Is 1% a big deal? Yes, sort of, but it may take a while for you to notice. Allow me to explain.

Blackjack players are a persnickety bunch. We measure a game’s advantage in tenths of one percent. A "good game" for a blackjack purist is a countable contest with a base edge that is close to zero percent, an edge so razor-thin that counting cards will push the edge firmly into positive territory. A positive edge of 1% (gasp!) is the Holy Grail for counters. That delivers long-term profit. On the flip side, we think an edge for the casino of 0.5% is a mediocre game, perhaps best left to tourists. In addition, if the edge dips to 1% or more against a player, well that’s just robbery at the tables. Get your ass out of the chair and play somewhere else!

I admit, this point of view is out of step with the strategic criteria of most casino patrons. Slot players happily whirl away a gargantuan edge, usually around 10% of their action. Most table players at games like roulette, Caribbean Stud, and Three Card Poker fork over between 2% and 5% of their action. Ditto for most video poker players. Casinos really clean up on those contests. Baccarat can be squeezed to 1%, but only blackjack, craps, and some video poker games offer bets with an edge below 1%.

This begs the question… Does 1% really make a difference? Would you really notice if a game has a 1% positive edge vs. 0%, or 1.5% negative edge vs. 0.5%?

From a purely mathematic point of view, the answer is yes, absolutely. The calculation goes like this…

Let’s say you have a 1% positive edge. You bet an average of $100 per hand, and you play about 60 hands per hour. That’s $60 per hour of "theoretical profit" multiplied by the number of hours you play. If you play 100 hours, then you win $6,000 on average. It’s not a windfall, but you can double or triple that amount by increasing your base bets. Conversely, if you reverse the edge to 1% for the casino (net 2% shift), then you’ll lose $6,000 on average.

So 1% seems like a lot, right? Yes, but in the real world, things aren’t so absolute. First, it’s tough to find a countable game. They’re not available in casinos the way duct tape is available at Wal-Mart. Which casino is going to let you sit and play 100 hours of profitable blackjack?

In addition, many players don’t count cards, so they’re stuck in a negative limbo, usually it’s about 0.8% to 0.5% edge for the casino, assuming they play perfect basic strategy. Moreover, in the real world, most players don’t play perfect basic strategy; they give up about 2%.

Casual players typically do four hours per session about four times a year, or about 16 hours annually. Avid players usually do 4 to 8 hours per week of live action (not counting online play), so it takes about three to six months to reach 100 hours.

Even after 100 hours, there is volatility to consider. Let’s say you aim for exactly average results, $6,000 after 100 hours. Exactly average results happen only about 1% of the time.

About 6% of players (approximately 1 in 20) will lose 60 decisions more than average, entirely negating the $6,000 profit they would otherwise have won (see graph at bottom of article.) And another 6% will win 60 more decisions beyond average, doubling to $12,000 or more. In other words, 12% of players will fall outside a "center window" of 120 decisions.

Meanwhile, 44% of players (including those mentioned above) will be outside of a window that extends 30 decisions on each side of the average, winning more than $9,000, or less than $3,000.

Only about 20% of players, 1 in 5, will hit the (almost) middle and land between $5,000 and $7,000.

The good news is that 92% of people who play with a 1% edge are essentially guaranteed to earn a profit, even if it’s only $100. The bad news (as I mentioned previously) is that very few players actually play with a 1% edge.

By the way, these spreads and percentages are the same regardless of the edge because of the way blackjack is designed; a change in the edge mostly affects payoffs rather than frequency of wins. Thus if the casino’s edge is 0.5%, and bets are $100, then the average loss is $3,000. About 6% of players will win $3,000 or more, another 6% will lose $9,000 or more, and so forth.

If the casino’s edge is 1.5%, then the average loss is $9,000. About 6% of players will lose less than $3,000 (or maybe even win money), another 6% will lose $12,000 or more, and… you get the picture.

Notice that there is some overlap. If you play for 100 hours and finish with a profit of $500, it’s impossible to determine the house edge just from that result, though a profit indicates the game probably wasn’t worse than 0.5% edge for the casinos.

The numbers are even murkier when the length of time is only 16 hours. If the casino’s edge is 0.5%, the average result is a loss of $500, but 37% of players will actually be profitable. Only 26% will be within 5 decisions of the average ($0 to $1,000), and another 37% will lose $1,000 or more.

Thus 1% is important because it makes a particular outcome more likely, but 1% guarantees nothing, at least for a single player. Casinos have an easier job extracting a profit from razor-thin margins because 1% for them is multiplied over infinite hours. Once you get into millions of decisions, 1% is like a lead weight inevitably pushing the scale.

Does this mean you can disregard the edge? No. but it means you should be realistic about the power of volatility. Luck happens. On the other hand, it’s possible to see a 1%+ change in the edge in exactly one trial. When a game pays 3:2 for naturals rather than 6:5, and a $100 bet is dealt a natural, the payout increases by $30.

That’s more than 1% in one huge chunk.

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© copyright 2012 Basil Nestor