# An Error of Commission?

A couple of weeks ago I discussed methods used by game developers to create a house advantage.  I realized that I left off two common one.  They are somewhat related as the second one was created in attempt to get rid of the first.  The first method is called taking a commission, which I've generally thought of as a misnomer, because it only applies to winning bets.  In the games of Pai Gow Poker and Baccarat, certain wagers pay a 5% commission when they win.  Another way of looking at this is that the Player is paid 19 to 20 for a winning wager, which I think is more accurate.  Commissions, to me, are paid on a wager, not on a winning wager.  If you pay a commission to a real estate agent, you don't pay it if you get a good deal or only on your profit, you pay it when your house sells - on the gross sales price.

If you wager \$20 and you lose, you lose \$20.  If the wager pushes, you get your full \$20 back.  If you win, you get \$39 - your \$20 plus the \$19 you win.  So, in reality, you're simply making a wager that pays a little less than even money.  In Pai Gow Poker, this applies to the base wager.  A mechanism such as this must be used because the only other advantage that the House has is that it wins hands that are copies.  But, with a 2-card hand and a 5-card hand, ties are not that common.  While this provides some advantage to the house, it simply isn't enough.  So, they pay 19 to 20 for winning hands.  At first glance, this might seem to create a 2.5% house advantage because the Player and Dealer win nearly the same number of hands.   However, since it is paid only only wins and about 42% of all hands finish as pushes, we find that it really only generates a little under a 1.5% house edge.  When combined with the house edge generated by the house winning copies and the overall house edge is about 2.73%.  This is offset somewhat if the Player chooses to act as the banker which provide an edge for the Player.  But, I'll save that for another day.

In Baccarat, the Player has the option to wager on either the Player or the Banker hand.  In reality, it is more like Hand 1 and Hand 2 because no hand really belongs to the Player if you can wager on the other hand.  Based on the drawing rules used in Baccarat, the Banker hand has a small advantage.  Because the Player can wager on this hand, this translates to an advantage to the Player.  To offset this, the House again takes a commission on winning wagers on the Banker Hand.   Again, winning wagers on the Banker Hand pay 19 to 20.  The net impact is that the Banker Hand wager has a 1.06% house edge, which is actually LOWER than the Player Hand Wager without a commission.

The problem with paying commissions is not that it costs the Player money.  Every casino game costs the Player money.  The real question is not what mechanism is used to generate the house edge, but how much of a house edge it generates.  In the case of these two games, it generates a relatively normal sized edge.  Pai Gow's edge is a little on the high side and Baccarat's is on the lower side.  But, nothing incredibly unusual about either.  The issue is that the commission is slow and messy.  Players don't always wager in multiples of \$20.  In these cases, the casino might use some method to accrue the commission and then take it when the amount adds up to a round amount.  Calculating a 19 to 20 payback is also not a simple thing for the Dealer.  Sure, a \$100 wager pays \$95 which is easy enough, but still messier than paying \$100.  But, what about when the Player wagers \$75?

These issues led to a desire to do away with the commissions in these games.  In both cases, a similar mechanism was used.   In the case of Pai Gow, a hand that is normally a sure loser for the House is turned into a Push.  In one common version of 'commission free' Pai Gow, if the Dealer has a Queen High Pai Gow hand, then the hand is automatically a Push.  This creates a house advantage nearly identical to the commission.   Now all wins can pay even money and the game is cleaner and simpler.   Only in the occasional situation where the Dealer has this hand is the normal flow interrupted at all, and the impact is relatively minimal to game speed.

In Baccarat, one of the common mechanisms is to take a sure winner for the Banker hand and turn it into a Push.  The most common hand is a Banker 3-card 7 which wins.  The impact, like in Pai Gow is a virtually identical payback but with the messy commission removed.  Now all wagers can pay even money and the only impact is that special Banker Hand and even when that happens it simply becomes a push.

In order to be an Expert Player, a Player needs to understand that all casino games are built with a House edge.  The edge comes from a variety of mechanisms.  The specific mechanism is not important to the end financial result.  It can impact the feel of the game and a Player may prefer one mechanism vs. another.  However, that House edge will be there no matter what.  If you play a no-commission version of Baccarat or Pai Gow, mathematically you're playing a nearly identical version of the game.  If you like the simplicity of the no-commission version, play that.  If you get annoyed and pushing hands you should win, then maybe these versions aren't for you.  At the end of the night, you'll probably be a nearly similar financial situation.