More decks means more edge

20 December 2018

By John Grochowski

QUESTION: Please explain to me why the house edge is higher when there are more decks in blackjack. The proportion of the cards is exactly the same. How does just adding more cards in the same proportions help the dealer?

ANSWER: This is a question I used to get a lot more often, but there are many fewer one-deck games than there used to be. I take it you’re in a location with a choice of how many decks to play.

Each card dealt has a greater impact on the proportion of remaining cards in a single-deck game than in a six-deck game.

Consequently, there are more blackjacks dealt with fewer decks, and players are paid a bonus on their blackjacks while the house is not. It’s best for players if that payoff is 3:2, but even with a 6:5 pay, players are getting something more when they have two-card 21s than the house gets.

Let’s say you’re playing a single-deck game and your first card is an ace. Of the other 51 cards in the deck, 16 are 10 values – the 10s, jacks, queens and kings. That gives you a 31.4% chance that your second card will complete a blackjack.

Now let’s say the game is six decks and your first card is an ace. There are 311 other cards in six decks, and 96 of them are 10 values. That means 30.9% of the available cards can complete a blackjack for you.

We can turn that around and say you have a 10 as your first card. The four of 51 cards, or 7.8% are aces that could complete your blackjack in the single-deck game, while 24 of 311, or 7.7%, are aces in the six-deck game.

In addition, double down situations are, on average, more favorable with fewer decks.

If you’re dealt 6:5 and double down in a single-deck game, 16 of the other 50 cards, or 32%, are 10 values that could give you 21. In a six-deck game after you’re dealt 6:5, 96 of the other 310 cards, or 31%, are 10-values.

Frequency of blackjacks and favorability of double down situations lead to single-deck games having lower house edges than multiple-deck games provided the games have the same rule sets. However, other rules impact the overall house edge, and a game with more decks may prove to be more favorable than a game with fewer decks.

One prime example: Paying only 6:5 on blackjacks increases the house edge by 1.4%, so a six-deck game that pays 3:2 will usually be a better bet than a one-deck game that pays 6:5.


QUESTION: I’ve noticed there are lots of video slots where the symbols that launch a bonus round are only on the first, third and fifth reels. In those games, are the reels longer so that there’s just an extra symbol on each one, or do the bonus symbols replace a jackpot symbol or something on those reels?

ANSWER: Slot reels do not have to have equal proportions of symbols. If a game is designed so that each video reel is 100 symbols long, then a bonus reel is just one of those 100 on any reel on which it appears.

However, it doesn’t have to be “replacing” any specific symbol on that reel. Reels No. 1 and 2, for example, don’t have to be identical except for the presence of the bonus symbol. Other symbols can be present in different proportions to help the game math to reach the desired payback percentage.