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Some insight: being able to add to the pile makes no difference to a regular game of nim. If Player A has a winning position in the game of nim, Player A may keep playing optimally as they would play a regular nim game. If, however, Player B decides to add k items to a pile, putting Player A in a losing position, Player A may add the same number, k, items to the same pile, reclaiming thier winning position. Or, even better, Player A may simply remove the items added by Player B.
Poker Nim
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Same as regular game of Nim!
Some insight: being able to add to the pile makes no difference to a regular game of nim. If Player A has a winning position in the game of nim, Player A may keep playing optimally as they would play a regular nim game. If, however, Player B decides to add k items to a pile, putting Player A in a losing position, Player A may add the same number, k, items to the same pile, reclaiming thier winning position. Or, even better, Player A may simply remove the items added by Player B.