These rules supersede the PHB rules on Tumble

Tumbling Move: By making a Tumble check (DC 15) you gain a +4 bonus to avoid Attacks of Opportunity caused by moving out of or within a threatened area. Each 10 you beat the DC by adds an additional +4 bonus. This stacks with the Mobility feat.

Tumble Past: You can attempt to tumble through an opponent's space as part of normal movement. Because you are entering an opponent's space, this provokes an attack of opportunity from the opponent. You must make a Tumble check (DC 25). If the attack of opportunity is successful or the Tumble check fails, you move back 5 feet in the direction you came, ending your movement there. Otherwise, you move through the opponent's space and can continue your move normally. The attack of opportunity generated by this use can be negated by the Tumbling Dodge ability. Each 10 you beat the DC by adds a +4 bonus to your AC against the Attack of Opportunity generated by the ability.

Tumbling Dodge: When you are hit as a result of an attack of opportunity you provoked, you may use an attack of opportunity or swift action to attempt a Tumble check to negate the hit. The hit is negated if your Tumble check result is greater than the opponent's attack roll. (Essentially, the Tumble check becomes your Armor Class if it is higher than your regular AC.)

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