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How Bet Size Affects the Chance of Reaching your Win Goal3 May 2006
For instance, beginning with $100, the odds you must overcome to earn $900 before busting out a 9-to-1 profit are 9-to-1. In terms of probabilities, the chance of starting at one point and reaching a higher level before going broke equals the stake divided by the final amount. So, the probability of going from $100 to $1,000 is 100/1,000 or 10 percent; from $50 to $200 it's 50/200 or 25 percent; from $250 to $500 it's 250/500 or 50 percent. And so on. This, regardless of how much you bet or the volatility the characteristic ups and downs of the game.
These estimates provide upper bounds on likelihood of success. In a real casino,
the house will have an edge which lowers the probabilities somewhat.
The effect is strongest in low-volatility games those in which bets pay close to even money. Blackjack is the most common example. Basic Strategy at a casino with moderately liberal rules yields an edge of roughly half a percent. The standard deviation, a measure of the volatility envision it as the average number of bet units you win or lose on each hand is 1.13.
Make believe you start with $100 and are willing to risk it all to double your money, to finish with $200. Absent the edge, the chance of success would be 100/200 or 50 percent. Betting $5 per round, your chance is 46 percent; at $10 per round, it's 48 percent; and at $25 per round, it's up to 49 percent.
A more ambitious goal might be to go from $100 to $500. In a fair game, your prospects would be 100/500 or 20 percent. Here, $5 per hand gives you just 14 percent chance; at $10 it's improved to 17 percent; and at $25 it's increased to 19 percent.
What if, instead, you start with $200 and will do or die to quit with $1,000?
The ideal probability you'll triumph is 200/1000 or 20 percent. The real-world
figures are only 10 percent betting $5, 14 percent at $10, and 18 percent at
Increasing the edge for the same volatility makes the effect of bet size more pronounced. Give the house 1 percent edge at blackjack with the objective of turning $200 into $1,000. The ideal chance of your dream coming true is still 20 percent. In contrast to having a 10 percent probability of success with $5 bets as with half as much edge, though, your chance is 4 percent.
Does this suggest it's wise to bet as high as you can? It might, if maximizing the probability of reaching some returns plateau were your sole criterion. And perhaps it is. But solid citizens usually weigh desired profit versus playing time. And, the higher your bet relative to your stake, the shorter your session is apt to be. Either because you bite the dust or reach your target quickly. But, in the latter case, would you really quit when you amassed that $500 or $1,000 you had in mind or tell yourself you're on a roll and should ride it out? Precisely the point thus portrayed by the perceptive punter's poet, Sumner A Ingmark:
Gamblers who think their luck runs in streaks,
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