Hi

I am trying to work out the probabilities of ToB cards. But before I finish this can I ask does the Thronemaster implementation take account of the fact that one player must pick first?

Let me explain. As an example: there are 4 skull cards out of a deck of 24 cards. I cannot find anywhere who draws first so lets assume it is the attacker.

Attacker chance of drawing a skull is 4/24 (16.6%)
Now one card has gone so...
Defender chance of drawing a skull is 3/23 (13.0%)

Does the Thronemaster implementation work like this? Who picks first? Or does it just give both players 4/24 chance of getting a skull as if each have their own deck?

(The same odds shift happens for other cards other than Skulls, but this is the easiest example)

Thanks
Ian

The probability is the same
for the "first draw" the probability is : 4/24
For the "second draw" the probability is : 4/24 * 3/23 + 20/24 *4/23 = 4/24

thankfully there are only 2 skull cards in a deck of ToB cards (still 2 too many)
but 16 % each battle that one of your units that would be even more fun

---

Mother of Dragons PBF #1 – Arryn

The probability is the same
for the "first draw" the probability is : 4/24
For the "second draw" the probability is : 4/24 * 3/23 + 20/24 *4/23 = 4/24
Edit: NVM!
When I math this out I get 1/46 + 10/69 = 23/138 = 1/6

Last edited by SerOberynMartell on 2021-Jan-21 20:56, edited 2x in total

---

MAESTER OF TOURNAMENTS
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World Cup Team USA: 2021-2023

Ah yes, thank you PhantasticPhil! It would have helped if I got the number of skull cards right, my bad.

So there are *2* Skull cards in the deck of 24.

So first to draw get a chance of 2 of 24 or 2/24 (8.3%)

The deck is now 23 cards one of which is a skull so their chance of picking that skull is 1 of 23 or 1/23 (4.3%)

But regardless of the actual numbers your replies confused me.

Just checking but did any of you write the code? If not I am hoping a site admin who knows the code can tell me how it is actually programmed.

As a footnote I found that this is called 'conditional probability' and described here in terms of the chance of drawing a second Ace from a deck of cards:

https://math.libretexts.org/Courses/College_of_the_Canyons/Math_100%3A_Liberal_Arts_Mathematics_(Gavilan_and_Radtke)/04%3A_Probability_and_Odds/4.02%3A_Conditional_Probability

or here

https://www.math.uni.edu/~campbell/mdm/hand.html

The only person that codes on this site is the site owner, JM Grip, so he is the only one that can confirm that. However, as ToB cards are reshuffled after every fight, the programming is less of an issue as you just make a "draw random two different cards among the 24 and give each of them to a player". And there are fortunately procedures for programmers so that they do not have to take care about how "random" works (a real random is actually extremely hard to program).

And JM is unfrotunately über busy, so I doubt he'll answer you.

It is actually not "real" conditional probability - Alrich as a statistician can confirm that because you don't know the first card to conclude - because a conditional probablility is assuming you know the first card and use that information before drawing the second one.

If you think about it, draw two cards, give the first one to player A and the second to player B.
Now, reshuffle, give the first card to player B and the second to player A. Does it change something as for probabilities ? No, obviously not. The only information you have, when you are player A, is that B cannot draw your card (if you have card number 7, obviously B cannot draw it), but the chances AT THE START to draw each of the 24 cards for B was exactly 1/24.

A bit counter-intuitive at start.

---

Judge
LoI&F: Seasons 10 and 11 King
France WCup team
2021: Bronze
2022: Silver

So there are *2* Skull cards in the deck of 24.

So first to draw get a chance of 2 of 24 or 2/24 (8.3%)

The deck is now 23 cards one of which is a skull so their chance of picking that skull is 1 of 23 or 1/23 (4.3%)

...

As a footnote I found that this is called 'conditional probability' and described here in terms of the chance of drawing a second Ace from a deck of cards:

https://math.libretexts.org/Courses/College_of_the_Canyons/Math_100%3A_Liberal_Arts_Mathematics_(Gavilan_and_Radtke)/04%3A_Probability_and_Odds/4.02%3A_Conditional_Probability

or here

https://www.math.uni.edu/~campbell/mdm/hand.html
We can't always condition on the fact that the first person drew a skull. As Alrich noted, there is a 2/24 chance that the first person drew a skull, and therefore the probability of the second person drawing a skull  in that case is 1/23. However, there is also a 22/24 chance that the first person doesn't draw a skull, in which case the second person has a 2/23 chance of drawing a skull. Adding those two probabilities together shows that the probability of the second person drawing a skull is still 2/24, therefore making it unnecessary to determine who draws first

---

MAESTER OF TOURNAMENTS
- World Cup: 2021-2023
- League of Ice and Fire: S18-
- World Championship: 2022-2024

World Cup Team USA: 2021-2023

The probability is the same
for the "first draw" the probability is : 4/24
For the "second draw" the probability is : 4/24 * 3/23 + 20/24 *4/23 = 4/24
Edit: NVM!
When I math this out I get 1/46 + 10/69 = 23/138 = 1/6
That's because 1/6 = 4/24

Thanks for the further explanations, it's a long time since I did probability at school and this thread reminds me how I didn't enjoy it all that much!!

I can see it now that this not Conditional Probability because we don't see the first draw.

So...

Given that when a player has the Valerian Steel Blade he can choose another card then a list of probabilities for each result should really be shown as two tables. The first table the simple 1/24 * the number of each card.

The second table being 1/23 for every card which you didn't pick * the number of each type of card. But an adjusted probability for the card you picked.

I think I am overthinking this for game purposes because it's obvious common sense that if you draw 1 of the 2 Skull cards the other person is only 1/23 likely to have the other.

But it is interesting from a probability point of view...

Thanks all!

As for the programming, honestly, I think there are functions in most languages that does that part for you.

You just describe to your program "card 1: +2 CS + 1 sword, card 2: +1 CS and 1 fort, card 3: +0 CS and 1 skull"... etc.

Then you tell your program "draw 2 different cards in these 24", and "if sword is used, replace card A by card C, that must be drawn in the remaining 22". It is not something in which you calculate your actual probabilities each time, but you just describe your cases and tell the computer to do the maths for you.

But the question is intersting indeed

Pretty much the same for events, actually, apart from the fact that they are not re-shuffled all the time, only if WiC is drawn.

---

Judge
LoI&F: Seasons 10 and 11 King
France WCup team
2021: Bronze
2022: Silver

something like that:
function getShuffledTidesOfBattle($battleData = false)
{
    $cards = array(
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1, // 8x +0 str.
        2,
        2, // 2x +0 str. + SKULL
        3,
        3,
        3,
        3, // 4x +1 str. + SWORD
        4,
        4,
        4,
        4, // 4x +1 str. + TOWER
        5,
        5,
        5,
        5, // 4x +2 str.
        6,
        6 // 2x +3 str.
    );
    // exclude drawn ToB cards during battle
    // ...
    $loop = rand(1, 5);
    while ($loop-- > 0) { // shuffle 1 to 5 times
        shuffle($cards);
    }
    return $cards;
}
Attacker gets the first cards, defender the second, but that is a neglectable detail. Drawing order has no meaning here.

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- What do we say to New Features? Not Today.

Thanks you JM Grip for sharing the code.

Great to hear from "The 8th God" himself

(Edit: is that JavaScript it is written in?)

Last edited by WarlordBatz on 2021-Jan-22 16:13, edited 1x in total