|
|
| the
number of possible hands |
 |
There are 52 cards in a pack,
and 3 cards in a hand, so the answer is any 3 from 52 - or
52C3 in
shorthand. The total comes to 22,100.
Here is a script to calculate
permutations. For example, any 6 from 49 ( or 49C6
) will give you the number of different lottery tickets you could
buy:
|
|
|
Three of a kind |
There are 4 suits, so for each denomination there are 4C3
= 4 prials; there are 13 denominations, which gives 4 × 13
= 52 possible prials.
|
|
In each of the four suits, you can have 12 straight flushes, starting
off from Ace through to Queen ( Note that both A-2-3 and Q-K-A are
allowed ). That gives 12 × 4 = 48 straight flushes. |
All one suit
All in sequence |
All consecutive |
As noted above, there are 12 different sequences (A-2-3 through to
Q-K-A). But each of the cards in these hands can come from any of
4 suits, so the number of possible straights is 12 × 4 ×
4 × 4 = 768. Subtract from that the 48 straight flushes,
and the final figure is 720. |
|
In each of the 4 suits, there are a possible 13C3
= 286 permutations of cards. 286 × 4 = 1144, but from
that we have to subtract the 48 straight flushes, leaving a true total
of 1096. |
All one suit |
Two of same rank |
There are 13 denominations, and with 4 suits there are for each denomination
4C2 = 6 possible doubles. So the number
of different doubles is 13 × 6 = 78. But for each of these
doubles, the hand can have any of 48 different cards as its third
card ( only 48, as a prial would result from drawing either of the
two remaining cards of the same denomination as your pair). Therefore
the total number of possible hands classed as a pair is 78 ×
48 = 3744. |
|
The techniques for calculating these possibilities are discussed
in the Poker section. For the moment, here is the full table for Brag.
|
Highest Card |
| Hand |
Total |
% |
Blank |
Breakdown
of Highs |
% |
| prial |
52 |
0.24 |
|
Ace |
3,840 |
17.38 |
| Straight
Flush |
48 |
0.22 |
|
King |
3,240 |
14.65 |
| Straight |
720 |
3.26 |
|
Queen |
2,640 |
11.95 |
| Flush |
1,096 |
4.96 |
|
Jack |
2,100 |
9.50 |
| Pair |
3,744 |
16.94 |
|
10 |
1,620 |
7.33 |
| Highs |
16,440 |
74.39 |
|
9 |
1,200 |
5.43 |
| TOTAL |
22,100 |
100.01 |
|
8 |
840 |
3.80 |
|
|
|
|
7 |
540 |
2.44 |
|
|
|
|
6 |
300 |
1.36 |
|
|
|
|
5 |
120 |
0.54 |
|
|
|
|
TOTAL |
16,440 |
74.39 |
NOTES
- The percentages
are rounded, and so don't quite add up
- It is easier to
get a prial than it is to get a straight flush
- In that respect
the precedences of Brag are unmathematical
- The median hand
[ i.e. the average of the two middle hands] is K-10-2
- So
anything better than that is a bonus
|
|
