This would be less a Kelly issue and more an issue of the bankroll variable you're using. Advantage gamblers generally find the concept of "sessions" meaningle

This would be less a Kelly issue and more an issue of the bankroll variable you're using. Advantage gamblers generally find the concept of "sessions" meaningless - essentially, one's entire gambling career is just one long session. So if for example you have $1K per week of expendable income that you wish to use for the bankroll, and you're willing to risk that amount for a year, then you'd likely want to approach the Kelly calculation with a $52K bankroll. You would have wild swings within that year, and very short sessions when you lost (because you couldn't play again until your next paycheck), but you would still be betting the correct amount for the total risk you're willing to take.