Taking Chances: Be Bold to Double Your Money

December 15th, 2007

Here’s an excellent piece of gambling advice on “Bold Play” from author and probability expert, John Haigh.

Click to visit Bodog Casino - players from around the world welcome except Canadians! US OK.This example uses Roulette as it is by far the most popular casino game, apparently taking around 60% of total casino stakes in the UK and Europe. The lesson to be learned from this example, however, is just as applicable to all casino games, even slot machines where max bets rather than single line betting is recommended for maximum returns. 


Paul needs £216 for an air ticket to see his team play in the European Cup final tonight. He has half that amount, £108, but might as well have nothing! Can the roulette wheel at his favourite casino help?

Faced with any similar problem, there is one maxim: in unfavourable games, bold play is best, timid play is worst.

To advise Paul, let’s begin by simplifying the situation, and suppose that even money bets on roulette also lose when zero turns up. Then the house advantage is the same whatever individual bet we make.

One bold play is to bang the entire £108 on Red. Then 18 times out of 37 – or 48.6% of the time Paul can cash his chips immediately for £216, and travel to the game. Otherwise, he’s lost all his money and must watch the game on TV!

Best roulette betsThere are other bold approaches. He could divide his money into 18 equal piles of £6, and be prepared to make successive bets on a single number until he has either run out of cash, or one bet has succeeded. Single numbers pay at 35:1, so one win is enough. To calculate his chance of success, we first find the chance that all his bets lose. Any bet loses 36 times in 37, so the chances they all lose is 0.61.  For this strategy, the chance that at least one bet wins is 39%, rather worse than the single bet on Red.

Paul has an alternative way to use the 35:1 payout on single number bets. He already has £108. so if he uses just £4 on the first bet (£3 is not quite enough), a win would take him to his target, so long as he has at least £76, a winning bet using a £4 stake gains enough; with less than this, he should stake £5, and when he has £41 left as bankroll, he must increase each bet to £6. In this way, he can plan to make a total of 22 bets if necessary (nine of £4, seven of £5, six of £6); if any of them win, he has reached his target, otherwise he is reduced to £1.

Roulette gamblingThe chance that they all lose is about 54.7%, so he succeeds only 45.3% of the time. His last-ditch hope is to win a 5:1 bet with the final £1, and then a 35:1 bet using the £6: this takes his chance up to 45.7% only. Overall, this is better than trying the 18 bets of £6, but not as good as one big bet on Red.

One final try: place his whole £108 bankroll on the odds-on bet of a split column. If that wins, he has £162, so he can now place £54 on Red; if that wins, victory! If that loses, he is back to £108 and can begin to repeat his sequence. This strategy wins only 47.3% of the time. All of these alternatives attempts are inferior to the original suggestion of a single bet on one of the even money chances. And, in reality, that bet is even more favourable than we have supposed, because of the zero rule on the bets on Red. Taking that into account, Paul has a 49.3% chance of getting to see the match. His stay at the casino will be short, but he has no interest in the extended pleasure of watching his fortune fluctuate; it is the airport or bust!

The numbers in this example were chosen to make it mathematically easy, but bold play means making as few bets as possible.

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