Posted again because my copy command did not pick up all 25 on the first try.



I have not used the Test Against Selected Modulus (TASM) in a while, but a situation has arisen where it may be useful.
A certain player (let us call him Player J) is in the top 25 but has no wins. Certainly a typo. But that is not the case. Player J is striving to attain first place without any wins.
Now this is where the TASM comes in. The TASM (Test Against Selected Modulus) is designed to spot pga’s of a particular player. Who is helping Player J attain his goal?
The TASM works as follows. Player J has a percentage profile of 00-30-10-09-13-14-20. If there are only six other players with whom Player J has played games, their collective percentage profile would have to be the modulus of Player J’s, or 100-70-90-91-87-86-80. Divided equally among the six players, each J-helper would have a percentage profile of 16-12-15-15-15-14-13. The TASM compares a player against this profile (rather than the uniform distribution profile used by the TAPL). The smaller the TASM, the greater the possibility that the player is a pga of Player J.
The TASM is only an approximation. First, the number of helpers of player J may be less or more than six. Second, some helpers may help more than others. Third, many players have played more games than Player J and obviously cannot have helped Player J in all of them.
Here is a list of the top 25 players and their TASM’s. The number of games per player have been normalized to match that of Player J. The smaller the TASM, the more likely a pga. It will be noted that Player J himself has a very large TASM. That is because he can’t be a pga of himself!


12 amenphis 2486◆ 215 15% 17% 14% 15% 11% 15% 10% ∫ 659 ∫
23 Obi-Wan Kenewbie 1695◆ 215 22% 11% 9% 13% 15% 13% 14% ∫ 744 ∫
2 Vohaul 3610◆ 215 22% 16% 11% 16% 10% 15% 6% ∫ 1617 ∫
7 lesplaydices 2679◆ 215 19% 17% 14% 12% 10% 6% 19% ∫ 1662 ∫
4 Linch 3108◆ 215 22% 17% 16% 10% 14% 11% 6% ∫ 1664 ∫
14 MadHat_Sam 2136◆ 215 21% 16% 8% 9% 10% 15% 18% ∫ 1678 ∫
25 sticks&stones 1547◆ 215 24% 9% 12% 22% 12% 9% 10% ∫ 1781 ∫
1 Zosod 4049◆ 215 23% 19% 11% 14% 13% 9% 8% ∫ 1797 ∫
17 bcmatteagles 2041◆ 215 24% 15% 19% 16% 8% 8% 8% ∫ 2096 ∫
11 fish28 2563◆ 215 15% 23% 16% 8% 14% 12% 10% ∫ 2196 ∫
16 Hart 2084◆ 215 22% 18% 14% 13% 18% 9% 3% ∫ 2436 ∫
9 wishbone 2656◆ 215 24% 18% 16% 9% 16% 12% 4% ∫ 2487 ∫
13 se�kin 2217◆ 215 18% 20% 12% 6% 18% 6% 18% ∫ 2624 ∫
19 Phoenix37 2011◆ 215 30% 12% 11% 9% 9% 10% 15% ∫ 2834 ∫
5 SodaPop 2948◆ 215 28% 12% 19% 13% 12% 4% 9% ∫ 2912 ∫
15 uukrul 2115◆ 215 26% 19% 19% 9% 12% 9% 3% ∫ 3641 ∫
24 DiceLord 1551◆ 215 24% 22% 14% 15% 10% 10% 2% ∫ 3738 ∫
18 Vermont 2031◆ 215 27% 19% 19% 9% 6% 8% 8% ∫ 3762 ∫
6 kissygirl 2794◆ 215 20% 25% 17% 14% 8% 7% 7% ∫ 3766 ∫
21 Grisu 1916◆ 215 23% 25% 16% 5% 8% 8% 11% ∫ 4452 ∫
3 dasfury 3169◆ 215 27% 24% 6% 13% 8% 9% 10% ∫ 4608 ∫
10 miguelz262 2563◆ 215 25% 26% 8% 12% 7% 9% 9% ∫ 4853 ∫
8 retareded rock 2679◆ 215 29% 21% 18% 2% 6% 4% 16% ∫ 6160 ∫
22 Big Jumblies 1742◆ 215 0% 30% 10% 9% 13% 14% 20% ∫ 7317 ∫
20 rerrr 1960◆ 215 26% 30% 9% 9% 11% 9% 1% ∫ 7767 ∫

player J has had 1 win, i always love the fun stats stuff skrum.

that's how you get to top 25 - by being in a disgraceful PGA......

someone should form another clan against Player J's.

Comments:

1) The assumption that the 100-70-90-91-87-86-80 should be divided equally among the players dilutes the value of the test. Why?

Consider the predicted behavior of the extreme cases: PGA with 1 person, and PGA with the whole table.

1a) If there is 1 PGA (call him K), all he has to do is give Player J a dominant position. In order to control the action, especially given the variance occurring late-game, K usually has to survive a long time. Since J is helping K, surviving will be easy. Therefore I expect K to have disproportionately higher 1st-3rd-4th finishes - much more than is indicated by your test basis of 16-12-15-15-15-14-13.

1b) If the whole table is PGA'd, it's very likely that they would both 1) not play seriously amongst themselves, and 2) try to engineer other scores amongst themselves. Both activities combined lead to unequal distributions.

A more likely scenario is that there's no PGA, and Player J is simply calling for second before the game starts (which gives greater alliance potential since J promises to give away first place).

Under the current flag rules, you don't have to call for second, all you have to do is flag when you are first. If there are only one or two other players you will still get points. But you have to wait until four players have flagged. So the lower place finish players can contribute to the objectives of the pga.

The ultimate winner can be an involuntary participant--a pleasantly surprised post-flag recipient (pspfr).

Once it is well-known that Player J wants points does not want to win, other players can manipulate the pga to their own ends, so there can be the original pga and a commensal pga.

The equal division of the 100-70-etc. is under the laws of probability.

Also, I forgot to mention that someone who has played fewer games than Player J cannot have helped Player J in all his games.

"Under the current flag rules, you don't have to call for second, all you have to do is flag when you are first. If there are only one or two other players you will still get points. But you have to wait until four players have flagged. So the lower place finish players can contribute to the objectives of the pga."

Incorrect in its entirety. To flag for second there must only be one other remaining player on the board -- good to see you've been playing alot!

I said, "you don't have to call for second". I didn't say "you have to flag for second".

This is an interesting concept. If players A-Z know what player J's intentions are they will automatically help player J knowing its another ally that wont backstab them in their quest for a win.

Therefore, everyone at the table automatially helps player J knowing it will in the long run assist them in getting 1st.

What a great social experiment. Sounds like player J might be on to something.
I'm curious what player J is up to, maybe Player J knows something we don't?

I'm not really worried about Player J, but most concerned about Preparation H.

cadpilot wins the thread