Fred Renzey: Average Number of Cards in Dealer's Completed Hand

[Fred Renzey]

I have it locked in my head from something I read somewhere 25 or 30 years ago that the average dealer's completed hand will contain 3.0 cards as opposed to 2.7 for the player. It may have been in a very old blackjack book, or perhaps even one of Julian Braun's published papers.

The reason is that although the player splits roughly 2% of his hands, the dealer hits 100% of her stiffs and never limits herself to just one hit by doubling down.

Rather than undertake what will probably grow into a lengthy computation, can Don, or Norm, or somebody verify or refute this?

[Don Schlesinger]

> I have it locked in my head from something I read
> somewhere 25 or 30 years ago that the average dealer's
> completed hand will contain 3.0 cards as opposed to
> 2.7 for the player. It may have been in a very old
> blackjack book, or perhaps even one of Julian Braun's
> published papers.

> The reason is that although the player splits roughly
> 2% of his hands, the dealer hits 100% of her stiffs
> and never limits herself to just one hit by doubling
> down.

> Rather than undertake what will probably grow into a
> lengthy computation, can Don, or Norm, or somebody
> verify or refute this?

No, not true. Average dealer's number of cards to complete the hand is about the same as the player's: 2.7. Globally, it is a little lower, because, when all the players at the table break, the dealer doesn't complete his hand. This has virtually no effect at a full table, but, since a lone player breaks about 16% of the time using BS, then the extra, average, 0.7 cards are NOT drawn roughly one hand out of six, thereby reducing the 0.7 by about 16%, or 0.11.

So, the 2.7 becomes 2.6 under those circumstances.

Regards,

Don

[Fred Renzey]