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Best of Alan Krigman
What does proficiency at blackjack get you?30 January 2012
Say, for instance, you’re a blackjack aficionado. You follow perfect Basic Strategy in a joint with fairly liberal rules. On a single round, edge amounts to about 0.4 percent of your initial bet while the representative win or loss – with blackjacks, doubles, splits, and pushes taken into consideration – is 113 percent of this wager. Assume you bet $10 at the start of a round. The establishment figures it earns 0.004 x $10 or $0.04 from your action due to edge; your poke, however, grows or shrinks by 1.13 x $10 or $11.30 when reconciled over the various outcomes.
As numbers of coups grow, the impacts of both edge and volatility increase. But edge moves money only in one direction and rises steadily, while volatility can go either way and therefore tends to be self-cancelling. The influence of edge accordingly starts lower but climbs faster that than of volatility. At a table with four spots in contention, you’ll be dealt about 250 rounds in three hours. After such a session, starting every hand with $10, the green eyeshade gang chalks you up for a donation of 250 x $0.04 or $10.00 as a result of edge; you, though, have 95 percent chance of finding yourself between $357 above or below this figure – between minus $367 and plus $347 – owing to volatility. After a million coups, more than most players will ever undergo but not all that many for the casino, 0.4 percent edge acting on a $10 million gross wager totals $40,000. In contrast, the 113 percent volatility per coup will put 95 percent of all players in a range $22,600 above or below this level – that is, in the hole between $17,400 and $62,600.
Since the vast majority of solid citizens will experience statistically few rounds, their fortunes will determined far more heavily by volatility than edge. This situation leads enquiring minds to ask whether blackjack proficiency, gauged by the edge solid citizens give the bosses above and beyond the mathematically possible minimum, is as important as most gurus seem to claim.
A practical answer here depends on how good or bad blackjack buffs get. Under reasonable conditions, an adept card counter might enjoy an advantage of about 2.0 percent over the casino. A competent Basic Strategy player allows the bosses an edge of roughly 0.4 percent with the rules normally now extant. Common departures from Basic Strategy raise the edge to the vicinity of 0.8 percent. A neophyte who mimics dealers’ rules – hitting totals of 16 or less, standing above this value, and never splitting pairs or doubling – would fight an edge around 5.3 percent.
Card counters achieve their advantage principally by raising their bets when cards previously withdrawn from a deck or shoe leave those still to be dealt rich in high ranks. A 2.0 percent edge might be obtained with a spread of 10-to-1, say between $10 and $100 per hand. The average wager under these conditions might be about $30 and the representative bankroll change per round approximately $38. For a fair comparison, assume the 0.4, 0.8, and 5.3 percent players also bet $30 per round; they’d then see volatility jumps of $34, $34, and $30 per round, respectively.
Here’s how the four groups of players would fare in a 250-round session:
1. Betting an average of $30 per round with 2.0 percent advantage, card counters would expect to earn $250. They’d have 95 percent chance of finishing between a loss of $1,050 and a profit of $1,350. And the probability they’d leave with a profit of any amount would be 66 percent.
2. Players betting $30 flat and battling an edge of 0.4 percent would expect to lose $30. They’d have 95 percent chance of ending between $1,105 down and $1,045 up. And the chance they’d quit with a profit would be 48 percent.
3. Individuals giving the house 0.8 percent edge would have an expected loss of $60 and a 95 percent chance of finishing between a loss of $1,135 and a gain of $1,015. The chance they’d leave the table with a profit of any amount would be 46 percent.
4. The 5.3 percent players would expect to lose $400. They’d have 95 percent chance of ending between $1,345 poorer and $550 richer. And their likelihood of pocketing a profit of any size is 20 percent.
Differences exist among the prospects for players in the alternate categories. Card counting skill is a major positive. Yet, even when favored by 2.0 percent, a card counter still has 34 percent chance of showing a loss after 250 decisions. Conversely, a bezonian with no real knowledge of the game has a 20 percent shot at earning a profit in 250 hands. Is it worth the time and effort needed to reach one level or another of expertise? Decide this for yourself, now that you know the value of doing so and the insights of that masterful muse, Sumner A Ingmark, who wrote:
Where is the point of diminishing returns.
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