Bet spreads and bankroll for counters

A counter makes money by betting more when the true count is high and the minimum when it is not; the pattern of bet sizes against true count is the ramp, and the ratio of top bet to bottom bet is the spread. Choosing a ramp is a trade between three things: expected profit, which rises with the spread; risk, which rises faster than profit; and cover, because the bet pattern is what casinos watch. This page explains each, with an illustrative ramp and the published figures that show how much spread and penetration matter.

Why the spread is where the money is

Most hands in a shoe are dealt at a true count of zero or below, where the house has the edge. The counter’s overall advantage is an average: a small loss on many minimum bets plus a larger gain on fewer big bets. The wider the gap between the two, the more the big bets dominate the average.

Wizard of Odds simulated a six-deck game (dealer stands on soft 17, double after split, surrender, resplit to four hands) using Hi-Lo with the Illustrious 18 and Fab 4:

Read down a column and penetration matters: the same 1-to-10 spread earns 0.368% at four decks dealt and 0.837% at five. Read across and spread matters: at 4.5 decks, tripling the spread from 1-5 to 1-15 nearly triples the edge. But the standard deviation column grows almost as fast as the edge, which is the risk side of the bargain.

The percentages are against total money wagered, with the average bet also rising, so hourly expectation scales faster than the advantage column alone. They are simulation results for one rule set and perfect play, not a forecast.

An illustrative ramp

The following is a typical shape for a six-deck game, not a recommendation and not optimised for any bankroll. Units are multiples of the table minimum.

BlackjackInfo gives a similar illustrative ladder of 1, 2, 4, 8 units at +1 or lower, +2, +3 and +4 or higher. The shape is what matters: flat at the bottom, rising roughly in step with the count, capped at the top. The cap exists for two reasons: bankroll, because the biggest bets carry the most variance, and cover, because a top bet far above the table’s normal action gets noticed.

At a £10 minimum the 1-12 ramp runs from £10 to £120 and the 1-8 ramp from £10 to £80. A ramp is only as good as the true count feeding it; see true count conversion.

The Kelly idea

The Kelly criterion, described on Wikipedia, gives the fraction of bankroll that maximises long-run growth of a repeated favourable bet. For a bet that loses the whole stake or wins b times the stake, with win probability p and loss probability q = 1 − p:

f* = p − q ÷ b

For an even-money proposition (b = 1) this is simply p − q, which is the player’s edge. Wikipedia’s coin example: a 60% coin at even money gives f* = 0.6 − 0.4 = 0.2, so bet 20% of the bankroll each toss.

Blackjack is not a simple even-money bet because of doubles, splits and 3:2 naturals, which increase the variance, so the practical counter’s version divides edge by variance rather than by the odds. The core prescription survives, and Wikipedia’s card counting article states it plainly: bet increases should be proportional to the player’s advantage, and the Kelly criterion demands no bet at all when the deck does not offer a positive expectation. A ramp is a discrete approximation of that rule, and the reason it stays flat at low counts is Kelly’s zero.

Two warnings from the same source. Betting more than Kelly increases the risk of ruin without increasing growth. And Kelly assumes you know your edge: overestimating the advantage, which counters routinely do through estimation and rounding errors, pushes the bet past the optimum. That is why most counters bet fractional Kelly, typically a half or a quarter, accepting slower growth in return for smaller swings and tolerance for error.

Risk of ruin: the orientation

Risk of ruin is the probability that a chosen bankroll is lost before the edge has time to work. It depends on the edge, the variance of the bets, and how long you intend to play. There is no closed formula that covers a real counter’s mixed bet sizes; Wizard of Odds’ risk of ruin page says as much and uses simulation instead.

His tables are for a flat-betting basic strategy player at a 0.41% house edge (six decks, S17, DAS, resplit to three hands, no surrender), so they do not describe a counter directly, but they show how bankroll and session length interact:

The lesson transfers: the units needed grow roughly with the square root of hands played, and reducing risk from 10% to 1% costs about half as much bankroll again. A counter with a positive edge has a finite lifetime risk of ruin rather than one that approaches 100%, but a wide spread raises the variance per hand considerably, so the number of maximum bets in the bankroll is the practical measure. Wikipedia’s card counting article records the common rule of thumb of about 100 times the maximum bet; a 1-12 ramp at a £10 minimum would need about £12,000 under that rule. Proper figures for your own ramp come from risk-of-ruin software rather than a rule of thumb; standard deviation and risk of ruin explains the inputs.

Why cover matters

The bet pattern is the counter’s signature. A player whose bets rise and fall with the count, and only with the count, is doing the one thing surveillance looks for. Wizard of Odds calls spreading “more art than science” and describes two kinds of cover: limiting the ratio of top to bottom bet (he suggests 1-to-15 is about the most aggressive for six decks), and making bet changes look like a gambler’s, raising only after a win, lowering only after a loss and leaving the bet alone after a push. He notes that the second kind comes “at a cost to profitability”.

Other cover costs are the same shape: skipping the most conspicuous index plays such as splitting tens, not jumping straight from the minimum to the maximum, and not leaving the table the moment the count turns negative. Each gives back some edge. The ramp you can actually play for hundreds of hours is worth more than the optimal ramp you get backed off from in twenty; the countermeasures themselves are described in casino countermeasures and legality.

What this does and does not promise

Everything above is conditional on a countable game, deep penetration, a wide spread, error-free counting and a bankroll sized for the variance. The simulated advantages are around half a percent to one percent of money wagered, which is small, slow and volatile; BlackjackInfo puts the realistic range at 0.5% to 1.5%. Losing sessions, losing weeks and losing months are normal outcomes for a counter with a genuine edge, and bankroll and variance is the place to understand why before any real money is involved.

Related reading

• True count conversion
• Illustrious 18 index plays
• Bankroll and variance
• Casino countermeasures and legality