I recently found the game "98 Cards" by VdH and wondered if there is an optimal strategy to play it.
- There is only one player.
- Cards with each of the numbers $2$ to $99$ are contained in the main stack once, in a random, unknown order.
- There are four stacks on the field; two of them starting with $1$ (rising stack), the other two starting with $100$ (descending stack).
- The player's hand contains the top 8 cards from the main stack.
- Each turn, the player puts two cards from their hand onto stacks. They may be put onto the same stack, or different ones. The condition: cards can only be put on a stack if their value is higher than the current top card of that stack, if it is a rising stack, and lower if otherwise.
- After each turn, the player draws two cards from the main stack, if there are any left. If the main stack is empty, the next turn starts without drawing.
- Rule of Ten's: If a card in the player's hand is exactly 10 lower than the current top card of a rising stack, it may be put there. The reverse is true for descending stacks.
The goal is to sort all 98 cards from the main stack into the four stacks. The game ends prematurely when there are no cards in the palyer's hand that could be put onto the stacks, and there are still cards left to sort.
Is there an optimal strategy to play this game? The Rule of Ten's is giving me some headaches here.
Feel free to correct spelling or grammar mistakes. If this question would suit mathSE better, please migrate. I could not find any tags besides "cards" that would fit the question in my opinion. Feel free to add any suitable ones.