KanBan Database architecture - ruby-on-rails

Question

I'm trying to implement a kanban agile board like Trello in my application. I'm wondering how to do it the best way. I'm considering these entities:
Board
has many Lists
List
has many Cards
Card
contains some content
However I'm stuck with ordering of Cards. Each Card should have a sort position to sort Cards in particular order in a List. When dragging a Card, I should change it's position and save it in the database. What is the most efficient way of doing this?
Adding a position field to each Card seems redundant since I would have to recalculate positions of all Cards in a List (or two) after I drag a Card to a different position (there will be hundreds of Cards). I was thinking of storing an array of all Card ids in a List and sort Cards by this array. What are pros/cons of this solution? And are there any better solutions?
I'm using Ruby on Rails and PostgreSQL.
UPDATE
Using #cske answer I came up with the following solution:
CREATE OR REPLACE FUNCTION move_buyer_card(
new_list_id INT
, param_id INT
, new_position INT
) RETURNS FLOAT4
LANGUAGE plpgsql SECURITY DEFINER
AS $$
DECLARE
var_lower_bound FLOAT4;
var_upper_bound FLOAT4;
var_new_weight FLOAT4; /*between 0 and 1*/
BEGIN
IF new_position < 2 THEN /*first position*/
var_lower_bound := 0;
SELECT MIN(weight) FROM Buyers
WHERE board_list_id = new_list_id
INTO var_upper_bound;
IF var_upper_bound IS NULL THEN /*empty list*/
var_upper_bound := 1;
END IF;
ELSE /*not first position*/
WITH ordered_cards AS (
SELECT id, RANK() OVER (ORDER BY weight ASC) AS rank, weight
FROM Buyers WHERE board_list_id = new_list_id
)
SELECT cards0.weight, cards1.weight from ordered_cards cards0
JOIN ordered_cards cards1
ON cards0.rank = cards1.rank - 1
WHERE cards1.rank = new_position
INTO var_lower_bound, var_upper_bound;
IF NOT FOUND THEN /*only 1 item in list OR last position*/
SELECT MAX(weight) FROM Buyers WHERE board_list_id = new_list_id
INTO var_lower_bound;
IF var_lower_bound IS NULL THEN /*empty list*/
var_lower_bound := 0;
END IF;
var_upper_bound := 1;
END IF;
END IF;
var_new_weight := var_lower_bound + (var_upper_bound - var_lower_bound) / 2;
UPDATE Buyers
SET weight = var_new_weight,
board_list_id = new_list_id
WHERE id = param_id;
RETURN var_new_weight;
END;
$$;

Answer 1

Consider this, trick is not storing the position, but a weight so you can insert between any two elements
create table listOfCards (
listId INTEGER
,cardId INTEGER
,weigth FLOAT4
,PRIMARY KEY (listId,cardId)
);
CREATE OR REPLACE FUNCTION addCard(
plistId INT
, pcardId INT
, ppos INT
) RETURNS FLOAT4
LANGUAGE plpgsql SECURITY DEFINER
AS $$
DECLARE
vlb FLOAT4;
vub FLOAT4;
vnw FLOAT4;
BEGIN
IF 2 > ppos THEN
vlb := 0;
SELECT min(weigth) FROM listOfCards WHERE listId = plistId INTO vub;
IF vub IS NULL THEN /*empty list*/
vub := 2;
END IF;
ELSE
with corder as (select cardId,RANK() OVER (order by weigth asc) as r,weigth FROM listOfCards WHERE listId=1)
select c0.weigth,c1.weigth from corder c0 JOIN corder c1 ON c1.r = c0.r + 1 where c1.r = ppos INTO vlb,vub;
IF NOT FOUND THEN
SELECT max(weigth) FROM listOfCards WHERE listId = plistId INTO vlb;
IF vlb IS NULL THEN /*empty list*/
vlb := 0;
END IF;
vub := (vlb+1) * 2;
END IF;
END IF;
vnw := vlb + (vub-vlb) /2;
INSERT INTO listOfCards(listId, cardId, weigth)
VALUES (plistId,pcardId,vnw )
ON CONFLICT ON CONSTRAINT listofcards_pkey DO UPDATE SET weigth = vnw ;
RETURN vnw;
END;
$$;
Usage:
select addCard(1,1,1);
select addCard(1,2,1);
select addCard(1,3,2);
select addCard(1,4,2);
select addCard(1,5,5);
select addCard(1,5,2);
select * from listOfCards ORDER BY weigth;
Result:
1,2,0.5
1,5,0.5625
1,4,0.625
1,3,0.75
1,1,1