Study 8J17 Main |
| by Richard Pavlicek |

Virtually all bridge players are familiar with the measurements of a bridge hand, but few are aware of the frequency of occurrence or the percentages involved. For instance, what is the chance of holding at least 13 HCP? Or at most 5 losers? Or exactly 4 controls? Or a balanced hand? Or a 6-card suit? Answers to these and a myriad of other questions can be found here.

HCP | Controls | Guards | Playing Tricks | Losing Tricks | Defensive Tricks | Freakness | Longest | Shortest |

All statistics were found by counting the number of bridge hands (out of 635,013,559,600 possible) that fit each listed quantity for each measurement, in some cases an extremely complicated task. Numbers are shown to four decimal places *unless exact*, so 0.0000 is greater than zero, and 100.0000 (percent) is less than 100, but simply round that way to the nearest 10,000th.

Every bridge player knows about high-card points (HCP), invented by Milton Work about a century ago, before Contract Bridge even existed. In case you’ve been living in a cave: Each ace = 4, each king = 3, each queen = 2, and each jack = 1.

High-Card Points Summary | |
---|---|

Hands evaluated | 635013559600 |

Unique values | 38 |

Minimum | 0 |

Maximum | 37 |

Mode | 10 |

Median | 10 |

Mean | 10 |

Standard deviation | 4.1302 |

The following table shows the number of hands and percent chance for each number of HCP. Percents are shown in three ways: for the *specific* number, *at least* that number, and *at most* that number. To find the chance of an interior range (e.g., 15-17 HCP) add the specific percents of each number in that range.

HCP | Hands | Specific | At Least | At Most |
---|---|---|---|---|

0 | 2310789600 | 0.3639 | 100 | 0.3639 |

1 | 5006710800 | 0.7884 | 99.6361 | 1.1523 |

2 | 8611542576 | 1.3561 | 98.8477 | 2.5085 |

3 | 15636342960 | 2.4624 | 97.4915 | 4.9708 |

4 | 24419055136 | 3.8454 | 95.0292 | 8.8163 |

5 | 32933031040 | 5.1862 | 91.1837 | 14.0025 |

6 | 41619399184 | 6.5541 | 85.9975 | 20.5565 |

7 | 50979441968 | 8.0281 | 79.4435 | 28.5846 |

8 | 56466608128 | 8.8922 | 71.4154 | 37.4768 |

9 | 59413313872 | 9.3562 | 62.5232 | 46.8331 |

10 | 59723754816 | 9.4051 | 53.1669 | 56.2382 |

11 | 56799933520 | 8.9447 | 43.7618 | 65.1828 |

12 | 50971682080 | 8.0269 | 34.8172 | 73.2097 |

13 | 43906944752 | 6.9143 | 26.7903 | 80.1240 |

14 | 36153374224 | 5.6933 | 19.8760 | 85.8174 |

15 | 28090962724 | 4.4237 | 14.1826 | 90.2410 |

16 | 21024781756 | 3.3109 | 9.7590 | 93.5520 |

17 | 14997082848 | 2.3617 | 6.4480 | 95.9137 |

18 | 10192504020 | 1.6051 | 4.0863 | 97.5187 |

19 | 6579838440 | 1.0362 | 2.4813 | 98.5549 |

20 | 4086538404 | 0.6435 | 1.4451 | 99.1985 |

21 | 2399507844 | 0.3779 | 0.8015 | 99.5763 |

22 | 1333800036 | 0.2100 | 0.4237 | 99.7864 |

23 | 710603628 | 0.1119 | 0.2136 | 99.8983 |

24 | 354993864 | 0.0559 | 0.1017 | 99.9542 |

25 | 167819892 | 0.0264 | 0.0458 | 99.9806 |

26 | 74095248 | 0.0117 | 0.0194 | 99.9923 |

27 | 31157940 | 0.0049 | 0.0077 | 99.9972 |

28 | 11790760 | 0.0019 | 0.0028 | 99.9990 |

29 | 4236588 | 0.0007 | 0.0010 | 99.9997 |

30 | 1396068 | 0.0002 | 0.0003 | 99.9999 |

31 | 388196 | 0.0001 | 0.0001 | 100.0000 |

32 | 109156 | 0.0000 | 0.0000 | 100.0000 |

33 | 22360 | 0.0000 | 0.0000 | 100.0000 |

34 | 4484 | 0.0000 | 0.0000 | 100.0000 |

35 | 624 | 0.0000 | 0.0000 | 100.0000 |

36 | 60 | 0.0000 | 0.0000 | 100.0000 |

37 | 4 | 0.0000 | 0.0000 | 100 |

U = 38 | 635013559600 | 100 | 3900 |

Study 8J17 Main | Top Hand Evaluation Stats |

Controls are counted simply as 2 for each ace and 1 for each king.

Controls Summary | |
---|---|

Hands evaluated | 635013559600 |

Unique values | 13 |

Minimum | 0 |

Maximum | 12 |

Mode | 3 |

Median | 3 |

Mean | 3 |

Standard deviation | 1.8150 |

The following table shows the number of hands and percent chance of each number of controls. Percents are shown in three ways: for the *specific* number, *at least* that number, and *at most* that number. To find the chance of an interior range (e.g., 3-4 controls) add the specific percents of each number in that range.

Controls | Hands | Specific | At Least | At Most |
---|---|---|---|---|

0 | 51915526432 | 8.1755 | 100 | 8.1755 |

1 | 84362730452 | 13.2852 | 91.8245 | 21.4607 |

2 | 130378765244 | 20.5317 | 78.5393 | 41.9923 |

3 | 132634453224 | 20.8869 | 58.0077 | 62.8792 |

4 | 106275127972 | 16.7359 | 37.1208 | 79.6151 |

5 | 70893050800 | 11.1640 | 20.3849 | 90.7791 |

6 | 36155455908 | 5.6937 | 9.2209 | 96.4728 |

7 | 15596471176 | 2.4561 | 3.5272 | 98.9288 |

8 | 5192436964 | 0.8177 | 1.0712 | 99.7465 |

9 | 1322059596 | 0.2082 | 0.2535 | 99.9547 |

10 | 258159616 | 0.0407 | 0.0453 | 99.9954 |

11 | 28236208 | 0.0044 | 0.0046 | 99.9998 |

12 | 1086008 | 0.0002 | 0.0002 | 100 |

U = 13 | 635013559600 | 100 | 1400 |

Study 8J17 Main | Top Hand Evaluation Stats |

Guards is a measurement I invented to define protection for notrump play. A suit is guarded (stopped) if at least as good as A, K-x, Q-x-x, J-x-x-x, 10-x-x-x-x or any six cards; *partially* guarded (half a stopper) if at least as good as K, Q-x, J-x-x, 10-x-x-x or any five cards; and *twice* guarded (double stopper) if at least as good as A-Q, K-J-x, Q-10-x-x or J-9-x-x-x. Guards assume you are *behind* the missing honors, or the suit is led around to you, so might not fulfill in practice, but experience has shown that optimism is a winning trait.

While a suit could also be *thrice* guarded (triple stopper) or more, this would have little if any relevance in actual play, so a double guard includes anything stronger as well. Therefore, each suit can have zero, 0.5, 1 or 2 guards, and the range for a bridge hand is 0 to 8 in 0.5 increments, except 7.5 is impossible.

Guards Summary | |
---|---|

Hands evaluated | 635013559600 |

Unique values | 16 |

Minimum | 0 |

Maximum | 8 |

Mode | 4 |

Median | 4 |

Mean | 3.7757 |

Standard deviation | TBD |

The following table shows the number of hands and percent chance of each number of guards. Percents are shown in three ways: for the *specific* number, *at least* that number, and *at most* that number. To find the chance of an interior range (e.g., 4-5 guards) add the specific percents of each number in that range.

Guards | Hands | Specific | At Least | At Most |
---|---|---|---|---|

0 | 403313120 | 0.0635 | 100 | 0.0635 |

0.5 | 1282854496 | 0.2020 | 99.9365 | 0.2655 |

1 | 8347621540 | 1.3146 | 99.7345 | 1.5801 |

1.5 | 11620495420 | 1.8300 | 98.4199 | 3.4101 |

2 | 48343143440 | 7.6129 | 96.5899 | 11.0230 |

2.5 | 42415369052 | 6.6794 | 88.9770 | 17.7024 |

3 | 118469367036 | 18.6562 | 82.2976 | 36.3586 |

3.5 | 60262891660 | 9.4900 | 63.6414 | 45.8486 |

4 | 148255312584 | 23.3468 | 54.1514 | 69.1954 |

4.5 | 46267945572 | 7.2861 | 30.8046 | 76.4816 |

5 | 94882534192 | 14.9418 | 23.5184 | 91.4234 |

5.5 | 14174326212 | 2.2321 | 8.5766 | 93.6555 |

6 | 32675670276 | 5.1457 | 6.3445 | 98.8012 |

6.5 | 2291913396 | 0.3609 | 1.1988 | 99.1621 |

7 | 4960141408 | 0.7811 | 0.8379 | 99.9432 |

8 | 360660196 | 0.0568 | 0.0568 | 100 |

U = 16 | 635013559600 | 100 | 1700 |

Study 8J17 Main | Top Hand Evaluation Stats |

Playing tricks is a measurement of trick-taking potential with your longest suit trumps. This is typically used to decide how high to bid with a 6+ card suit (more often 7+) but can be applied any time. The top three cards in each suit are estimated for trick production (see chart) and 1 trick is added for each card over three in any suit; hence every hand has at least 1 playing trick. Common practice is to consider half-trick increments, implying that a full trick will materialize about half the time.

K, Q-x, K-x, J-10-x, Q-x-x | 0.5 |

A, K-J, K-Q, A-x, Q-J-x, K-x-x, A-x-x | 1 |

A-J, A-Q, K-J-10, K-Q-x, A-J-x, A-Q-x | 1.5 |

A-K, K-Q-J, A-Q-10, A-K-x | 2 |

A-Q-J, A-K-J | 2.5 |

A-K-Q | 3 |

Refinements: In an 8-card suit each listed holding with an ‘x’ (except Q-J-x) is increased by half a trick, e.g., A-x-x-x-x-x-x-x = 6.5 tricks. In a 9 or 10-card suit, only the top two cards matter (each card over two is a trick), e.g., A-K-x-x-x-x-x-x-x = 9 tricks. And for the real dreamers, with 11+ cards only the ace matters; if you have it assume all winners, else all but one.

Playing Tricks Summary | |
---|---|

Hands evaluated | 635013559600 |

Unique values | 25 |

Minimum | 1 |

Maximum | 13 |

Mode | 5 |

Median | 5.5 |

Mean | 5.3685 |

Standard deviation | 1.5783 |

The following table shows the number of hands and percent chance for each number of playing tricks. Percents are shown in three ways: for the *specific* number, *at least* that number, and *at most* that number. To find the chance of an interior range (e.g., 6.5 to 7.5 playing tricks) add the specific percents of each number in that range.

Tricks | Hands | Specific | At Least | At Most |
---|---|---|---|---|

1 | 1022787584 | 0.1611 | 100 | 0.1611 |

1.5 | 1834835968 | 0.2889 | 99.8389 | 0.4500 |

2 | 8288385280 | 1.3052 | 99.5500 | 1.7552 |

2.5 | 13587961408 | 2.1398 | 98.2448 | 3.8950 |

3 | 29907404912 | 4.7097 | 96.1050 | 8.6048 |

3.5 | 41453445520 | 6.5280 | 91.3952 | 15.1327 |

4 | 61513033480 | 9.6869 | 84.8673 | 24.8196 |

4.5 | 70986532496 | 11.1787 | 75.1804 | 35.9983 |

5 | 80169517920 | 12.6249 | 64.0017 | 48.6232 |

5.5 | 77238005980 | 12.1632 | 51.3768 | 60.7864 |

6 | 70723648784 | 11.1373 | 39.2136 | 71.9237 |

6.5 | 57473116632 | 9.0507 | 28.0763 | 80.9744 |

7 | 44455847496 | 7.0008 | 19.0256 | 87.9752 |

7.5 | 30812461108 | 4.8523 | 12.0248 | 92.8275 |

8 | 20488020544 | 3.2264 | 7.1725 | 96.0539 |

8.5 | 12080979332 | 1.9025 | 3.9461 | 97.9563 |

9 | 6865130592 | 1.0811 | 2.0437 | 99.0374 |

9.5 | 3412850548 | 0.5374 | 0.9626 | 99.5749 |

10 | 1635279380 | 0.2575 | 0.4251 | 99.8324 |

10.5 | 673249156 | 0.1060 | 0.1676 | 99.9384 |

11 | 269155616 | 0.0424 | 0.0616 | 99.9808 |

11.5 | 86893416 | 0.0137 | 0.0192 | 99.9945 |

12 | 27926304 | 0.0044 | 0.0055 | 99.9989 |

12.5 | 5652256 | 0.0009 | 0.0011 | 99.9998 |

13 | 1437888 | 0.0002 | 0.0002 | 100 |

U = 25 | 635013559600 | 100 | 2600 |

Study 8J17 Main | Top Hand Evaluation Stats |

Losing trick count (LTC) is a method of evaluating hands for suit play. Each suit has 0-3 losers, so an entire bridge hand has 0-12 losers. More specifically, a void suit = 0 losers; a singleton = 1 loser (unless the ace, then 0); a doubleton = 2 losers (unless A-K, then 0, or with ace or king = 1); suits of 3+ cards have one loser for each missing ace, king and queen.

Refinements: In a suit of 8-10 cards only the ace and king matter; i.e., A-K = 0 losers, A or K = 1 loser, else 2 losers. (With exactly 8 cards this is slightly optimistic — a *half* loser would be fairer for a missing queen — but LTC advocates rarely use fractions, and going long is better than no adjustment at all.) With 11+ cards only the ace matters, hence 0 or 1 loser accordingly.

Losing Tricks Summary | |
---|---|

Hands evaluated | 635013559600 |

Unique values | 13 |

Minimum | 0 |

Maximum | 12 |

Mode | 8 |

Median | 8 |

Mean | 7.5566 |

Standard deviation | 1.5739 |

The following table shows the number of hands and percent chance for each losing trick count. Percents are shown in three ways: for the *specific* number, *at least* that number, and *at most* that number. To find the chance of an interior range (e.g., 4-5 losers) add the specific percents of each number in that range.

Losers | Hands | Specific | At Least | At Most |
---|---|---|---|---|

0 | 1611768 | 0.0003 | 100 | 0.0003 |

1 | 39329036 | 0.0062 | 99.9997 | 0.0064 |

2 | 454375244 | 0.0716 | 99.9936 | 0.0780 |

3 | 3126502788 | 0.4924 | 99.9220 | 0.5704 |

4 | 14069567832 | 2.2156 | 99.4296 | 2.7860 |

5 | 43541225304 | 6.8567 | 97.2140 | 9.6427 |

6 | 94901190408 | 14.9448 | 90.3573 | 24.5875 |

7 | 145807470468 | 22.9613 | 75.4125 | 47.5488 |

8 | 155515164912 | 24.4901 | 52.4512 | 72.0388 |

9 | 111719209440 | 17.5932 | 27.9612 | 89.6320 |

10 | 51111464400 | 8.0489 | 10.3680 | 97.6809 |

11 | 13274928000 | 2.0905 | 2.3191 | 99.7714 |

12 | 1451520000 | 0.2286 | 0.2286 | 100 |

U = 13 | 635013559600 | 100 | 1400 |

Study 8J17 Main | Top Hand Evaluation Stats |

Defensive tricks, also known as “quick tricks,” is a measurement of defensive prospects with your shortest suit trumps. At most 2 tricks can be counted in each suit per the formula: A-K = 2, A-Q = 1.5, A or K-Q = 1, K = 0.5; hence the range for a bridge hand is 0 to 8. Note that a king does not have to be guarded, as a singleton king usually has the same chance to win a trick.

Refinements: In a 7 or 8-card suit only *one* defensive trick can be counted (no halves) for which you must have the ace. For example, A-K-x-x-x-x-x = 1 (only a fool would expect A-K to cash) and K-Q-J-x-x-x-x = 0. Further, you cannot count any defensive trick in a 9+ card suit — not a likely issue since you’d rarely be defending.

Flukes: A hand with A-K-Q in *every* suit arguably has 9 defensive tricks, since a third trick is assured in whichever suit is trumps; similarly, at least A-K-J in every suit is arguably worth 8.5 tricks. These rare cases are ignored, so the maximum per suit is always 2.

Defensive Tricks Summary | |
---|---|

Hands evaluated | 635013559600 |

Unique values | 17 |

Minimum | 0 |

Maximum | 8 |

Mode | 1 |

Median | 1.5 |

Mean | 1.7782 |

Standard deviation | 1.1248 |

The following table shows the number of hands and percent chance for each number of defensive tricks. Percents are shown in three ways: for the *specific* number, *at least* that number, and *at most* that number. To find the chance of an interior range (e.g., 2.5 to 3 defensive tricks) add the specific percents of each number in that range.

Tricks | Hands | Specific | At Least | At Most |
---|---|---|---|---|

0 | 54389790360 | 8.5651 | 100 | 8.5651 |

0.5 | 61602628572 | 9.7010 | 91.4349 | 18.2661 |

1 | 113660108928 | 17.8988 | 81.7339 | 36.1650 |

1.5 | 96416902372 | 15.1834 | 63.8350 | 51.3484 |

2 | 111050090784 | 17.4878 | 48.6516 | 68.8362 |

2.5 | 72935403696 | 11.4856 | 31.1638 | 80.3219 |

3 | 59887556392 | 9.4309 | 19.6781 | 89.7528 |

3.5 | 31112636760 | 4.8995 | 10.2472 | 94.6523 |

4 | 20067427740 | 3.1602 | 5.3477 | 97.8125 |

4.5 | 7980162216 | 1.2567 | 2.1875 | 99.0692 |

5 | 4055992444 | 0.6387 | 0.9308 | 99.7079 |

5.5 | 1214000280 | 0.1912 | 0.2921 | 99.8991 |

6 | 502896536 | 0.0792 | 0.1009 | 99.9783 |

6.5 | 99889520 | 0.0157 | 0.0217 | 99.9940 |

7 | 33145000 | 0.0052 | 0.0060 | 99.9992 |

7.5 | 3843840 | 0.0006 | 0.0008 | 99.9998 |

8 | 1084160 | 0.0002 | 0.0002 | 100 |

U = 17 | 635013559600 | 100 | 1800 |

Study 8J17 Main | Top Hand Evaluation Stats |

Many years ago I devised a method to rank the 39 generic hand patterns on a linear scale. The formula counts 1 point for each card over four or under three in each suit, plus 1 extra point if the hand has any singleton (or 2 extra points if the hand has any void). This creates a simple scale that I have found useful in many ways. For instance, a balanced hand is easily defined as having freakness less than 3.

4-3-3-3 | 0 |

4-4-3-2 | 1 |

5-3-3-2 | 2 |

4-4-4-1, 5-4-2-2 | 3 |

5-4-3-1, 6-3-2-2 | 4 |

6-3-3-1 | 5 |

5-4-4-0, 5-5-2-1, 6-4-2-1, 7-2-2-2 | 6 |

5-5-3-0, 6-4-3-0, 7-3-2-1 | 7 |

6-5-1-1, 7-3-3-0, 7-4-1-1 | 8 |

6-5-2-0, 7-4-2-0, 8-2-2-1, 8-3-1-1 | 9 |

8-3-2-0 | 10 |

6-6-1-0, 7-5-1-0, 8-4-1-0, 9-2-1-1 | 11 |

9-2-2-0, 9-3-1-0 | 12 |

7-6-0-0, 8-5-0-0, 9-4-0-0, 10-1-1-1 | 13 |

10-2-1-0, 10-3-0-0 | 14 |

11-1-1-0 | 16 |

11-2-0-0 | 16 |

12-1-0-0 | 18 |

13-0-0-0 | 20 |

Freakness Summary | |
---|---|

Hands evaluated | 635013559600 |

Unique values | 18 |

Minimum | 0 |

Maximum | 20 |

Mode | 1 |

Median | 3 |

Mean | 2.9829 |

Standard deviation | 2.2056 |

The following table shows the number of hands and percent chance for each freakness (missing numbers 15, 17 and 19 are impossible by the formula). Percents are shown in three ways: for the *specific* number, *at least* that number, and *at most* that number. To find the chance of an interior range (e.g., freakness 3-4) add the specific percents of each number in that range.

Freakness | Hands | Specific | At Least | At Most |
---|---|---|---|---|

0 | 66905856160 | 10.5361 | 100 | 10.5361 |

1 | 136852887600 | 21.5512 | 89.4639 | 32.0873 |

2 | 98534079072 | 15.5168 | 67.9127 | 47.6042 |

3 | 86189672140 | 13.5729 | 52.3958 | 61.1770 |

4 | 117942306768 | 18.5732 | 38.8230 | 79.7502 |

5 | 21896462016 | 3.4482 | 20.2498 | 83.1984 |

6 | 61166193660 | 9.6323 | 16.8016 | 92.8307 |

7 | 26049899304 | 4.1023 | 7.1693 | 96.9329 |

8 | 8651399328 | 1.3624 | 3.0671 | 98.2953 |

9 | 8399095848 | 1.3227 | 1.7047 | 99.6180 |

10 | 689049504 | 0.1085 | 0.3820 | 99.7265 |

11 | 1548621360 | 0.2439 | 0.2735 | 99.9704 |

12 | 116001600 | 0.0183 | 0.0296 | 99.9887 |

13 | 63860368 | 0.0101 | 0.0113 | 99.9987 |

14 | 7941648 | 0.0013 | 0.0013 | 100.0000 |

16 | 231192 | 0.0000 | 0.0000 | 100.0000 |

18 | 2028 | 0.0000 | 0.0000 | 100.0000 |

20 | 4 | 0.0000 | 0.0000 | 100 |

U = 18 | 635013559600 | 100 | 1900 |

Study 8J17 Main | Top Hand Evaluation Stats |

The longest suit of a bridge hand must be from 4 to 13 cards. This was once challenged by my Uncle Cedric who opened 1 on Q-x-x in a drunken stupor. When asked about the psych he blathered, “It wasn’t a friggin’ psych! What else could I bid with five doubletons?”

Longest Suit Summary | |
---|---|

Hands evaluated | 635013559600 |

Unique values | 10 |

Minimum | 4 |

Maximum | 13 |

Mode | 5 |

Median | 5 |

Mean | 4.9008 |

Standard deviation | 0.8342 |

The following table shows the number of hands and percent chance for each longest suit. Percents are shown in three ways: for the *specific* number, *at least* that number, and *at most* that number. To find the chance of an interior range (e.g., 6-7 card suit) add the specific percents of each number in that range.

Longest Suit | Hands | Specific | At Least | At Most |
---|---|---|---|---|

4 | 222766089260 | 35.0805 | 100 | 35.0805 |

5 | 281562853572 | 44.3397 | 64.9195 | 79.4202 |

6 | 105080049360 | 16.5477 | 20.5798 | 95.9679 |

7 | 22394644272 | 3.5266 | 4.0321 | 99.4945 |

8 | 2963997036 | 0.4668 | 0.5055 | 99.9613 |

9 | 235237860 | 0.0370 | 0.0387 | 99.9983 |

10 | 10455016 | 0.0016 | 0.0017 | 100.0000 |

11 | 231192 | 0.0000 | 0.0000 | 100.0000 |

12 | 2028 | 0.0000 | 0.0000 | 100.0000 |

13 | 4 | 0.0000 | 0.0000 | 100 |

U = 10 | 635013559600 | 100 | 1100 |

Study 8J17 Main | Top Hand Evaluation Stats |

The shortest suit of a bridge hand must be from 0 to 3 cards.

Shortest Suit Summary | |
---|---|

Hands evaluated | 635013559600 |

Unique values | 4 |

Minimum | 0 |

Maximum | 3 |

Mode | 2 |

Median | 2 |

Mean | 1.6977 |

Standard deviation | 0.7237 |

The following table shows the number of hands and percent chance for each shortest suit. Percents are shown in three ways: for the *specific* number, *at least* that number, and *at most* that number.

Shortest Suit | Hands | Specific | At Least | At Most |
---|---|---|---|---|

0 | 32427298180 | 5.1066 | 100 | 5.1066 |

1 | 194023212812 | 30.5542 | 94.8934 | 35.6607 |

2 | 341657192448 | 53.8031 | 64.3393 | 89.4639 |

3 | 66905856160 | 10.5361 | 10.5361 | 100 |

U = 4 | 635013559600 | 100 | 500 |

Check total of *At Least + At Most* should be 100(U+1). For example, if the specific percents for “Shortest Suit” are designated [abcd] then *At Least* column is a+b+c+d+b+c+d+c+d+d, and *At Most* column is a+a+b+a+b+c+a+b+c+d, so the sum of both columns is 5(a+b+c+d) or 500 percent.

Study 8J17 Main | Top Hand Evaluation Stats |

© 2012 Richard Pavlicek