Aceside is correct. Each time the lone player busts, the dealer doesn't complete his hand. On average, the BS player busts about 16% of the time. So, assuming a 4.5/6 game, where 234 cards will be dealt, plus a couple more after the cut card comes out, and an average of about 44 rounds, the player will break about seven times. As the dealer doesn't then take any additional cards, you save about seven cards per shoe--in effect, that much extra penetration. Not worth anything to the BS player, but something to the counter. Note, finally, that the counter breaks fewer times than the BS player, because of using indices to stand when the BS player hits and may bust.
Don
by: Don Schlesinger
Is the effect one of getting more possible opportunities during the shoe even though the cut card is in the same place?