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