House advantages vary by casino game
March 10, 2015 3:02 AM
by Elliot Frome
I received a rather strange question this past week from an inventor. He wanted to know if doubling down in blackjack is an advantage for the Player or the Casino.
I find it strange because my expectation is that someone trying to invent games would probably understand what creates house advantages and what creates player advantages. I don’t necessarily expect the average player to fully understand this, but if you’re trying to invent a game, you need to understand what levers to pull in order to make the game’s math work out correctly.
House advantages vary greatly in games, but there are some commonalities. The player acting first is usually a house advantage because he has to essentially guess where he stands in the game.
In the case of blackjack, virtually the entire advantage comes from this. The player has to hit first and if he busts, he loses, regardless of what the dealer does. In essence, busted ties go to the House. In blackjack, the player has three items that bring the payback back to an acceptable level. He wins 3 to 2 on Blackjack. The dealer only wins what you wager if the dealer has blackjack.
Imagine if you wagered $10 on your hand, but had to pay $15 if the dealer has a blackjack and you don’t.
The player can also split and double down. How do we know these two items are player advantages?
Without even running the math on it, we can be pretty sure these are player advantages because they are optional. Any time the player has the option to bet at least a certain amount or more, this usually indicates it creates a player advantage.
This does not mean you always bet more. It simply means doing it at the right time is advantageous to the player. In the case of blackjack, the player may double down on any two cards (usually). If the player chooses to do this with a 12 or a 7, then it will not be a player advantage.
If he does it when he is supposed to (with 9’s, 10’s, 11’s and certain soft hand combinations) then the player will find the payback will increase. If the house never allowed the player to double down, the payback of blackjack would be far less than 99.5%. This is the reason there are some casinos that don’t allow the player to double down on soft hands. This is one way a casino can reduce the payback of the game.
The same is true for splitting. Split when you are supposed to and it is to your advantage. If it were forbidden to split Pairs, the payback of blackjack would be reduced. Splitting and doubling down make the strategy for blackjack considerably more complex. It can increase human error, which can lower the real payback even if it doesn’t affect the theoretical one.
When a player doubles down, he doubles his original wager and “agrees” to take one and only one card as a hit. For many double down situations, this doesn’t change the player’s hand at all relative to not doubling. If the player has an 11 vs. a 5, even if he didn’t double, the proper strategy would be to take exactly one card.
In these cases, he is not changing the outcome of the hand at all, but is doubling his wager. Obviously, he would want to do this anytime he is more likely to win than to lose.
In cases where he might want to take another hit, the player is actually reducing the probability of winning the hand (slightly) but doubling the wager. So, it might come down to a preference of winning a hand 60% of the time with a $5 wager vs. winning a hand 55% of the time with a $10 wager.
Which would you prefer? It’s a trick question. Both result in the same net unit win over time. This shows that when you double down, the win frequency can only be reduced by a small amount relative to not doubling.
We see similar circumstances in a variety of games. In Four Card Poker, you can get the option to bet up to 3 times your original wager. This must be a player advantage because you are never forced to do this. You can always bet 1x if you want. It just wouldn’t be the correct mathematical play.
Just like in blackjack, you need to know when to play 3x. In Four Card Poker you never bet 2x. In blackjack, there would be times when, if allowed to triple down, you would want to do so even though you wouldn’t double down.
In Ultimate Texas Hold’em, it is a bit more complex. Your opportunity to wager more is tied to having less information. It’s still an option to play 4x or to check and wait for more cards. This is a major player advantage. If a casino were to offer UTH without the option to wager 4x and just dealt each player two cards and the flop and then said you wager 2x or check, the payback of UTH would plummet several percentage points. Choices are always good for the player. He can always choose the one that is beneficial to himself.
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Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at ElliotFrome@GamingToday.com.