Question:
Posted by Rogcat on June 16, 1997 at 19:16:01: In Reply to: A blast from the past (long) posted by Bryce Carlson on June 15, 1997 at 12:56:41:

Great story. Maybe someone can answer this question. I've often heard reference to the odds of getting a natural (BJ) in a single deck game is greater than multi deck. Is this true? If true, please explain the theory behind the math.



Answer:
Re:Yessssssss!!!!

Posted by Jim on June 17, 1997 at 09:03:37: In Reply to: Re: A blast from the past (long) posted by Rogcat on June 16, 1997 at 19:16:01:

Finally an easy one that even I can answer..........

Yes the odds are slightly better of getting a BJ in single deck compared to multi-deck. The effects of removal are greater in single deck than in multi-deck. The odds of a BJ in single deck are:

Ace first:	4/52 * 16/51	= .02413 or 1 out of 41.44 hands.
Ten first:	16/52 * 4/51	= .02413 or 1 out of 41.44 hands.
Total :		= .04826 or 1 out of 20.72 hands.

In multi-deck the removal of one card (shown in the denominator of the second part of the equation) has much less effect. So for four decks:

Ace first:	16/208 * 64/207	= .02378 or 1 out of 42.05 hands.
Ten first:	64/208 * 16/207	= .02378 or 1 out of 42.05 hands.
Total:		= .04756 or 1 out of 21 hands.

That is one of the reasons that there is greater expectation with single deck compared to multi-deck, there are slightly more blackjacks. I hope this makes sense.

Jim