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Gaming Guru  What bets offer the most chance to reach win goals before hitting loss limits?23 January 2012
By Alan Krigman Some solid citizens visit casinos intending to risk modest bankrolls in shots at a day’s pay. They figure their prospects are decent if they set conservative profit targets and quit as soon as they reach or surpass them. This notion is generally correct. But it’s not the whole story. Ideally, were bets to have no edge, the probability of hitting a target before biting the dust would precisely equal the amount with which a player starts – the bankroll, divided by how much the person will have by achieving the win goal – the bankroll plus the profit. So, for instance, to double a $100 stake – earning $100 to end with $200, the chance of heading home happy is 100/200, which is 0.50 or 50 percent. With a $50 win goal on the same stake, the likelihood of prevailing is 100/150, which is 0.6667 or 66.67 percent. Moving in the other direction, setting a $200 profit target, the outlook becomes 100/300, which is 0.3333 or 33.33 percent. The probability of attainment being inverse to the ratio of starting to desired ending levels holds in the real world where the casino has an edge. The effect of this statistical advantage is to lower players’ prospects at any level of initial and final amounts. The reduction isn’t straightforward, though. It depends on the parameters of the bets being made. These are bet size, payoff ratio, and chance of winning. Together, the latter both determine not only the edge but also the volatility. To picture the effect, assume you play double-zero roulette and are trying to decide whether to bet on a four-number corner with a 4/38 (10.53 percent) chance to win 8-to-1, a six-number double-street with a 6/38 (15.79 percent) chance to win 5-to-1, or a 12-number column with a 12/38 (31.58 percent) chance to win 2-to-1. The payoffs and the probabilities of winning shift in tandem, such that the edge is the same in all cases, 5.26 percent. Say you have a $100 bankroll, are comfortable betting $5 per spin, and want to earn $100. Ideally, your chance of triumph is 50 percent. However, owing to the edge and other parameters, the actual probabilities are 43 percent on the corner, 39 percent on the double street, and 25 percent on the dozen. Were you to set a $50 profit target, your outlook would be 62 percent on the corner, 59 percent on the double street, and 48 percent on the column. With a more ambitious $200 earnings objective, your chances become 25 percent on the corner, 20 percent on the double street, and 8 percent on the column. Based strictly on the win goal versus loss limit criterion, the higher-paying bets with the lower hit rates would be the more appropriate choice. Were you able to calm the butterflies in your stomach and bet $10 with the same bankroll and the aim of doubling your money before busting out, your probabilities of success would be 47 percent on corners, 45 percent on double streets, and 37 percent on dozens. Your prospects would likewise improve for the smaller and larger win goals. Raising your bets enhances your outlook when reaching a win goal before hitting a loss limit is your sole criterion. What happens if the edge varies among the alternatives? At craps, for example, you may want to compare Place bets on alternate numbers. Payoffs and expected frequencies of wins on these bets differ in a manner that influences edge as well. A $5 four has a 3/9 (33.33 percent) chance to win $9 and 6.67 percent edge. A $5 five has a 4/10 (40.00 percent) chance to win $7 and 4.00 percent edge. And a $6 six (the minimum booked on this number at a nominal $5 table) has a 5/11 (45.45 percent) chance to win $7 and 1.51 percent edge. Pretend, as with the roulette illustrations, you have a $100 bankroll and are hell-bent on going for broke in an attempt to double your money Placing the four for $5, you’ll come through in 18 percent of your sessions. With $5 on the five, your chance would be 24 percent. And venturing $6 on the six, you’d be up to 39 percent. Here, contrary to the trend at roulette, the highest-paying lowest-probability option – the four – affords the dimmest hope of joy, while the converse is true for the lowest-paying highest-probability bet – on the six; the bet on the five is intermediate. The flip-flop relative to the roulette situation occurs because all the bets cited for that game have the same edge, while in craps, the house advantage on the four is greater than that on the five, which in turn exceeds that on the six. Chances would improve across the board were you to lower your win goal and deteriorate if you raise it, but the trend would be the same. Similarly, higher bets would increase your likelihood of success but wouldn’t alter the order of rankings associated with the alternate propositions. Wouldn’t it be wonderful if one hard-and-fast rule covered all situations? Wouldn’t the footwear industry be thrilled if one size shoe fit all feet? Then neither punters nor podiatrists would be inclined to extrapolate from this advice from the beloved bard, Sumner A Ingmark: Leave casinos feeling horrible. Should you play the multi-line slots – and if so, how?16 January 2012
It’s easy to follow the action on plain-vanilla single-line three-, four-, or five-reel slot machines. When the reels – physical or virtual – stop, you glance along the horizontal line across the middle of the window looking for winning combinations; these are generally multiple instances of identical symbols, such as three aardvarks, four duck-billed platypi, or five red-breasted nuthatches. ... (read more)
How do betting strategies affect your blackjack performance?9 January 2012
Blackjack card counters can get an advantage over the casino by raising their bets when favorable ranks dominate what remains to be dealt from a deck or shoe. Given the rules dealers must follow and the options available to players, the house has a small edge when ranks are uniformly distributed. If cards ... (read more)
Why don’t more craps players make Lay bets? Or, do they?2 January 2012
Lay bets are wagers having greater probability of winning than losing, but payoffs less than the amount at risk. Craps has two major classes of these propositions.
One class, available to players who bet Don’t Pass or Don’t Come, comprises the Odds they can lay after the point is established. The Odds are auxiliary wagers giving neither bettors nor bosses an edge. ... (read more)
Fun and (Table) Games: Try BaccaratSo, you want to try the tables. Say you fancy a casino classic cloaked in tradition, but simple enough that everyone makes a straightforward bet then waits for the outcome. As a novice you might opt for a game with low inherent volatility, where your bankroll normally drifts up and down gradually; this ... (read more)Everything You Should Know about Baccarat, and MoreBaccarat is a good choice if you're seeking casino table action but nervous about trying. It's elegant, has relatively low house advantage, and is often offered in mini versions with an affordable minimum bet. It's also simple to play. The dealer does the complicated part. You need only decide whether to wager on Banker, Player, or Tie. ... (read more)You Can Join in the Excitement at Craps with these Simple BetsLots of people sense that craps is exciting, but are too cowed to try it. They can't figure out the rhyme or reason for wagers. Or what determines whether anyone loses or wins - and, when the latter, how much. And, they're afraid they'll need too big a stake to play. All to toss two dice and bet on how they'll land. ... (read more)Is Card Counting at Blackjack Worth Your While?I was coddling a cappuccino at a casino's posh high roller club a few weeks ago with some blackjack-playing cronies, Basil and Courtney. Basil is a club member. Courtney and I were his guests. Basil follows basic strategy to the letter. He bets $100 most of the time, with ... (read more)How Casinos Measure House Advantage, and What the Values MeanEverybody knows why casinos get rich. They have an advantage on every bet in games of independent trials. But only a handful of hopefuls understands how the handicap is achieved. Many solid citizens think it's just that the bosses have more chance of winning every round than the players... ... (read more) |
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