Parlays
Parlays are sucker bets....period.
First let's look at a non-advantage bettor betting at a -110 style shop paying 13/5 on 2-team parlays and 6/1 on 3-team parlays (fair parlays odds at a -110 shop are actually about 13.223/5 and 5.958/1 respectively -- but 13/5 and 6/1 are still pretty close). If the bettor's picks are no better than a coin flip then betting two or three teams straight, we of course know his expected profit or loss ("P&L") to be -4.545%. But what if instead the bettor bets a two team parlay? Well, (assuming that all bets are independent) we know his chances of winning the 2-team parlay are 25% (50% x 50%) and his chances of winning the 3-team parlay are 12.5% (50% x 50% x 50%). Which means his expected P&L on the 2-team:
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= 25% x 13/5 - 75% x 1 = [B]-10%[/B]
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= 12.5% x 6 - 87.5% x 1 = [B]-12.5%[/B]
OK, so that about sums it up for your 50/50 bettor. Parlaying (independent) coin flip bets is always a bad idea from a pure expected P&L perspective (although for a risk-lover it could be a very good idea). But what about for the advantage bettor, say a bettor who is able to pick 55% winners? The expected P&L for the 55% bettor:
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= 55% x 100/110 + 45% x -110/110 = [B]5%[/B]
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= 55% x 55% x 13/5 + (1 - 55% x 55%) x -1 = [B]8.9%[/B]
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= 55% x 55% x 55% x 6 + (1 - 55% x 55% x 55%) x -1 = [B]16.463%[/B]
The downside of betting parlays, however, is that one drastically increases one’s risk, which in turn is detrimental to the long-term growth of one's bankroll To illustrate using an extreme example you'll note that while betting a 25-team parlay at a -110 book paying the fair parlay odds of 10,487,336/1 will yield the 55% bettor an expected P&L of a whopping +238.64%, one mustn't neglect the fact that such an outcome only occurs about 0.0000323% of the time. Now that’s not what I’d call a particularly likely occurrence. Not a good bet for the sufficiently risk-averse investor.
Now you may have noticed that I keep emphasizing that the parlayed bets need to be independent for the above to hold true. Well, what happens if the bets aren’t independent (i.e., correlated)? Well the answer is actually that betting correlated parlays will further increase expected P&L for both advantage bettors and (depending upon the degree of correlation) could even transform a parlay into a positive expectation bet for a nonadvantage bettor.
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