Another option is a 1v2 duel, if one of you wants to take on the other two at the same time. The easiest way to do one of these would likely be to adapt the Official Tag Duel Rules.
Note that these rules are from 2013, and thus they don't take the 2014 rule changes (specifically, the "first player doesn't get a Draw Phase" and the "each player can have a Field Spell" changes) into account. I'll note how you can change the rules to account for these.
An adapted version of those rules might be as follows:
Basic rules:
- There are two teams; one team (Team 1) has one duelist, and the other (Team 2) has two duelists. Team 2 has a "primary" and "secondary" member, called Duelists 2A and 2B, respectively.
- Each duelist on Team 2 has their own field (5 Monster Zones, 5 S/T Card Zones, 1 Field Card Zone, 1 Deck Zone, 1 Extra Deck Zone, 1 Graveyard), and their own deck. Combined, these make up team 2's side of the field.
- The single player on Team 1 (optionally) has a "double-size" side of the field, with 10 Monster Zones and 10 S/T Card Zones instead of the usual 5. In this case, duelist 1 follows standard 1v1 duel rules, apart from the increased field size.
Alternatively, they may choose to play with two decks, in which case the standard Official Tag Duel Rules (as detailed at the above link) can be used verbatim. In this case, duelist 1's right deck & field count as 1A, and their left deck & field count as 1B.
- Each team starts with 16,000 Life Points; duelists 2A and 2B share their LP between them.
- Duelists 2A and 2B are allowed to use cards in their partner's Graveyard as if they were in their own Graveyard. Examples given are:
- Duelist 2A can use their "Call of the Haunted" to target a monster in Duelist 2B's Graveyard.
- Duelist 2A has two different "Lightsworn"s in their graveyard, and duelist 2B has two different "Lightsworn"s in their graveyard; between the two of them, they have four different "Lightsworn"s. Duelists 2A and 2B are both allowed to summon "Judgment Dragon".
- Duelist 2A has a LIGHT monster in their graveyard, and duelist 2B has a DARK monster. Either one of them is able to summon "Chaos Sorcerer" by banishing these monsters.
- Duelist 2A has 2 DARK monsters in their graveyard, and duelist 2B has 2 DARK monsters in their graveyard. Neither 2A nor 2B can summon "Dark Armed Dragon", as they have 4 DARK monsters between their two graveyards.
- There can only be one Field Spell active at a time.
As mentioned above, this conflicts with the 2014 1v1 ruling that each player can control 1 Field Spell. If you want to use the new ruling, you can choose that 1) each team is allowed to control 1 Field Spell (in this case, if 2A has a Field Spell active, and 2B activates one, 2A's would be destroyed), or 2) each player is allowed to control a Field Spell. Since you're not playing an official duel, choose whichever of these options you prefer.
- Each duelist has their own Extra Deck, and cannot summon monsters from their partner's Extra Deck.
- Both members of a team are allowed to use monsters on either of that team's sides of the field. Examples given are:
- Duelist 2A has a Level 4 monster on the field. 2B can use this monster as an Xyz Material for "Number 39: Utopia".
- Duelist 2A has a monster set on the field. 2B may tribute it to Tribute Summon "Jinzo".
- Teammates can't activate speed 1 effects on their partner's field. Examples given are:
- Duelist 2A has a "Cannon Soldier" face-up on their field. 2B cannot activate its effect on their turn.
- Duelist 2A has a "Dark Hole" set on their field. 2B cannot activate it on their turn.
- Teammates can talk, compare hands, and share information (both between themselves and with their opponent). They can't use their partner's cards without their consent, and have to come to an agreement first. This communication must be verbal, must be loud enough for their opponent to hear, and must be in a language their opponent understands. (I'm sure the "verbal" rule can be waived if necessary, such as if one of the teammates is deaf and/or mute. No idea whether this applies to you or not, just pointing it out because the official rules don't.)
- A team loses if they run out of Life Points, if they deck out (in team 2's case, if either 2A or 2B decks out), or if an opposing duelist achieves a special win condition (like "Final Countdown" or "Exodia the Forbidden One").
Note that special win conditions must be achieved by a duelist, not a team. If 2A has Exodia's limbs in their hand, and 2B has Exodia's head in theirs, team 2 doesn't win the duel.
- Card limits and banlists apply to each team as a whole, instead of to individual players.
- If 2A has a "Black Luster Soldier - Envoy of the Beginning" in their deck, 2B can't have another one.
- If 2A has a "Dark Hole" in their deck, and 2B has a "Dark Hole" in their deck, then neither 2A nor 2B can add a second "Dark Hole" to their deck.
- If 2A has a "Mystical Space Typhoon" in their deck, and 2B has two "Mystical Space Typhoon"s in theirs, then neither 2A nor 2B can add another MST to their deck.
Turns:
- Teammates sit beside each other, and each team sits across from the other team. 2A sits to the right of 2B. Duelist 1 can either sit across from 2B (which is where 1A would sit in a regular tag duel), or in the middle of their side. (E.g., if team 1 is on the left side of the table, and team 2 on the right, duelist 1 can sit either on the middle of the left side, or across from 2B.)
- Duelist 2A gets their turn before duelist 2B; after 2A's turn ends, three turns will pass before 2A gets another turn. Since duelist 1 is alone, they get the turns 1A and 1B would normally have; after 1's turn ends, one turn will pass before 1 gets another turn. (And thus duelist 1 gets two turns to every turn 2A or 2B gets.)
- The first duelist who can attack is the one who goes fourth. (In the example below, this would be duelist 1, on their second turn.)
Similar to the Field Spell issue, the official Tag Duel rules don't appear to have been updated to account for turn 1 no longer having a Draw Phase. To account for this, the best decision is probably that the duelist who goes fourth is the first duelist allowed to conduct a Draw Phase, to match the rules on attacking.
- After turn order is decided, turns proceed normally. If team 2 goes first, for example, turn order is as follows:
- Duelist 2A.
- Duelist 1.
- Duelist 2B.
- Duelist 1.
- Duelist 2A.
- And so on...
- If you don't want duelist 1 to have so many turns, then you could change the turn order as follows (assuming team 2 goes first):
- Duelist 2A.
- Duelist 2B.
- Duelist 1.
- Duelist 2A.
If you do this, duelist 1 should get an advantage (such as double LP, or drawing 2 cards per turn) to compensate for only getting half as many turns as team 2.
Attacking:
- Duelists can only attack with monsters they control. 2A can't attack with monsters on 2B's field, and vice versa.
- If a team controls at least one monster, they can't be attacked directly, even if one member of that team has no monsters. If 2A controls a monster and 2B doesn't, duelist 1 can't attack 2B directly.
Effects:
[Note that examples in this section are difficult to modify, due to these rules normally depending on the position where each player is sitting. For these rules, duelist 1 should probably be counted as sitting directly across from both 2A and 2B. If duelist 1 is double-decking so you can follow the official rules, then remember that their right-side deck/field/hand is 1A, and their left-side deck/field/hand is 1B.] * If a card affects your opponent, and would have an effect on their hand, deck, extra deck, graveyard, or banished zone, then: * If activated by duelist 1, they choose whether it affects 2A or 2B. * If activated by either member of team 2, it affects duelist 1. * If a card affects your opponent's side of the field, then it affects their entire side of the field. * If activated by duelist 1, it affects duelists 2A and 2B. * If activated by duelist 2A or 2B, it affects duelist 1. * If a card affects all duelists/monsters/spells/traps/etc., then it affects all relevant targets (whether belonging to 1, 2A, or 2B). * If a card affects "both Duelists" or "each player", then: * If activated by duelist 1, it affects themself and either 2A or 2B (1's choice). * If activated by either 2A or 2B, it affects duelist 1 and the duelist that activated it. * If either 2A or 2B activates a card that refers to another card(s) "you control", or to "your" hand/deck/extra deck/etc., then it counts cards in both 2A's and 2B's control/hand/deck/extra deck/etc. This is also true if 1 activates a card that refers to another card(s) "your opponent controls", or to "your opponent's" hand/deck/extra deck/etc. * Both 2A and 2B can allow their partner to use monsters they control for Tribute Summons, Ritual Summons, Extra Deck Summons, or other appropriate card effects. * The "owner" of a card is the duelist whose deck it started in. 2A isn't the owner of 2B's cards, nor is 2B the owner of 2A's cards. * If a card prevents your opponent from doing something, it prevents both of your opponents (if applicable). If a card prevents you from doing something, it also prevents your partner from doing it. Examples given are: * If duelist 1 controls a face-up "Kycoo the Ghost Destroyer", neither 2A nor 2B can banish cards from the graveyards. * If duelist 2B activates "Reckless Greed", then team 2 will skip its next 2 Draw Phases; 2A and 2B will each skip one Draw Phase.
Other:
- During a duelist's turn, any other duelist can activate speed 2 or higher effects. This follows the rules for activating an effect on their opponent's turn, even if it's actually their teammate's turn. Example given is:
- Duelist 2A attacks duelist 1's monster with a LIGHT monster. Any player can activate "Honest".
- When a duelist takes an action, all other duelists are allowed to respond; responses are allowed in turn order. Example given is (assuming the 2A-1-2B-1 order mentioned above):
- Duelist 2A activates a Spell Card. Duelist 1 is allowed to chain a card. After they chain or decline, 2B is allowed to chain a card, and then 1 gets another chance to chain. If 1 declines their initial chance, and 2B chains a card, 1 is no longer allowed to chain a Counter Trap to counter the effect in Chain Link 1 (i.e., 2A's spell).
- In case of SEGOC (multiple trigger or trigger-like effects activating or meeting their activation timing at the same time), then the order is:
- Turn player.
- Their partner (if applicable)
- Opponent(s)'s effects (with opponents choosing the order, if applicable).
For example, all three players have "Mermail Abysslinde" on the field, and the turn player activates "Dark Hole".
- If duelist 1 is the turn player, then 1's Linde is link 1, and duelists 2A & 2B decide which of their Lindes is link 2 and which is link 3.
- If duelist 2A is the turn player, then 2A's Linde is link 1, 2B's Linde is link 2, and 1's Linde is link 3.
- If duelist 2B is the turn player, then 2B's Linde is link 1, 2A's Linde is link 2, and 1's Linde is link 3.
- Card effects that count turns count all appropriate turns. Examples given are:
- If duelist 1 activates "Swords of Revealing Light" when 2B will get the next turn, it will remain in effect until the end of 2B's second turn after activation. (The three opponent turns counted are 2B's turn, 2A's turn, and 2B's second turn.)
- "Final Countdown" counts all duelists' turns.