I would guess the speaker means that when playing he always makes the maximum use of his abilities.
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red apple"I have never played with less than my greatest abilities"?I have never been tired or distracted while playing chess. I have always played my best.
red apple2. I have never played with a competitor weaker than myself.You can only say that if you've lost every game you've played.
red appleWhen the man says "I regret that I can not offer you much..." is he offering money to the other chess player? Is he asking the chess player to lose the game intentionally in return?Yes, it seems so.