Parlays and Round Robins Can Be Good Bets - Bankroll Management

Conventional wisdom stipulates that parlays are bad bets for the typical sports bettor. Most people are sucked in by the large payouts for small investment, but if you miss 1 pick, you lose your bet.

But what if you're extremely concerned about bet limits, for example? Parlays aren't actually a bad idea, as suggested by Ed Miller, author of The Logic of Sports Betting, on Ed Feng's Football Analytics Show. But there are some major caveats that have to hold true:

1. Your win rate is profitable, obviously (> 52.38%)
2. You have extremely diligent bankroll management
3. You have very high volume - this won't work over a small number of bets
4. Your book is not adding juice on parlays - this is extremely important

Take, for example, a series of three -110 bets with a win rate of 55%. And say we try three strategies, with a base risk of $100 on each straight bet ($300 total), $100 on the parlay, or $50 on each round robin parlay ($150 total).

The math works out: you're expected to make varying degrees of gross profit, but a better ROI by using either non-straight bet strategy.

		Straight			Parlay			Round Robin
Result	Prob	Risk	Profit	ROI	Risk	Profit	ROI	Risk	Profit	ROI
WWW	16.64%	300	273	90.9%	100	600	600.0%	150	390	260.0%
WWL	13.61%	300	82	27.3%	100	-100	-100.0%	150	30	20.0%
WLL	11.14%	300	-109	-36.4%	100	-100	-100.0%	150	-150	-100.0%
WLW	13.61%	300	82	27.3%	100	-100	-100.0%	150	30	20.0%
LWL	11.14%	300	-109	-36.4%	100	-100	-100.0%	150	-150	-100.0%
LWW	13.61%	300	82	27.3%	100	-100	-100.0%	150	30	20.0%
LLW	11.14%	300	-109	-36.4%	100	-100	-100.0%	150	-150	-100.0%
LLL	9.11%	300	-300	-100.0%	100	-100	-100.0%	150	-150	-100.0%
	100.00%	E[X]	15	5.0%	E[X]	16	16.5%	E[X]	13	8.9%
		Min	-300		Min	-100		Min	-150
		Max	273		Max	600		Max	390
		Min W	82		Min W	600		Min W	30
		Min L	-109		Min L	-100		Min L	-150
		% Win	57.48%		% Win	16.64%		% Win	57.48%