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If an ability would produce one or more mana of an undefined type, it produces no mana instead.

Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

To “tap [a permanent] for mana” is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, “Mana Abilities.”

An ability that triggers whenever a permanent “is tapped for mana” or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.

A replacement effect that applies if a permanent “is tapped for mana” or tapped for mana of a specific type and/or amount modifies the mana production event while such an ability is resolving and producing mana or the specified type and/or amount of mana.

If an object’s enters-the-battlefield triggered ability or replacement effect refers to X, and the spell that became that object as it resolved had a value of X chosen for any of its costs, the value of X for that ability is the same as the value of X for that spell, although the value of X for that permanent is 0. This is an exception to rule 107.3i.

The tap symbol is {T}. The tap symbol in an activation cost means “Tap this permanent.” A permanent that’s already tapped can’t be tapped again to pay the cost. A creature’s activated ability with the tap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The untap symbol is {Q}. The untap symbol in an activation cost means “Untap this permanent.” A permanent that’s already untapped can’t be untapped again to pay the cost. A creature’s activated ability with the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

If a token would be created tapped and attacking, but the token’s controller isn’t an attacking player, that token is created tapped but not attacking. If a token would be created blocking a creature, but the token’s controller isn’t a defending player, that token is created but isn’t blocking.

On the other hand, if the effect that creates the token grants a triggered ability to the token, the player who controls the token at the time the ability triggers will be the player who controls that ability. For example, if your opponent activates the second ability of Jace, Cunning Castaway, the token has the ability. If the ability triggers, you’ll control it, so you’ll have to sacrifice the token.

The above procedure means that if each player in a two-player game has resolved Crafty Cutpurse’s triggered ability and one would create a token, it really will enter the battlefield under that player’s control. The token would enter the battlefield under player A’s control, so player B’s effect affects it. Now that token would enter the battlefield under player B’s control, so player A’s effect affects it. Each replacement effect has now been used, so the token will enter the battlefield under player A’s control.

Crafty Cutpurse’s replacement effect is applied before any other replacement effects that would also modify how the token enters the battlefield. For example, if an opponent controls Anointed Procession, your Crafty Cutpurse’s effect applies before that of Anointed Procession and you won’t get twice as many tokens.

Crafty Cutpurse won’t retroactively change the control of tokens that have already entered the battlefield.

If two or more players each have resolved Crafty Cutpurse’s triggered ability and a token would be created, the token’s would-be controller chooses one of the applicable Crafty Cutpurse effects to apply. Then the new would-be controller of the token repeats this process among the remaining Crafty Cutpurse effects, and so on, until there are no more possible such effects to apply. Each effect can be applied to the token only once this way.

If the effect that creates the token also creates a delayed triggered ability, Crafty Cutpurse doesn’t change who controls that ability. For example, if your opponent activates the ability of Kiki-Jiki, Mirror Breaker, that opponent controls the delayed triggered ability. When the ability triggers, that player can’t sacrifice the token, so it remains on the battlefield.