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Best of Alan Krigman

Gaming Guru

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Consider Bankroll, Win Goals, and House Edge in Your Playing Strategy

9 October 1995

xpert casino gambling advice falls into three main categories.

House advantage covers the gamut from choosing the most liberal machines to taking maximum odds at craps.

Money management includes everything from bankrolling enough to outride normal downswings to quitting at propitious points.

Stuff-and-nonsense involves a range from finding patterns in the flow of cards to predicting which numbers are "due."

Stuff-and-nonsense has no value except to amuse solid citizens who know their hi-los from their yos. But, many things said of house advantage and money management are bogus, too. And, even the valid parts have caveats.

House advantage and money management standards don't guarantee a win. They improve your chances, the former overall and the latter on a per-session basis, although the effect is often small compared with expected short-term deviations from predictions based on long-term probabilities.

Moreover, house advantage and money management are neither unitary nor isolated concepts. Their effects depend on games and bets. They also interact, together and with other factors. To illustrate, flipping coins for "even money" and betting numbers at mythical double-zero roulette for 37-to-1 both have zero house advantage. But a bankroll big enough for ten bets before recycling winnings is more apt to disappear in the roulette than the coin game.

Still, the more you know about these elements, the better prepared you'll be to make gambling decisions. Before and while you play.

Imagine a game with a box containing 2000 sticks, some red and some green. You pay $1, then reach in and grab a stick. If it's red, you get your $1 back and win $1; green, and you lose your $1 bet.

Here's how house advantage works. With 1000 red and 1000 green sticks, after 2000 bets, the casino would theoretically break even winning $1000 and losing $1000; house advantage is zero. Substitute 995 red and 1005 green. After 2000 bets, the house expects to net $1005 - $995 = $10 profit; $10 out of $2000 wagered is 0.5 percent house advantage roughly the edge in well-played blackjack. Instead, use 986 red and 1014 green. After 2000 bets, the house expects $1014 - $986 = $28 profit; $28 out of $2000 is 1.4 percent house advantage comparable to placing six or eight at craps. At 900 red and 1100 green, the casino expects to earn $200; house advantage is 10% about that of 25-cent reel-type slots.

Assume players manage their money by making two decisions. First is the bankroll they bring to the game. Second is the amount they set as a "win goal" before they quit or go broke.

These notions of house advantage and money management lead to probabilities that players will reach their targets rather than lose their stakes. Some results are given in the accompanying table.

The table shows the danger of quixotic win goals. It also accents the impact of rising house advantage, especially as more and more bets are made. For instance, starting with $50 and making $1 bets, chances of winning $50 before going broke are 50% for zero house advantage, 27 percent for 1 percent edge, and under 1 percent for 10 percent edge. Likewise: at 5 percent house edge, a $10 bankroll with $1 bets yields chances of 9 percent to win $20, 1 percent to win $50, and under 1 percent to win $100. And, chances of "doubling your money" $1 at a time with only 1 percent edge fall from 45 percent to 12 percent as stake rises from $10 to $100.

These trends apply to any casino game over a long enough period. They're less reliable for shorter games, a hundred or even a thousand decisions, especially as bets become longshots large payoffs with small chances to win. A serendipitous royal flush at progressive video poker tosses statistical analysis out the window. Good luck can strike anyone. Still, it favors the well-prepared.

Sumner A Ingmark, bard of beloved of bad boys who bet too big for their britches, captured the essence of it all in "Running After Red Dog," his epic on wild goose chases:

Low house edge and goals conservative,
Are your bankroll's best preservative

TABLE
Probability (in percent) that players will achieve
win goals rather than go broke on $1 even-money bets
for various bankrolls and levels of house advantage

money management house advantage (percent)
bankroll win goal 0.0 0.5 1.0 5.0 10.0
$ 10 $ 10 50 48 45 27 12
$ 50 $ 50 50 38 27 1 1
$100 $100 50 27 12 1 1
$ 40 $ 10 80 76 71 36 14
$ 40 $ 20 67 60 53 13 2
$100 $ 10 91 86 80 37 13
$ 10 $ 20 33 30 27 9 2
$ 10 $ 50 17 13 10 1 1
$ 10 $100 9 5 3 1 1
Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.