly the case with the UR Way Egalite and Super Pay Egalite side bets (see this post and this post), which are among the most crushable of all baccarat side bets. Messing with the Tie bet is playing with fire.

Here are the rules for the LTM baccarat side bet:

• If the hand ends in a tie, and the highest card among all those played in the hand has baccarat value 0, 1, 2, 3, 4 or 5, the LTM side bet wins and the player is paid 55-to-1. That is, LTM wins if the hand ends in a tie and no card played in the hand is a 6, 7, 8 or 9.
• Otherwise the LTM side bet loses.

Here are the rules for the HTM baccarat side bet:

• If the hand ends in a tie, and the highest card among all those played in the hand has baccarat value 6, 7, 8 or 9, the HTM side bet wins and the player is paid 10-to-1. That is, HTM wins if the hand ends in a tie and at least one card played is a 6, 7, 8 or 9.
• Otherwise the HTM side bet loses.

Another way of explaining these two side bets is as follows. If the hand does not end in a tie then both wagers lose. If the hand ends in a tie, then the highest card of all those played in the hand is used to resolve the bet. If the highest card is 0, 1, 2, 3, 4 or 5, then LTM wins and HTM loses. If the highest card is 6, 7, 8 or 9 then LTM loses and HTM wins.

Here is the combinatorial analysis for LTM:

In particular:

• The house edge is 16.455%.
• The hit frequency is 1.492%.
• The standard deviation is 6.789.

Here is the combinatorial analysis for HTM:

In particular:

• The house edge is 11.739%.
• The hit frequency is 8.024%.
• The standard deviation is 2.988.

Each of these wagers has a substantial house edge, however the edge for HTM is much lower than the edge for LTM. Intuitively, one would think that this would make HTM more vulnerable to card counting than LTM. Surprisingly, the opposite is true.

Here are the EORs and a suggested card counting system for LTM:

This card counting system isn't perfect. Giving Aces a tag of 0 is a compromise I made to make the system balanced. However, it is completely intuitive why this system works. As the shoe is depleted of cards of rank 6, 7, 8 and 9, any tie that occurs is more likely to not include one of those four cards. It follows that the card counter is happy any time one of these cards gets played, hence the tag +2. The reader may recognize that the LTM system bears great similarity to the Ten-count for card counting Lucky Ladies (see this post).

The following table gives the card counting statistics for using the system given above to count LTM, with the cut card placed at 14 cards and the usual burn card rules:

A win rate of 2.914 units per 100 hands puts LTM in the stratosphere of beatable baccarat side bets. For example, it is four times more vulnerable than the Dragon 7 side bet in EZ Baccarat. Although LTM has a huge standard deviation, the DI value of 11.4 underscores the value it offers.  There is no question in my mind that APs will go after this bet if the table max is sufficiently high.

HTM , on the other hand, is quite robust; it is unlikely anyone would bother trying to count it. Here are the EORs and a suggested card counting system for HTM:

Naturally, the counter is glad whenever a card with baccarat rank 0, 1, 2, 3, 4 or 5 exits the shoe, hence each of these cards has tag +1. The cards 6, 7, 8 and 9 each have negative tags, again following intuition, though the values of these tags are strange.

The following table gives the card counting statistics for using the system given above to count HTM, with the cut card placed at 14 cards and the usual burn card rules:

With a win-rate of 0.09 units per 100 hands and a DI of 2, this one isn't worth a sneeze. There won't be any team play with one counter counting LTM and the other HTM. In the case of HTM, be happy, don't worry.

For any casino that offers LTM and HTM, I caution watching for players who back count shoes, never bet HTM, and come in late in the shoe betting table max on LTM, possibly on multiple spots.  In my opinion these wagers are good ideas that may find some success in the baccarat side bet marketplace, but the casino should be on guard.