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Can you make big bucks at the casinos starting with a small bankroll?

3 October 2011

You can make big bucks at the casinos working from small bankrolls. But no matter what strategy you follow attempting to do so, you need a stroke of luck because the more profit you demand, the less you’re apt to succeed. There’s no getting around the laws of the universe.

Some folks try betting on low-probability high-payoff longshots at the tables. An example might be a single number at roulette, which pays 35-to-1, $350 for $10 at risk. This has 2.6 percent chance of success on a double-zero wheel. At $10 per spin on a $100 bankroll, the likelihood of winning at least once in 10 spins – netting anything from $260 to $3,500 – is 23 percent. At a normal rate of play, about a spin every minute and a half, individuals following this strategy face 77 percent chance of being sent to the showers in 15 minutes.

Another well-trodden path players fantasize will lead to the coveted pot of gold involves feeding the slots. One appealing feature is that individual bets may be comfortably low; you can play machines taking anything from a cent on up. Understandably, you can’t win much for a penny so the bulk of the wagers today are a dollar or so each. Another attraction of the slots is that although returns may reach thousands or sometimes millions of times the amount bet, they start at 1-for-1 (technically, pushes but touted as wins). Big jackpots are exceedingly rare, but 1-for-1 and other small returns occur regularly. The frequent low returns lead to high enough hit rates that individuals get lots of entertainment and excitement value while nurturing hope that the next spin will change their lives, in most instances as the house’s edge slowly picks their pockets.

Slot-like side or bonus bets at some table games are another popular choice. The primary action may pay 1-to-1 or other small multiples of the wager. People who size such bets to modest bankrolls therefore may be unable to amass much of a fortune even during a long winning streak. Auxiliary bets paying according to schedules similar to those on the slots dangle the possibility of rich rewards for $1 – occasionally less – a shot, regardless of the nominal table minimum. Hit rates are lower than on machines, but the amount at risk may small enough compared to the main wagers that series of losing side bets erode a stake but don’t usually knock players for a loop.

A third approach to grabbing big bucks on small bankrolls is what’s fancifully termed “playing with the house’s money.” The idea is to bet high using previous earnings rather than dough brought from home. The concept can be carried to any degree, and can involve pressing winning bets directly or raiding accumulated profits. As a simplified case, pretend you think a $100 stake will support $5 bets on Pass at craps. When you win a hand, you’ll raise to $10 on the next using your own $5 and the $5 you just bagged from the bosses. Success on the second bet will put you $15 ahead. Failure will be tantamount to losing on the first round because the stack in your rail will only shrink by $5. Pass has 49.29 percent chance of triumph. So this system is like betting $5 to win $15 on a proposition fighting odds of 50.71-to-49.29 – almost 1-to-1. Or, is it?

Well, no. Earning $15 takes two wins in a row. You’re down $5 if you lose the first hand or win the first and lose the second, putting the chance of losing $5 at 0.5071 + 0.4929 x 0.5071 = 75.70 percent. You’re up $15 by winning both. That’s 0.4929 x 0.4929 = 24.29 percent. Odds against success are therefore 0.7570-to-0.2429 (3.11-to-1), apropos of a normal 3-to-1 payoff.
How does using the house’s money this way affect your prospects? On the average, the two-bet parlay on Pass, starting with $5, has a 40.5 percent chance of doubling and 21.6 percent of tripling a $100 poke. Betting a flat $5 per hand, probabilities would be 36.2 and 17.0 percent, respectively. For a flat $10 per hand, prospects are 42.9 percent for earning the $100 and 24.4 percent for the $200. On this basis, the flat $10 is best, the parlay second, and the $5 bet worst.

Likelihood of staying in the game for a satisfying length of time on a given bankroll works oppositely. A crowded table is good for an average of about one decision on a single Pass bet every two minutes. That would be 120 decisions in a four-hour session. With the parlay, 120 wins or losses on Pass can be expected to yield 80 outcomes – 40 one-round $5 losses and 40 two-round coups of which 20 each would be $10 wins and $10 losses. This would lead to a 65 percent chance of still having money, whether the player was ahead or behind, after four hours. The $5 flat bet would afford 91 percent chance of not busting out in this much time. At $10 flat, longevity would fall to 58 percent. The $5 flat bet would therefore offer the best chance for survival, followed by the parlay then the $10 flat bet. Pressing with “the house’s money” is the same as betting equivalent amounts of your own, which – of course – your winnings surely are.

With good luck, any of these methods may win, letting players think they have the keys to Fort Knox. But fortune smiling on statistically small numbers of trials proves nothing. Except, maybe, that anyone can be at the right place at the right time. As the poet, Sumner A Ingmark, penned:

Oh, ye who scant data extrapolate,
Don’t cry when your theories evaporate.

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.