Wash beets, cut off top stem, and place in a pot with water to cover. Peel potato and carrots, and add to the pot. Bring to a gentle boil. Remove carrots and potato as they become fork tender - be careful not to overcook. Let cool. As beets become tender, remove to a bowl of cold water. Slip off the peels, and cool slightly.
Dice beets.(Use about 4 - 6 cups diced). Dice carrots, potatoes. Make a small dice,for all vegies, about 1/2 cm or 1/4 inch. Chop onion fine. Place all in a large bowl. Add the diced dill pickles. Pour over 1/2 - 3/4 cups dill pickle juice. Stir gently.
Cover and refrigerate until ready to serve.
When serving, stir in about 2 heaping tablespoons mayonnaise, or to taste.