doublestrike and trample?

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if a creature has doublestrike and trample how is the combat damage delt?
lets say its a 5/5 doublestrike, trample being blocked by a 4/4.
and also if it was a 5/5 doublestrike, trample being blocked by a 6/6?
thanks and sorry if its a little vague.
If a 5/5 doublestrike trampler is blocked by a 4/4, during the first strike combat damage step, the 5/5 can assign 4 damage to the 4/4 and 1 damage to the defending player. Then, during the normal combat damage step, since the 5/5 trampler is not blocked by anything, all of its damage is assigned to the defending player, so they'll take 5 more, for a total of 6 damage.

If it was blocked by a 6/6, it would assign its 5 damage during the first strike combat damage step to the 6/6, then during the normal combat damage step, it could assign 1 damage to the 6/6 (since 1 damage at this point would be lethal to it), then assign the remaining 4 damage to the defending player.

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If a 5/5 doublestrike trampler is blocked by a 4/4, during the first strike combat damage step, the 5/5 can assign 4 damage to the 4/4 and 1 damage to the defending player. Then, during the normal combat damage step, since the 5/5 trampler is not blocked by anything, all of its damage is assigned to the defending player, so they'll take 5 more, for a total of 6 damage.

If it was blocked by a 6/6, it would assign its 5 damage during the first strike combat damage step to the 6/6, then during the normal combat damage step, it could assign 1 damage to the 6/6 (since 1 damage at this point would be lethal to it), then assign the remaining 4 damage to the defending player.

just a clarification...
in the first example
during the second combat step the 5/5 trampler is not blocked by anything which is true, however, it is important to note that it IS still blocked. In the same example if the 5/5 double striker didn't have trample, it would not deal 5 damage to the defending player during the second combat damage step.

also in the second example, the blocker survived to the second combat damage step so it would also deal 6 damage to the attacking creature

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