Look at Emilia's Notebook

While the coin was tempting... you turned to where Emilia had left the book that had been in her lap when you first arrived. You decided to pick that up and examine it first, to see if it had any relevance.

You opened to about the middle of the book where you thought Emilia had been before, and felt like a genius. It had a picture of the coin right here, sketched out! Not only that, but lots... lots of notes. Written descriptions, accounts of what must be previous uses of these coins, mathematical equations...

You started to read carefully, studying what looked like a summary Emilia wrote on the coins.

In the 3-month trial, I have finally quantified the 'talent enhancement' properties of the Venus-Mars coins with a formula based on observations of Mr./Ms. A. Kensington ("Coinbearer") in their chosen talent of chess. Over the duration of the experiments, Coinbearer or I would flip or alter the position of the coin at different intervals throughout the day, and then Coinbearer would play chess against an AI designed to estimate a player's Elo rating compared to known ratings of online databases and grandmasters. With a large enough sample size of games, average results are consistent enough to provide an approximate formula for charge based on type of flip.

x(n) = x(n-1) + (1-(x(n-1)*c)) where n greater than 2
x(n) = 0.5 where n = 1 or where x(n-1) less than 0.5
x(n) is current toss's charge, x(n-1) is previous coin toss's charge, c is the charge change amount.
Max charge is represented as 1.0

Based on these results, a person's talent, measured as the percentile their talent places them in relative to everyone else in a given subject, can be improved to the level of a grandmaster in a predictable number of flips, depending on the flip method. Each subsequent flip, however, results in diminishing returns. The exception to this rule is the first coin toss, or any coin toss where talent is below the 50th percentile will bring the Coinbearer to exactly the 50th percentile before any additional gains are made.

_

-Note that all charge rates have error +/-0.03

The minimum wait period between charge events is 1 hour. Therefore, Coinbearer could reach maximum potential in 11 hours with fastest charge method starting from zero talent whatsoever! Reaching the 93rd percentile only takes 4 flips.

Note: Coinbearer could not surpass the Elo of the highest rated ranked player. This suggests that the talent is capped at whatever the natural skill cap currently is. With exactly the same rating as the top grandmaster, it's theorized that each would on average win half their games, if no other factors are considered. Therefore the Coinbearer could never be considered the unquestioned 'best' at their talent as that would require being able to surpass the natural talents of a grandmaster.

Unlike diminishing returns of charge rates, coins have a linear discharge rate. Discharge formula is:

x(d) = x(d-1) - 1/7 where x(d) is the starting charge of the current day, x(d-1) is the ending charge of the previous day. x(d) cannot go below 0.

Essentially, in one week with no coin tosses, Coinbearer loses all talent whatsoever. This discharge occurs the moment a new day begins, regardless of timezone or any other factors, and is instantaneous. After seven days, Coinbearer not only could not win a single game of chess in the Elo ranking program, they had to be repeatedly reminded of the rules and capabilities of each piece.

Because of the discharge rate being linear, the first day's discharge puts Coinbearer in 85th percentile--still highly skilled but clearly not on par with grandmaster levels. Coinbearer describes it as like having an 'off-day' when they feel like they are on the cusp of understanding the higher level play when they refer to their past games. Frustration clearly apparent. The best charge rate reaches the 87th percentile in 3 tosses, therefore it takes nine tosses even at the 85th percentile to reach maximum skill again--nearly a third of a day has to be devoted to the coin tosses. This is a considerable time commitment requiring a rigid schedule of tosses. With the minimum charge amount, the Coinbearer can only achieve 99.7th percentile after 24 tosses, which is the maximum amount before another discharge event.

Note 2: a 'toss' is considered valid once a coin has touched skin of the Coinbearer or other person, and then when it has made at least 0.5 rotations and comes to rest without touching any skin at all. Further experiments needed for toss conditions and if conditions can be consistently manipulated. The coin can be handled as a normal coin between minimum valid coin toss times.

This is all like a dense whitepaper, and it was not so easy to read. Lots of calculations, and the promise of becoming as incredible as a chess grandmaster in whatever talent was pretty incredible! Even if you could just be better than average, that would be a step up in that regard. That was true for a lot of things.

Still, you were just looking at math. Emilia mentioned something about side effects, where is that information? You flipped through the pages, searching for more information about the coin.

Eventually as you flipped back in the notebook, you came across another page describing this 'Kensington' person, and you had originally thought the Mr./Ms. part that Emilia wrote had just been a mistake and she didn't bother to cross out the wrong one. But as you read further...

Mr. A. Kensington, age 27, male. Professional driver and hospitality. Desired talent: chess proficiency. Mr. Kensington eagerly took the coin, either unfazed or unbelieving of the potential side effects. First coin flip resulted in Mars-head result, showing no physical change. Second flip one hour later resulted in Venus-head, causing Mr. Kensington's body to instantly change to a female variant of himself. In this state, Ms. Kensington had recognizable features of her former body, appearing much like a sister to Mr. Kensington. Age appears roughly equivalent, as does demeanor and personality, so the mind is unchanged in this state. The only aspects that have truly changed are the body, as clothing and identification records all retain her old appearance.

Ms. Kensington continued the experiment after a half-day of acclimation to the new situation. The next coin toss resulted in Mars-head, which again instantly altered Ms. Kensington into her original male form. Mr. Kensington still showed enhanced aptitude at chess versus baseline measurements, so the talent level is retained regardless of which form is active for the Coinbearer.

Tests of long-term discharges have demonstrated that even when talent level reaches zero, the Coinbearer does not revert back to their original body. The only way to alter Ms. Kensington is to perform another coin toss event, it would appear.

After offering a large sum of money for Ms. Kensington to distribute among her family as she pleases, she has agreed to the final experiment: destruction of her coin while she is not in her original form. The original hypothesis was that she would revert back to her original body and baseline chess talent, however upon destruction that does not appear to be the case. Her talent level reverted to zero, and her body has remained like that after a month of observations. Ms. Kensington remains at the estate for long-term monitoring, particularly to see if she can naturally recover any chess talent or if her body ever reverts.

That last part was rather scary, that is a real tragedy for this Kensington person if they are stuck in some way they didn't want... but the more you thought about it, the more it felt like this was a pretty incredible deal. You could match the best person in the world at any skill you wanted, and all you had to do was deal with being a woman for part of the day? That seems like it would be so easy! You could pick something you don't even need to be the best at to be satisfied, and then find a good mathematical equilibrium where you can achieve the best results with the minimum number of tosses or turns. At worst, you lose an hour a day to being a girl, and you can just do that during your shower or while eating breakfast or something--could even be kind of fun! All you have to do is pick a good talent, protect that coin with your life, and not tell anybody. Or maybe tell some close friends. Or... you'll figure that part out later.

Your eyes turn back to the coin. What could go wrong?