Calculating '21s' from a single deck....

Quote: DJTeddyBear

"how two cards are dealt."

The term you're looking for is permutations. While a combination denotes a specific way of selecting a specified number of elements at a time from a larger number of elements, a permutation denotes a way of arranging that specified number of elements. For example, the number of different two-pair-only hands in five-card poker is given by saying that, out of the thirteen ranks, three will be selected, two of those ranks in turn each selecting two of the four suits and one of them selecting one. The two-pair-only hand - single combination - you end up holding is, say Qh, Qd, 5d, 5c, 7s. While you may be dealt these cards one at a time in any of 5! = 120 possible sequences, the specific cards selected from the deck remain the same.

LOL. I see the forum 'bug' has you. Sarcasm, MATE, is not appreciated. First of all, you stated ACE/KING and KING/ACE as being 1 not 2 - even though you just gave two. Probability maths needs to address whether the order is important or not, and in this case is it not important so therefore there are two ways to acheive the same outcome. Besides, this is an easy answer to find as its plastered all over the internet on math expert sites and gambling statistic sites - and they ALL claim 128/2652. But like you said, you're not a maths expert.

But then again, Im not an English expert either and I think it was pretty clear that I was asking about three card combinations overall.

But thanks anyway....

Must be the John Patrick sites. I stick with my answer. Only 1 way to make ace/king of clubs, or any other 2 card hand no matter what card comes first. BTW, there are 22100 total possible 3 card hands but your math may find more.

Sometime ago, for a laugh and before seeing http://wizardofodds.com/games/three-card-blackjack/, I looked at the totals that were formed with three cards (assuming an Ace was 1 or 11) but ignoring the totals from the first two cards (if you had 20 you wouldn't really hit to get the three-card 21). For instance there are four ways to get 6 (being three 2s and deciding which suit to omit), since A23 would be considered as 16.
30 560
29 480
28 576
27 740
26 856
25 1040
24 1180
23 1384
22 1544
21 2012
20 1688
19 1640
18 1540
17 1448
16 1304
15 1172
14 984
13 828
12 620
11 200
10 136
9 92
8 48
7 24
6 4

Quote: IGC

I know there are 128 ways to make 'blackjack' from the 2652 different two-carded combinations you could be dealt - but taking it one stage further seems quite a difficult task.

Quote: Ibeatyouraces

There are only 1326, 2 card combos in a single deck, 64 of which make 21 or blackjack. You forgot to divide by 2.

Are you actually arguing if the answer should be 128/2652 or 64/1326 ? Personally, I think you are both wrong. The correct answer is 32/663.

Also acceptable is one in 20+23/32.

Watch poker. There are EXACTLY 1326 possible 2 card starting hands in hold-em. Being dealt two cards in a single deck bj game is no different when shuffled every hand.