Glossary and Terminology
AoIG - Academy of Intellectual Games has created as a non-profit organization. AoIG main goal is to promote Mind Sport Games (MSG), like bridge, chess, poker, backgammon, trivia games, and others in a social settings and format of the fair sport competition. AoIG is organization, which had created by players, to be run by players and to benefit players.
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AoIG Rating (A_{R}) is AoIG way to measure MSG Player overall playing ability. As it was shown on healthy MSG pyramid (see article Principles of PM Competition), there are two main motivations for players to excel in a game they play - PRIDE and MONEY. So nobody should be surprised if we draw a very simple formula for our overall rating:
A_{R} =(1+M_{R}) * P_{R},
Where M_{R} is a Money rating
And P_{R} is a Pride rating
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Athlete/Mind Sport Athlete/Player is a willing participant of a tournament, with a paid entry fee (usually paid by player himself, but could be paid on behalf of a player by a sponsor), who agrees to release the AoIG , organizers and sponsors from any and all liability for running tournament, conditions of contest, directors ruling or other procedural matter and agrees for his name to be used for publicity and promotion of the Game.
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Coefficient of Fairness of PMT (C_{fpmt}). - In a Fair or Enriched payoff tournament, where "Winners play for FREE" the C_{fpmt} is always 1.
C_{fpmt} will be < 1, if at least one of the above conditions would not met. In such cases the following formula is used:
C_{fpmt} = (PMP - Winners under-paid PM) / (PMPET + EEFT),
Where Winners under-paid PM is $ amount, which should be added to PMP to enforce "Winners play for FREE" rule.
Let's use an example of 10 players tournament, here each player put $15 in (PMPE = $15; PMPET = 10x$15 = $150), and a $5 EEF to get in tournament (EEFT=10x$5=$50), the 5th place finisher - top 50% - had received $11.25, which was $3.75 short of the "Winners play for FREE" promise. Therefore C_{fpmt} = (150 - 5) / (150 + 50) = 0.725.
An other rule of thumb, than closer C_{fpmt} to 1, than it will be more FAIR to the average player. So, do the Fair PMTs promote mediocrity? Not at all. But they do appeal to the most number of players, without lowering competitiveness of the event. For details on how it really works see Principles of PM competition.
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Early Entry Fee (EEF) is the lowest fee player can pay (due to early registration) to get into tournament. EEF will be used to cover administrative and facilitation expenses of running tournament. For Price Money Entry of each player see Price Money Pool Entry (PMPE).
As main AoIG , guide line player will be allowed to pay an EEF for at least 1 week advanced registration. From 7 days to 1 day (24 hours before start of tournament) , the price to get in is 1.25 EEF (extra 25%) and 1.5 EEF (50% more) at-the-door or day of tournament start registration.
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Early Entry Fee Total(EEFT) is total entry fee for N participants, based on early registration. PMP/(PMPET + EEFT) ratio is used in determination of type of PMT.
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Fair Prize Money Tournament (FPMT) is PMT with fair or enriched payoff, where "Winners play for FREE" principle is enforced.
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Game Unit (GU) - usually a 4 hours of play.
In Chess, it is approximately 1 game with standard control.
In Bridge, it is 24 boards (15 mins for 2 boards).
How many GUs it takes to determine a winner is a important part of formula
used in Money Rating and Pride Rating
calculation.
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Individual Challenge Match (ICM) is a match between two players or two teams of players. The winner(s) of the match will increase their Money Rating if the following 3 conditions are met:
1. ICM had been played for Prize Money (of course)
2. ICM had been played under umbrella of AoIG
or any other Official Game Promoter (OGP).
3. Date and time of the match should become a public domain at least 7 days
before start of the match.
General public should be admitted to observe the match in progress for free
or by buying a ticket for a price not greater than 1/100 of PMP.
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Mind Sport Game (MSG) is a type of game where the more skillful player will always prevail on long run by using logic, calculation, intuition and previous experience. MSG competition is NOT a gamble, even if the success of each individual move/call made by player can depend on numerous factors like, next card to be dealt, throw of the dice, or his opponent's chance to find the best response in a complex position. We believe, when more skillful and experienced player has better chances to win a tournament - it is a fair competition. AoIG will play an active roll in setting the most fair condition for competition for each of the game we promote.
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Money Rating (or M_{R}) is AoIG way to measure athlete current money making ability. By participating in any tournament player can only increase his money rating. AoIG will calculate M_{R} earned by player using formula below:
M_{R} = PM * C_{fpmt} * PMAR / GU * 100,
Where PM = Prize Money player receives for his performance.
To better understand how "money" points calculation work, let's examine 10 people tournament payoff schedule we use for local sponsored tournaments. It is a fair payoff tournament where EEFT = $0, in other words, players do not pay an administrative cost of running the tournament, it is paid by sponsor. Athletes only contribute to the PMP. All Prize Money are given in PMPE unit:
Table 1.#players | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Place | |||||||||
First | 2 | 2 | 2 | 2.5 | 3 | 3 | 3 | 3.5 | 3.5 |
Second | - | 1 | 1.5 | 1.5 | 1.5 | 2 | 2 | 2 | 2.25 |
Third | - | .5 | 1 | 1 | 1.5 | 1.5 | 1.5 | 1.75 | |
4^{th} | - | - | .5 | .5 | 1 | 1.25 | 1.25 | ||
5^{th} | - | - | - | .5 | .75 | .75 | |||
6^{th} | - | - | - | - | .5 | ||||
7^{th} ..10^{th} | - | - | - | - | |||||
C_{fpmt} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | .975 |
The C_{fpmt} is 1 for any number of players for the exception of 10 players table where the "Winners play for FREE" principle is compromise - 5^{th} place is in a top 50%, which is a winner position, but paid only 75% of PMPE. (The C_{fpmt} could be proportionally less in case of negative payoff tournament, which is given when tournament is running without a sponsor.
Lets say it takes on average 2 hours (0.5 GU) to finish tournament, therefore $20 PMPE for only half of unit will have an effect of $40 PMPE per GU.
Notice that M_{R} points could not be calculated just based on a table shown above - the amount of PM, the PMPE and EEF should be specified in a US$, as well. Lets take the 2^{nd} place finisher, he will earn M_{R} points according to the Formula:
M_{R} points = PM * C_{fpmt} * PMAR / 0.5 * 100.
Result for second place finisher depends on number of players and has shown below:
Table 2.## players | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
PM (in $) | 0 | 20 | 30 | 30 | 30 | 40 | 40 | 40 | 45 |
C_{fpmt} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.975 |
PMAR | 1.3 | 2 | 2 | 2.5 | 3 | 3 | 3 | 3.5 | 3.5 |
M_{R} points | 0 | 0.8 | 1.2 | 1.5 | 1.8 | 2.4 | 2.4 | 2.6 | 3.1 |
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Money Stakes per Game Unit (MSpGU) is an other way to measure a level of PMT (also see PMTR).
Examples: 7 rounds chess tournament with EEF=$100 will translate to MSpGU=100/7 ~$14.3 per GU.
Poker tournament with EEF=$1000, which design to run for about 10 hours to determine a winner same as MSpGU=1000/2.5 = $400 per GU.
Some people will say that bigger Money Stakes not necessary will attract the better players, just the richest players, who can afford to loose more. In general, we tend to disagree with such statement.
The AoIG 's ultimate goal for each PMT, that all participants have fun and some educational experience. In a payoff structure of Fair PMT with C_{fpmt} = 1, there are two groups of players in relation to the educational experience: bottom half pays for it, and top half got paid for providing it.
Now, when looking at the Money Stakes / Entry Fees of PMT from this angle one can see, that experience players (regardless of financial status) will seek the highest stake (MSpGU) tournament, where they still can identify themselves with the "top half". On the other hand, players who can identify themselves with the bottom half will play on a level where they can afford to pay for an educational experience.
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Official Game Promoters (OGP) - AoIG will recognize existing National and World federations as an OGP. Any other organization can be placed on a list of OGPs, if AoIG has enough evidence that such an organization has resources and agree to run a PMTs under AoIG's guide lines of the fair sport competition. OPG's primary business may not be related to MSG industry.
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Pride Rating (or P_{R} ) is
AoIG
way to measure the player performance based on his/her placements in tournaments
he/she had participated. P_{R} doesn't necessary measure the
"absolute" strength of player against very best, it just shows how
well player had performed in the "fights he had chosen".
Unlike
M_{R}, P_{R} can
go not only up, but down as well. P_{R} should always be calculated
for defined period of time - P_{R} of multi-tournament event
or P_{R} usually calculated for a calendar year:
P_{R} = (T1_P_{R }+ T2_P_{R} + & + Tx_Pr) / X
Where Tx_Pr is one tournament pride rating:
Tx_Pr = (N_{PB} + N_{Pbellow}) * GUs * C_{123}
X is the number of tournaments
N_{PB}_{ }is number of players, which has been "beaten" and ½ for each tie. Bridge pair/teams clarification: each out-performed pair counted as 2 (two players), each out-performed team counted as 4 (minimum numbers of players on a team).
N_{Pbellow} is number of players below the player's flight (if flighted).
GUs - game units.
C_{123} is placement bonus. Below is mathematical way to say, that placement bonus can be greater than 1 only if number of players in PM Group( N_{P})>4.
C_{123} for N_{P}<=4 = 1;
C_{123} for N_{P}>4
C_{123} (>3) = 1;
C_{123} (3) = 3/2 =1.5;
C_{123} (2) = 2;
C_{123} (1) = 3
To insure a fair comparison player have 100% of earned points counted forward P_{R} when he had played in at least 3 tournaments(T>=3). If T=1 only 50% counted, when T=2 only 75%.
Last important rule: The winner(s), 1^{st} place, of any PM Group could not lower his/her Pr as the result of the tournament he/she won. If P_{R} of the PM Group winner after tournament X is lower that after tournament (X-1), than P_{R} considered to be locked until player continues to win the PM Groups he enters OR his/her P_{R} should go up.
Let's calculate P_{R }points earned by second place finisher in the scenario used for M_{R} calculation (for the simplicity of this example let's assumed this is the lowest flight):
Table 3.## players | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
C_{123} | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
GUs | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
P_{R}points | 0 | 0.5 | 1 | 1.5 | 3 | 3.75 | 4.5 | 5.25 | 6 |
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Prize Money Pool (PMP) is the total amount of money, which would be paid to the winners of tournament with N participants. PMP always made up from two parts - players and sponsors contribution. The previous statement could be expressed in the formula: PMP = PMPET + SC.
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Prize Money Pool Entry (PMPE) is monetary contribution of each player to the total PMP. AoIG uses a "revolutionary" approach to the player's contribution to PMP.
After an Entry Fee is paid to cover organizational expenses, player(or team) is free to choose the playing level group (could be flighted or stratified, by the choice of tournament organizers) he feels he belongs to. AoIG 's guide lines to the size of PMPE per 1 GU (Usually about 4 hours of play):
Table 4.Group ## | PMPE/GUs in $$US | General description | Game specific rating | |
Chess: USCF Rating |
Bridge: ACBL Points |
|||
G-0 | 5 .. 9 | First step | 0 .. 1199 | 0 .. 5 |
G-1 | 10 .. 19 | Beginner | 1200 .. 1399 | 5 .. 50 |
G-2 | 20 .. 49 | Novice | 1400 .. 1799 | 50 .. 100 |
G-3 | 50 .. 99 | Amateur | 1800 .. 1999 | 100 .. 500 |
G-4 | 100 .. 199 | Skillful | 2000 .. 2199 | 500 .. 1000 |
G-5 | 200 .. 499 | Regional Expert | 2200 .. 2399 | 1,000 .. 5,000 |
G-6 | 500 .. 999 | National Expert | 2400 .. 2599 | 5,000 ...10,000 |
G-7 | 1000+ | World Expert | 2600 + | 10,000+ |
Note! Currently there is no real correlation between size of the entry fee MSG athletes are willing to pay and their skill level. Nor there is tight correlation between chess and bridge rating and the playing skill level of the athletes. In chess the rating is compromised (especially in G3,G4, and G5) due to the "sand bagging" efforts of some not very "game ethical" players; in bridge the rating is off the mark due to it's own nature - always to go up with time. AoIG Rating (A_{R}) is solution for many of the above mentioned problems.
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Prize Money Pool Entry TOTAL (PMPET) is total monetary contribution of all N participants to the PMP of the tournament.
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Prize Money Tournament (PMT) is a tournament where player will receive a cash payoff, depending on how successful was his performance.
There are three types of PMT depending on a size of PMP in relation to the EEFT and PMPET:
1. Negative Payoff is were PMP is less than (PMPET + EEFT).
2. Fair Payoff is where PMP equal to (PMPET + EEFT)
3. Enriched Payoff is where PMP is greater than (PMPET + EEFT).
The size of PMP usually depends on number of participants and Sponsors Contribution (SC). Sometimes the minimum PMP is guarantee in advance and it can only be bigger if number of players will be greater than designated minimum.
Currently, almost all PMT organizers do not differentiate between Price Money Pool Entry and Entry Fee. Usually, the first is collected as a part of the second. Some tournaments proudly advertise that 70 % to 75% of Entries Fees will go to the PMP.
AoIG takes different approach. We separate the entry fees to cover organizational expenses from the money going into PMP, from the very beginning. That allows to created fair structured tournament, where every player pays the same to cover tournament expenses; but after that, every player can choose which prize money group/section to enter depending on his own estimation of his playing abilities.
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Prize Money Tournament Ratio (PMTR or PMR) is result of division 1^{st} prize by EEF ->PMR=1^{st} prize / (PMPE + EEFT). In calculation of MSG Rating we use Prize Money Adjusted Ratio (PMAR), which is design to prevent "artificial" bust to PMTR by given more than 65% of PMP to the 1^{st} place.
Use of PMAR instead of PMTR also beneficial during calculation of MSG Rating for individual challenge matches (ICM), when by definition the winner gets 100% - only 65% of it will be counted toward MSG Rating to promote tournament concept as a preferred format of competition.. So if 1^{st} prize > 0.65 * PMP, than
PMAR = 0.65 * PMP / PMPE, in all other cases PMTR (or PMR) = PMAR.
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Sponsor Contribution (SC) is the sponsor monetary contribution (if any) to the PMP of the tournament.
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"Winners play for FREE" principle is where the top 50 % of the tournament participants will receive prize money equal or greater than PMPE.
Here is an example of this principle enforcement for fair payoff PMT for number of participants from 2 to 12 (All payoff numbers are given in PMPE = 1 Unit).
Table 5.#players | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Place | |||||||||||
First | 2 | 2 | 2.5 | 3 | 3 | 3 | 3.5 | 3.5 | 3.5 | 3.5 | 4 |
Second | - | 1 | 1.5 | 1.5 | 2 | 2 | 2 | 2.25 | 2.25 | 2.25 | 2.25 |
Third | - | - | 0.5 | 1 | 1.5 | 1.5 | 1.75 | 1.75 | 2 | 2 | |
4^{th} | - | - | - | .5 | 1 | 1 | 1.5 | 1.5 | 1.5 | ||
5^{th} | - | - | - | - | .5 | 1 | 1.25 | 1.25 | |||
6^{th} | - | - | - | - | - | .5 | 1 | ||||
7^{th}-12^{th} | - | - | - | - | - | - |
The "winner play for free" distribution table is manually constructed for up to 25 participants. For N = 26 and up, the full formula had developed by Alex ULANOVSKIJ. Just a short overview - the 1^{st} place will receive Sqrt(N) rounded for the next desired number, 2^{nd} place 60% of that and 3^{rd} about 40%, N/2 place finisher will receive the PMPE back, and for odd Ns, (N/2 + 1) will receive 50% of PMPE back.
After that, from N/2 - 1 going up to the 4^{th} place, every player's payoff will be increased by the following increment:
For even Ns the increment = $PMPE x (N-4*Sqrt(N) + 6)/((N-1)/2 - 3)*(N/2 - 4), and
for odd Ns the increment = $PMPE x (N-4*Sqrt(N) + 6)/(((N-1)/2 - 3)*((N-1)/2 - 4).
Check Fair Payoff to the 50% of the field to see distribution tables for number of players/pairs/teams from 2 to 20, from 21 to 40,and from 41 to 60. (MS Excel is required)
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