Cards Dealt per Hand

How many cards are dealt per hand?

The books tell us that the average hand in Blackjack (including the dealer hands) contains about 2.7 cards. I thought I would look at this a bit further. We always temper this estimate by saying that the number of players can affect the average because the dealer and players play differently. So, I first looked at the effect of number of players. This chart shows the number of cards used by the dealer for 1 to 5 players in orange. (Six decks, H17, nDAS, Basic Strategy.) With one player, the dealer averages 2.78 cards per round. This increases to 2.91 cards per round with two players. This is because the dealer does not need to finish his hand if the players all bust or receive a Blackjack, and the more players there are the less likely this will occur. As additional players are added, the cards used by the dealer continue to increase - but nearly the entire increase is seen going from one player to two players. The cards used by the player is about 2.71 per round. The players use fewer cards, even though the player can split, because the dealer hits all stiffs. And unfortunately there are a lot of stiffs. The green bars display the overall cards per person (dealer and player) per round. This changes less by number of players than one might think. This is because the cards per round increases from one to two players because of the increase in dealer cards, but then decreases as additional players are added and the lower number of cards used by players brings down the overall average.

I would have included charts showing the impact on these stats of different numbers of decks, different rules, different strategies and dealer peek vs. dealer no peek, but it turns out that the numbers barely change.

How about different counts?

One aspect that does change the average number of cards per round is the count. In this chart, we see the overall average cards by the Hi-Opt I true count. The red line displays the number of cards per person from true counts -13 to +13. The green line is used as a reference and is set to the average of 2.74 cards. Here we do see an effect with cards ranging from 2.53 to 3 cards per person per round. Higher counts use fewer cards because there are more large cards available.

What is the breakdown of hand lengths?

In this chart, we see the breakdown of player hand lengths. The red bars are for counts of -10 and down, blue bars for counts +10 and up and green bars display all counts. From left to right we see the percentage of hands that are 2 through 6 cards in length. There are longer hands, but too small to display on this scale. The differences are great with 70% of players' hands two cards in length at very high counts dropping to 40% at very low counts.

Sim details

• Six decks, H17, nDAS, fixed rounds, Hi-Opt I, Illustroius 18 indexes, trunc, half deck estimate
• One and five players
• One billion rounds each