True Count Rounding: How Much Cost?
Truncating a true count instead of rounding it bleeds roughly 0.08 to 0.14 units of expected value per hour off a competent counter's edge, and that hemorrhage compounds every time you raise your bet. Most players never quantify this because they fixate on the running count and treat the division as a formality. That formality is where your money quietly dies. π€
The math is unforgiving. True count equals running count divided by decks remaining, and the remainder you discard is not neutral noise β it is systematically biased against you when you floor, because flooring understates true count in positive territory and overstates it in negative territory. You end up underbetting your genuine advantage and overbetting your genuine disadvantage. That double-sided error is the silent tax on every floored true count.
The Real Cost Per Hour, Not Per Hand
Let us put hard numbers on it. A six-deck game, 75% penetration, one-and-a-half decks cut off, heads-up play at 100 rounds per hour. An aggressive spread that pushes from one unit to twelve at a true count of five. Floor your true count and you misprice the boundary hands β the ones sitting at true 1.8, at true 3.4, at true 4.7. Those are precisely the hands where your bet ramp steps up, and flooring throws them into the lower bucket. The aggregate damage lands in the range of 0.1 units per hour, which on a $25 unit is $2.50 an hour evaporating into thin air. Over 500 hours that is a four-figure leak. πΈ
Now scale it. A $100 unit spread across two hands, 200 hours a year, and the floored true count error alone strips somewhere between $4,000 and $5,600 annually. That is not variance. That is structural, predictable, and entirely avoidable. Anyone who tells you rounding is a rounding error has never actually run the simulation with a bet ramp that steps at half-count boundaries.
Why Flooring Feels Safe and Costs More
Flooring is the default in most mental arithmetic because it is the path of least cognitive resistance. You divide 14 by 4.5, get 3.11, and you bet the true-3 tier. Fine. But that same player divides 14 by 3.5, gets 4.0, and bets the true-4 tier β except the actual expectation curve is steeper than the step function they are using. The cost of true count rounding is concentrated exactly at these discontinuities, and the betting correlation between your ramp and the real edge collapses by several percentage points.
The brutal truth is that flooring introduces a downward bias in the most profitable zone of the shoe. You are systematically telling yourself you have less edge than you do, which means you underbet the hands that carry the most value. Conversely, in negative territory, flooring pushes you toward more conservative departures β which is actually the safer side, but it does not offset the positive-count underbet. The asymmetry is real and it favors the house. π―
Rounding vs. Truncation: The Exact Delta
Proper rounding β nearest integer, with 0.5 rounding up β cuts the expected loss roughly in half compared to flooring, because it eliminates the systematic one-directional bias. The residual cost of nearest-integer rounding against a fully precise (fractional) true count is small, on the order of 0.02 to 0.05 units per hour in the scenarios above. That is the true floor of the rounding cost, and it is the price you pay for arithmetic you can actually execute at the table without tanking the game.
Fractional true count, computed to one decimal, recovers essentially all of it but demands you carry division precision under pressure. Fewer than one in fifty players can sustain that accuracy across a four-hour session without errors that cost more than the rounding saved. The sweet spot is nearest-integer rounding with a disciplined bet ramp that places step boundaries at half-count intervals, not at integers. That single adjustment β moving your ramp trigger from true 4 to true 3.5 β claws back most of the leakage with zero extra mental load.
Where the Cost Actually Bites: Bet Ramp Geometry
Your bet ramp is a step function. The shoe's edge is a smooth curve. The gap between them is the house edge recovery gap, and rounding decides how wide it opens. If your top bet triggers at true 5, flooring means you only reach that tier when the floored count hits 5 β which happens at a real true count somewhere between 5.0 and 5.99. You are late by up to a full count on your biggest bets. Across a shoe, that lateness costs more than the arithmetic error itself.
Fix it by shifting every ramp threshold down by half a true count when you floor. That compensates for the downward bias at the exact points where money concentrates. It is a crude correction, but crude and applied beats elegant and ignored. The players who survive year after year are not the ones with the sharpest division β they are the ones who price their own arithmetic sloppiness into the ramp and move on. π