Yes, bhaav karma can be affected by games, depending on your intention, attachment, anger, greed, pride, deception, and violence while playing.

In Jain understanding:

• If a game creates excess attachment, competition with ego, anger on losing, mocking others, deceit, or harmlessness is violated in mind, then it can increase ashubha bhav and bind bad karma.
• If you play lightly, with awareness, without attachment, without hurting anyone, and without wasting your vow-based discipline, then the karmic impact is less.

Can we avoid it to play?

Yes, if you want to be more careful in Jain dharma, you can:

• avoid games that involve violence, cruelty, gambling, or strong addiction
• avoid games that increase raag-dwesh (attachment and aversion)
• keep the mind calm, restrained, and non-violent
• play only in a limited, disciplined way, if at all

Simple Jain rule:

If a game makes the mind more impure, agitated, or attached, it is better to avoid it.

So, yes, games can affect bhaav karma, and a Jain should prefer moderation or avoidance when they disturb inner purity.