Redwings
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SBR Founder Join Date: 8/10/2005
Taking it a step further ... if the games were all offered at -110, then a loss of the Martingale series would result in a loss of 18.4481 units, while a win of the series would result in a gain of 1 unit.
This is the equivalent of US-style odds of -1844.81.
Odds of -1844.81 on a bet winning with probability 15 16 implies vig of 1.1682%, while vig of 1.1682% on a bet winning with probability 1 16 implies odds of +1481.31.
So ... a a 4-tier Martingale all at -110, has the exact same characteristics of a bet on the favorite at an unbiased market of -1844.81 / +1481.31. Now granted that is a pretty tight market but is it really what a Martingale player is looking to accomplish?
What about you, AAO? Are you satisfied betting chalk at low vig?
SBR Founder Join Date: 8/28/2005
You can't change a collection of -EV bets into a +EV bet simply by selecting a sufficiently creative (although there's nothing particularly "creative" about Martingale) staking strategy.
In that sense there's absolutely nothing to be gained betting Martingale.
Now that said, one thing you can accomplish with Martingale is the lowering of your effective vig (calculated as a percentage of max possible loss). For example ... if we assumed a 4-game series with each game offered at odds of +300 and at 4.545% vig (an admittedly unlikely scenario -- but we're just keeping it simple), then by Martingaling the 4-game series you'd "lower" your vig to 2.870% (loss = 2.160 units, win = 1 units, win prob = 66.40%).
This would result in a bet on the favorite NOT to sweep at odds of about -216.
Now if that were the bet you really wanted to make, AND if you were assured you'd be able to make each bet at +300 even after the previous game had been decided, AND if the odds on the favorite not to sweep as a single bet were worse than -216, then indeed the Martingale series would provide your best value.
But that's the union of the 3 necessary conditionals that in reality probably won't hold. Of course even if they did, the above analysis completely overlooks the issue of risk. Even if the games were (equivalently) +EV and independent of previous results, there would be no reason (now from a Kelly perspective) to ever increase your bet size after a loss. Ever. You'd be decreasing your bet size after each loss (and you'd keep betting even after a win).
If you want to bet Martingale you should only do so because you find it fun (the satisfaction of the above 3 conditions within a sufficiently risk-neutral framework notwithstanding -- and I'll also mention that the fun you initially envisioned at the start of the series would likely be a fair bit greater than the fun you actually experienced after 3 consecutive losses); but if you think you've found some sort of sensible betting system in Martingale then you're sorely mistaken.
SBR Founder Join Date: 8/28/2005