good luck you with your game

Zoya! Hi. Long time no see))

Valery, we say BETTER LUCK NEXT GAME

Hi Uly! You're right - long time no see. it so nice to get in touch with an old friend .(is it correct?)
How are you doing? )
The some number of people on quora wrote that the correct option is "with game". Are they clueless?:))

Hi Zoya, I’m doing well! Nice to see you on here again. You say “Good luck with your game” to someone who’s about to go play a game. But here, the Russian has следующей, so we would say “good luck on your next game.” I don’t know about Russian, but in English, if you say NEXT game, it implies that they lost THIS game. A shorter, more natural way to say this is “better luck next game.”

It's clear to me now! Всё верно, здесь есть слово следующей, значит подразумевается, что последнюю игру они проиграли. On your next game - буквально "на следующей игре".

https://www.google.com/search?tbm=bks&q=%22better+luck+for+the+next+game%22

https://www.google.com/search?sxsrf=ALeKk03UPTs9BgmgjqkS3jSWuS_r_N76BQ%3A1589378233502&source=hp&ei=ufy7XuahG8am_Qa1nrqYCg&q=%27better+luck+next+game%22&oq=%27better+luck+next+game%22&gs_lcp=CgZwc3ktYWIQAzIGCAAQFhAeMgYIABAWEB46BAgjECc6BwgAEEMQiwM6BQgAEIMBOggIABCDARCLAzoFCAAQiwM6BAgAEEM6AggAOggIABAWEAoQHjoGCAAQDRAeUNYJWNQnYIQqaABwAHgAgAHyAYgBxxOSAQYxNS43LjGYAQCgAQGqAQdnd3Mtd2l6uAEC&sclient=psy-ab&ved=0ahUKEwim4pKo_7DpAhVGU98KHTWPDqMQ4dUDCAg&uact=5

Valery, could you improve your translation?
This community exists for good, interesting translations. Are you agree with me?