The easiest way would be to use Dueling Network. It easily imitates the feeling of a duel, free, gives access to every card, and has various options that make it very useful. The greatest advantage is the fact that it is not automated. Meaning for duels that take multiple days, one can simply recreate the field to the way it was by picking out the cards from the deck. While the deck itself won't be in the same order, it was random in the first place.
The players would each make their move, record it, then write their posts based on their moves or write the posts as the duel goes on. I feel that this would better capture the feeling of being in the Yu-Gi-Oh! Universe. At the bottom of each post, a sort of status post would be there to give a quick and detailed summary of the duelist's current field status.
It can be something simple as:
-Monster
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Spell/Trap
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-Monster
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Spell/Trap
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-Monster
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Spell/Trap
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Cards in Deck:
Cards in Hand:
LP:
Ignore the fact that spoiler code doesn't work right now >_>
Then rather than limiting people with the card rarity and going through the long and tedious process of building a deck, simply create different deck tiers. A higher tier deck cannot challenge a deck of a lower tier, but a deck of a lower tier can challenge a deck of a higher tier.
Basic Example
Tier 1
-Chaos Dragons
-Dino Rabbit
Tier 2
-Twilight
-Lightsworn
Tier 3
-Exodia
-Blackwing
Exodia and Blackwing can challenge any deck in this list as they are the lowest tier and thus can challenge each other or a deck of a higher tier if they wish. Twilight and Lightsworn can challenge each other or the tier 1 decks, Chaos Dragons and Dino Rabbit, but not Exodia or Blackwing. To duel Exodia and Blacking, those two tier 3 decks must be the ones to challenge the Tier 2 Deck (in other words, the lower tier deck must consent to dueling the higher tier deck meaning they can request that their opponent uses a lower tier deck). While the Chaos Dragons and Dino Rabbit decks can only challenge eachother. This makes sure that everyone is dueling against a deck that won't completely dominate theirs unless they wish to duel a deck that strong.
In Tournaments if we want to make some for plot purposes, there would be a set tier for that tournament that forbids any deck higher than that tier. So if a tournament was set to tier 1, any deck could be used. A tournament set to tier 2 would forbid the Chaos Dragons and Dino Rabbit decks. And a Tier 3 tournament would only allow the Exodia and Blackwing decks.
The mods will be responsible for determining the final tier placement of a deck which will be the only tricky issue, but generally information on how strong a deck is can be found online and through members.
This way people can build decks that represent their character and still face fair duels. An issue I have with giving every card a rarity value is the amount of time it would take to do so and how some more common cards can be more useful than the rarer cards at many times. For example, in a Chaos Dragon Deck, I rather have a Foolish Burial or Dragon Ravine in my hand than something like a red eyes darkness metal dragon. I can use the former two to send eclipse dragon to the graveyard to banish redmd and then use eclipse as food for a chaos summon for BLS envoy, lightpulsar dragon, darkflare dragon, chaos sorcerer, etc. and then get redmd back into my hand while summoning a strong monster at the same time. Rare cards are nice and all, but they need the support of the lesser cards to maximize their use. They need to be used at the right moment. However, this method or another similar method can serve as a back-up in case something disallow someone from using Dueling Network.
Another tool I would like to mention is YGO pro. The downside to it however is that it is automated meaning you would have to rp through the duel in one go since you can't recreate the field like you can with Dueling Network and continue the duel on another date.
Note that this does not include plot vital duels. If we need the plot to go a certain way and it is dependent on the outcome of a duel, set up a predetermined winner and then use dueling network to do the middle part of the duel before the ending where the predetermined winner will win. Otherwise, unless we want to leave fate in the heart of the cards, duels will just be a form of interaction between characters.
Example Play:
Duelist #1:
“I'll start. Draw!”
Looking at his hand, Duelist #1 began calculating his moves.
Not the hand I was hoping for, but it will have to do.
“I set one card face down in defense position and end my turn!”
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Cards in Hand: 5
Cards in Deck: 34
Field:
-1 Monster set face down in defense position
Graveyard: No cards
Removed from play: No cards
Life Points: 8000
Last Action: Ending turn
Duelist#2:
“My turn! Draw!”
Drawing the sixth card to his deck, Duelist #2 began formulating a strategy. From left to right his hand was: Foolish Burial, Allure of Darkness, Darkflare Dragon, Tour Guide from the Underworld, Solar Recharge, and Charge of the Light Brigade.
Alright, this will do quite nicely.
“First I activate Charge of the Light Brigade. By discarding the top three cards from my deck to the graveyard, I can pick any level four or lower lightsworn monster from my deck and add it to my hand.”
Taking the top tree cards of his deck: plaguespreader zombie, monster reborn, and Sangan, Duelist #2 placed them into the graveyard. Then from his deck he selected Lyla the Lightsworn Sorceress to add to his hand.
Monster reborn always gets milled. I hate my luck sometimes. Plague is a nice mill however.
“I add Lyla the Lightsworn Sorceress to my hand. Next I play Solar Recharge. By discarding one Lightsworn monster from my hand to the graveyard, I can draw two cards then discard two cards from the top of my deck.”
Sending his newly acquired card to the graveyard, Duelist #2 draws two new cards: Ryko the Lightsworn Hunter and Night Assailant. He then mills the top two cards of his deck: Solar Recharge and Lumina the Lightsworn Summoner.
Damn could have used that second Solar Recharge, but my hand and graveyard are still good.
“Next I activate Allure of Darkness. I draw two cards and then banish one dark attribute monster from my hand. If I cannot then I must discard my entire hand.”
Drawing two new cards: Eclipse Wyvern and Galaxy-Eyes Photon Dragon, and banishing Night Assailant Duelist #2 begins exploring his brand new options.
Damn I was hoping to mill Eclipse Wyvern. Wait, Darkflare's cost!
“By banishing one light and one dark attribute monster from my graveyard I can special summon Darkflare Dragon from my hand!”
Banishing Sangan and Lyla, Duelist #2 summons his first monster of the game, Darkflare Dragon.
“I activate Darkflare's Dragon effect! By discarding one dragon monster from my hand and one dragon monster from my deck to the graveyard, I can banish one card in either of our graveyard. I discard the Eclipse Wyvern in my hand and Lightpulsar Dragon from my deck.”
Placing Eclipse Wyvern in his graveyard, Duelist #2 begins a chain.
“Eclipse Wyvern's effect activates! When it sent to the graveyard, I can banish any level seven or higher light or dark attribute dragon from my deck. If Eclipse Wyvern is banished from the graveyard, I can add the card I originally banished to my hand. I banish Red-Eyes Darkness Metal Dragon from my deck.
I summon Tour Guide from the Underworld in attack position! When Tour Guide is normal summoned, I can select a level three fiend from my hand or deck and special summon it to the field. I summon my second Tour Guide from the Underworld. I now overlay my two Tour Guides to exceed summon Number 17: Leviathan Dragon! I now activate Leviathan Dragon's effect! Once per turn, by detaching one xyz material, I can increase its attack points by 500.”
With his graveyard and removed from play pile set and primed, Duelist #2 begins his OTK.
“By banishing one light and one dark attribute monster from my graveyard, I can special summon Lightpulsar Dragon from my graveyard! I banish Eclipse Wyvern and Tour Guide from the Underworld. Eclipse Wyvern's effect now activates and I add Red-Eyes Darkness Metal Dragon to my hand!”
That face down is worrying me though. Better take some safety measures.
“I activate Plaguespreader Zombie's effect!”
Placing Ryko from his hand to the top of his deck, Duelist #2 special summons Plaguespreader Zombie from his graveyard.
“I now tune Lightpulsar Dragon with Plaguespreader Zombie! Clustering hopes will become a new shining star! Become the path its light shines upon! Synchro Summon! Take flight, Stardust Dragon! By banishing one dragon type monster from the field, I can special summon Red-Eyes Darkness Metal Dragon from my hand. I banish Leviathan Dragon. Now I activate Red-Eyes Darkness Metal Dragon's effect! Once per turn, I can special summon one dragon type monster from my hand or graveyard. Return to the field, Lightpulsar Dragon!”
Now for the finisher.
“I tribute Red Eyes Darkness Metal Dragon and Lightpulsar Dragon to special summon Galaxy-Eyes Photon Dragon! Lightpulsar Dragon's effect activates! When it is sent to the graveyard, I can special summon one level 5 or higher dark attribute dragon type monster from my graveyard. Revive, Red-Eyes Darkness Metal Dragon! As Red-Eyes was re-summoned, I can activate his effect once more! Return to the field, Lightpulsar Dragon! Time to end this! Stardust Dragon attack, shooting sonic!”
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Cards in Hand: 1
Cards in Deck: xx (sorry, don't feel like going through my example to count)
Field:
-Galaxy-Eyes Photon Dragon
-Red-Eyes Darkness Metal Dragon
-Stardust Dragon
-Lightpulsar Dragon
-Darkflare Dragon
Graveyard: (Don't feel like checking through the example)
Removed from play: See graveyard
Last Action: Attacking Facedown
Duelist #1:
“I activate Ryko the Lightsworn Hunter's effect and target Galaxy-Eyes Photon Dragon. When this card is flipped, I can destroy any card on the field and then discard the top tree cards of my deck to the graveyard.”
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Cards in Hand: 5
Cards in Deck: 34
Field:
-Ryko [Activating Effect][Will be destroyed]
Graveyard: No cards
Removed from play: No cards
Life Points: 8000
Last Action: Activating Ryko's effect
Duelist #2:
“I activate Stardust Dragon's effect! When a card effect that would destroy another card is activated, I can tribute Stardust Dragon to negate the effect and if I do, destroy that card. At the end phase of the turn that this effect is activated, I can special summon Stardust Dragon to my field. Stardust Dragon, Victim's Sanctuary!”
Negating his opponent's facedown, Duelist #2 begins the final assault. Unless his opponent has something like Tragodia or Gorz, the game is his.
“Attack my dragons!”
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Cards in Hand: 1
Cards in Deck: xx (sorry, don't feel like going through my example to count)
Field:
-Galaxy-Eyes Photon Dragon
-Red-Eyes Darkness Metal Dragon
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-Lightpulsar Dragon
-Darkflare Dragon
Graveyard: (Don't feel like checking through the example)
-Stardust Dragon [Can be revived during the end phase]
Removed from play: See graveyard
Life Points: 8000
Last Action: Attacking Directly in this order:
1. Galaxy-Eyes Photon Dragon
2. Red-Eyes Darkness Metal Dragon
3. Lightpulsar Dragon
4. Darkflare Dragon
Duelist #1
“Ugh!”
Taking the first hit, Duelist #1 summons Gorz the Emissary of Darkness from his hand and activating its effect.
“When I take damage while controlling now cards I can special summon Gorz from my hand. Then depending on the type of damage I took, one of two effects activates. As it was battle damage that I took, I can summon a level 7 light fairy token with an atk and def equal to the damage I just took. This duel is not over yet!”
Cards in Hand: 4
Cards in Deck: 34
Field:
-Gorz the Emissary of Darkness
-Token [3000/3000]
Graveyard:
-Ryko the Lightsworn Hunter
Removed from play: None
Life Points: 5000
Last Action: Special Summoning Gorz and a token
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As you can see, there are two ways to role-play the duels. One way is being secretive of your hand and providing only the visible information so your opponent can't use extra knowledge against you. The other way is to provide all of your information, trusting your opponent won't cheat. Overall, the former method is best if you are typing out posts as you duel and doing it in one go. The latter method is best if you need multiple sittings to finish the duel or if you write the posts after dueling.