Optimized deck specificially for Legacy of the Duelist Link Evolution available card list and to beat the AI. Has other cards in Side deck to change other for facing human opponents online as needed. (Not Obelisk, he's in there as an old inside joke and reminder of past mistakes.)
Some useful combos:
N. summon Kageki, S. summon Kagemusha -> tribute for Legendary Six Samurai Shi En
N. summon Fuma, S. summon Kizan -> tribute for Legendary Six Samurai Shi E
N. summon any 4-star monster with Dojo on the field, trade Dojo and one Bushido for Fuma from deck -> tribute for Legendary Six Samurai Shi En
Cards like Smoke Signal, Dojo, Reinforcement of the Army, and Gateway are to be focused at first on getting out Shi En if at all possible as he is your heavy hitter and defender. If that is doable/done they are to be used in bringing a Grandmaster and as many of your Kizan copies to your hand. One of Mizuho/Shinai are acceptable choices if you already have the other.
Warrior Returning Alive should be focused on cards like Grandmaster and Kizan as they can special summon from the hand and Mizuho/Shinai given the right conditions.
Hatsume is a slightly less used card as her effect to special summon a monster out of the GY is already answered by Warrior Returning and Gateway when done right. But her real potency is to bring back Shi En as neither of the other options bring a card to the field by themselves
Shadow of the Six Samurai effect target Kageki: Kageki's original ATK goes from 200 to 2000 and his own effect adds 1500 totaling to 3500 ATK for remainder of turn.
Double-Edged Sword Technique's potential cost sounds scary but is avoidable. Use only to special summon two monsters for extra deck monster tribute and immediately tribute them to get (another) Shi En (or Rihan). They will not be destroyed and you will pay no LP in end phase.
Gateway of the Six + two copies of any of these: Shien's Dojo, Six Samurai United, and/or Temple of the Six With this combo on the field each normal and special summon will place 2 Bushido counters on Gateway, and one each on the other two cards. Gateway can take counters from other cards so you have 4 counters gained for every summon and you can bring one monster than be special summoned from the hand and special summon it immediately to get another net gain of 4 counters and repeat until one of the two happens: You run out of monsters zones for summoning or you run out of cards to special summon from the hand.
Final Notes:
I keep this TCG legal but I did mention that it is optimized for dueling the game's AI. When doing so you need not follow TCG limitations and can absolutely break the game by using 3 copies of Gateway of the Six.
I like to keep the main deck free of Shien Monsters as they usually are more trouble than help but I do have a copy of Great Shogun Shien in the side deck as he's the ONLY one you should ever consider using. He benefits greatly from Six Samurai and costs nothing to summon when done right. He even limits spell/trap activation to once per turn. But he is not the great pairing for Legendary Six Samurai Shi En you may think. When Shi En negates a Spell/Trap that doesn't count as your opponent activating a Spell/Trap and their count for that turn is still at 0 so they can attempt to activate another. Also, Shogun Shien does not benefit Six Samurai effects by being on the field (no Bushido Counters, no counted presence for ATK boosts or Special summons).