Of course a lot of us remember the average points of Bronze, Silver and Gold cards in the original (non-HC) Gwent.
Modells for simplifying the concept without inserting errors are always an easy helper/indicator for deckbuilding, balance and expectations during a game.
The 2 Modells I came across thus far are "Average Provisions" and "Transformed Provisions", which I will describe below in detail, as well as the assumptions they are based on.
In case you have any other Modell(s) feel free to introduce and explain it/them, the point of this threat is to come up with and spread an ideal (as far as we accomplish that) Modell for gaging the value and effectiveness of cards, as well as simplifying spending Provisions in the deckbuilder.
Without further delay I will now introduce "Average Provisions" and afterwards "Transformed Provisions".
Average Provisions:
#P = total number of Provisions
#D = total amount of cards in one's deck
#A = Average Provisions
#L = Leader Provisions
#A = #P / #D = (150 + #P) / #D
If we now do the sensible thing and play a minimum size deck of 25 cards we get #D = 25
=> #A = (150 + #P) / 25 = 6 + #L/25
With the last part being between 10/25 = 0.4 and 19/25 = 0.76.
Thus the average provision cost in a homogenous deck is [6.4 : 6.76]
So all cards with provision cost of 6 or lower give Provisions to the higher ones and get you themselves and additional Provisions.
And all cards with Provision cost of 7 and above give you themselves and demand Provisions.
example:
The original Witcher Trio each having 6 Provisions meant you get a 9 point play and 3*(#A - 6) = 1.2 - 2.28 Provisions.
The nerfed Witcher Trio each having 7 Provisions means you get a 9 point play and lose P_l =3*(7 - #A) = 0.72 - 1.8 Provisions, which means you get a 9 point play and pay 0.72 - 1.8 Provisions, in case we take the average Point/Provision ratio as being 1 we get a 9 - P_l = 7.2 - 8.28 point play for 6.4 - 6.76 Provisions, which is definitely above the used average Point/Provision ratio and not by little, being 0.8 - 1.52 above that standard.
Note: Of course we did not take the thining aspect into consideration, given that this only gages the Point by Provision effectiveness.
Pros:
(i) Very easy to take into consideration
(ii) The assumption of a 25 card deck is (next to) always true, so this is one less assumption we had to make
(iii) Building the deck in a less highroll manner or basing the calculations on that results in a more homogenous deck and thus less RNG dependence
Cons:
(i) The assumption of a 25 card deck (see above why this is hardly an issue)
(ii) The assumption the deck wants to be build a homogenous way, although the calculation being based on that not leading to more homogenous decks,
given that the calculation is not reliant on that.
=> The Modell becomes based on larger positive and negative numbers, which is in and on itself not an issue.
Transformed Provisions:
TP = transformed Provisions
bP = base Provisions (as in the deckbulder)
tPL = transformed Provision limit
L = Leader Provisions
D = total amount of cards in one's deck
TP = bP - 4 => TP can take values from [0:11]
tPL = 150 + L - 4 * D
Based on the assumption of a 25 card deck we get D = 25
=> tPL = 150 + L - 4 *25 = 50 + L => TP can take values from [60:69]
This Modell is based on the constant transformation of the Provision costs, as well as the total number of available Provisions under the assumption of a constant decksize and the lowest Provision cost cards not taking away Provisions as it would appear and thus simplifying the entire calculation considerably.
Example:
We now decide to put Griffin (bP = 7, TP = 3) and Old Speartip (bP =15, TP = 11) in our deck.
=> We use up 15 + 7 = 22 Provisions in our deck and use up 11 + 3 = 14 of our tPL and thus tPL = 50 + L - (11+3) = 36 + L
So now we still have 36 + L actual Provisions we can spend above the minimum we can put in our deck.
Note:
Given that we are actually aware of L right away the calculations become even easier than the above.
Pros:
(i) Potentially the simplest way of talking about Provisions
(ii) Increasing the decksize can easily be corrected by reducing tPL by 4 per card or using the original cost, rather than TP, on all additional cards
(iii) Based on purely positive Values and thus not adding a necessity for "negative Provisions" later on
(iv) Getting an actual understanding of the Provisions spend on putting a card in one's deck
Cons:
(i) A correction becomes necessary to increase the decksize past 25 cards (neglegible)
(ii) More useful in the deckbuilder, given that the expected value of cards has an offset from TP and thus spreads more away from 1
To put my personal opinion on the above 2 Modells:
I used to use the first during the Beta of Homecoming and the first weeks afterwards and drifted towards prefering the second Modell (which is also shown by me finding only a few Cons, although this should not be the result of a bias).
Opinions and especially actual arguments based on Numbers are appreciated.
Modells for simplifying the concept without inserting errors are always an easy helper/indicator for deckbuilding, balance and expectations during a game.
The 2 Modells I came across thus far are "Average Provisions" and "Transformed Provisions", which I will describe below in detail, as well as the assumptions they are based on.
In case you have any other Modell(s) feel free to introduce and explain it/them, the point of this threat is to come up with and spread an ideal (as far as we accomplish that) Modell for gaging the value and effectiveness of cards, as well as simplifying spending Provisions in the deckbuilder.
Without further delay I will now introduce "Average Provisions" and afterwards "Transformed Provisions".
Average Provisions:
#P = total number of Provisions
#D = total amount of cards in one's deck
#A = Average Provisions
#L = Leader Provisions
#A = #P / #D = (150 + #P) / #D
If we now do the sensible thing and play a minimum size deck of 25 cards we get #D = 25
=> #A = (150 + #P) / 25 = 6 + #L/25
With the last part being between 10/25 = 0.4 and 19/25 = 0.76.
Thus the average provision cost in a homogenous deck is [6.4 : 6.76]
So all cards with provision cost of 6 or lower give Provisions to the higher ones and get you themselves and additional Provisions.
And all cards with Provision cost of 7 and above give you themselves and demand Provisions.
example:
The original Witcher Trio each having 6 Provisions meant you get a 9 point play and 3*(#A - 6) = 1.2 - 2.28 Provisions.
The nerfed Witcher Trio each having 7 Provisions means you get a 9 point play and lose P_l =3*(7 - #A) = 0.72 - 1.8 Provisions, which means you get a 9 point play and pay 0.72 - 1.8 Provisions, in case we take the average Point/Provision ratio as being 1 we get a 9 - P_l = 7.2 - 8.28 point play for 6.4 - 6.76 Provisions, which is definitely above the used average Point/Provision ratio and not by little, being 0.8 - 1.52 above that standard.
Note: Of course we did not take the thining aspect into consideration, given that this only gages the Point by Provision effectiveness.
Pros:
(i) Very easy to take into consideration
(ii) The assumption of a 25 card deck is (next to) always true, so this is one less assumption we had to make
(iii) Building the deck in a less highroll manner or basing the calculations on that results in a more homogenous deck and thus less RNG dependence
Cons:
(i) The assumption of a 25 card deck (see above why this is hardly an issue)
(ii) The assumption the deck wants to be build a homogenous way, although the calculation being based on that not leading to more homogenous decks,
given that the calculation is not reliant on that.
=> The Modell becomes based on larger positive and negative numbers, which is in and on itself not an issue.
Transformed Provisions:
TP = transformed Provisions
bP = base Provisions (as in the deckbulder)
tPL = transformed Provision limit
L = Leader Provisions
D = total amount of cards in one's deck
TP = bP - 4 => TP can take values from [0:11]
tPL = 150 + L - 4 * D
Based on the assumption of a 25 card deck we get D = 25
=> tPL = 150 + L - 4 *25 = 50 + L => TP can take values from [60:69]
This Modell is based on the constant transformation of the Provision costs, as well as the total number of available Provisions under the assumption of a constant decksize and the lowest Provision cost cards not taking away Provisions as it would appear and thus simplifying the entire calculation considerably.
Example:
We now decide to put Griffin (bP = 7, TP = 3) and Old Speartip (bP =15, TP = 11) in our deck.
=> We use up 15 + 7 = 22 Provisions in our deck and use up 11 + 3 = 14 of our tPL and thus tPL = 50 + L - (11+3) = 36 + L
So now we still have 36 + L actual Provisions we can spend above the minimum we can put in our deck.
Note:
Given that we are actually aware of L right away the calculations become even easier than the above.
Pros:
(i) Potentially the simplest way of talking about Provisions
(ii) Increasing the decksize can easily be corrected by reducing tPL by 4 per card or using the original cost, rather than TP, on all additional cards
(iii) Based on purely positive Values and thus not adding a necessity for "negative Provisions" later on
(iv) Getting an actual understanding of the Provisions spend on putting a card in one's deck
Cons:
(i) A correction becomes necessary to increase the decksize past 25 cards (neglegible)
(ii) More useful in the deckbuilder, given that the expected value of cards has an offset from TP and thus spreads more away from 1
To put my personal opinion on the above 2 Modells:
I used to use the first during the Beta of Homecoming and the first weeks afterwards and drifted towards prefering the second Modell (which is also shown by me finding only a few Cons, although this should not be the result of a bias).
Opinions and especially actual arguments based on Numbers are appreciated.
