Discount Gambling

I just tried out ShuffleMaster’s new Dealer Bluff Six Card Poker game at Pala Casino, just north of San Diego. It’s a new idea in poker-based table games, where the dealing machine knows the value of its hand, and bets against you. When I first saw this game last week, I was really puzzled. How would you play your hand? Would it cost a lot of money to figure out how aggressive the machine was? How was I supposed to analyze this game?

I looked into the details of the game, and its actually pretty simple how it all works. By its stated math, its not a bad game at around 0.5% house edge (element of risk). The player first bets an equal Ante and Blind bet. All players and the dealer are dealt six cards, from which to make a five card hand. The dealer acts first, and either checks (0x), or bets 1x ,2x, or 3x the Ante, based on its hand strength, and simple randomization. This simple randomization is stateless (independent from hand-to-hand), and uses a published wager matrix (“house-way”). The player may either fold (or check if no dealer bet), call, or raise (double the dealer bet). The dealer calls all player bets/raises. The hand is resolved just like their Ultimate Texas Hold’em game, where the Ante plays only if the dealer qualifies with a pair or better, the Play bet always gets even-money action, and the Blind bet pays only if the player wins, and according to a paytable. The game is easy to analyze, because of the simple, stateless, and published dealer betting strategy (“house-way”). Given house-way, a player basic strategy is determined, and the house edge is calculated.

The game is kind of fun, because the dealer acts first, and you benefit from this position. If you raise the dealer, it must always call (it can’t come over the top, and re-raise you). Sometimes you have easy folds, or easy raises. However, basic strategy requires you to call or raise a lot of hands, even when the dealer is betting 3x, since it bluffs a lot. This of course adds to your variance, and sometimes you’ll wonder why you had to call 3x “to keep the dealer honest”.

As usual in these ShuffleMaster games, the Ante bet is -EV because of the pair qualifier needed to pay, and the Blind bet is -EV because of the paytable. The Play bet is +EV, because you’re acting last, and the dealer must call your bets/raises, and cannot re-raise. However, the dealer may bluff, so you need to know (exactly) how the betting logic works. If you have this info (or can learn it), then the Play bet will always be +EV. The game is designed so that the sum of these 3 EVs yield a reasonable house edge.

This is why I have reservations about the game. Player basic strategy is completely dependent upon how the dealer bets his hand. ShuffleMaster goes out of its way to provide all the data on this process, and even provides the players with basic strategy and percentage tables in their literature. At Pala, there are ample supplies of this literature at the table. The dealer house-way is provided. However, if house-way should change for any reason, the player using an out-of-sync basic strategy may be severely penalized.

This table provides the percentages of the way the dealer will bet his hand, using a random number generator. No previous knowledge of the player’s history, bet amount, or anything else is used to determine the dealer’s bet.

Based on this house-way wager matrix, basic player strategy is optimized as follows:

If everything operates exactly per these assumptions, then the house edge is only 0.5% (element-of-risk), or about 2% of the Ante bet. This is only $.10 per $5 Ante bet, and is very reasonable. However, if the dealer strategy is not exactly as described by the stateless house-way table above, the player return could be much worse. For example, the dealer cannot sub-divide the last “Nothing” row, into various sub-percentages based on A-high, K-high, etc. It’s assumed that it treats all no-pair hands the same, and applies an equal bluff probabilities to them, regardless of high card value.

What’s worse, if the dealer behaves significantly differently from the house-way table, the effect on the player using a basic strategy optimized for it could be disastrous. As an experiment, I tweaked the wager matrix to make the dealer more honest (bluff less) in a few rows, to see the effect.

First, I made the dealer more conservative with its high pairs. I shifted the majority of these bets to 1x, thereby giving the player less opportunities to come over the top with a raise to 2x, or even 6x. I modified the following single table row to

and the results were very significant, increasing the house edge to about 5.2% (element-of-risk), or -17.8% of the Ante bet! This really surprised me. The house could (not intentionally, of course) change a few small settings, and really hurt the player relying on the published basic strategy. Unless the player could look at the stats maintained by the betting mechanism, it’s a real leap of faith to get involved with this game for any period of time.

Next, I looked at the effect of making the dealer more conservative with its nothing hand, making it check the vast majority (80%) of the time, and betting 1x the rest of the time (20%). Again, this reduces the ability of the player to just call and win with a reasonable hand, or come over the top with a big raise.

The effect of this row change was less significant, increasing the house edge to about 2.0% (element-of-risk), or -6.6% of the Ante bet. If both these row changes are applied together, the effects are additive. Of course, if the player knows about these changes, then he can modify his basic strategy to again be +EV on the Play bet. Again, since the dealer acts first, must call all player raises and cannot come over the top, the Play bet will always be +EV, given knowledge of how the dealer behaves. The above house edge effects for the wager matrix changes are based on a player using the published basic strategy.

I stopped after looking at these two simple, but significant effects. That’s all I needed to see.

Usually, I’m very naive, and always assume the casino is operating according to fair rules, and everything is on the up-and-up. However, with the advent of this new type of game, where the shuffler actually reads all hands it deals (it must, as the dealer hand is the last out of the shuffler, and the operator hits the ‘stop’ button to tell the betting logic use the last hand), I’m getting a little nervous. Also, the nature of a heads-up poker game requires knowledge of your opponent. Although ShuffleMaster provides a complete model of this opponent, its always possible that something gets lost in the process, a transcription error occurs, and/or something changes, and basic strategy gets out of sync with the actual dealer behaviour.

I think the game could be fun and safe, provided that ShuffleMaster provides a few assurances to the players. First, they need to make it extremely clear, and verify, that there’s only one version of the wager matrix. Furthermore, this can never change. Additionally, they could provide assurances to the players that the betting logic is audited by built-in stats collection in the shuffler, and periodically checked against the published, unchanging house-way. If they can provide these assurances, you can feel safe walking up to the game for the first time, and betting following basic strategy. Otherwise, while possible, it’s a pretty big task for people to figure out the dealer betting strategy, and to devise the appropriate counter-strategy. I’m just there to have fun, not to play Big Blue (that can see your cards).