alb said:
AA Win $400.91 AA Win $105 + Win $105 = $210
AB Lose AB Win $105 + Lose = $105
BA Lose BA Lose + Win $105 = $105
BB Lose BB Lose + Lose = Lose
Total: spent $440 Total: spent $440
returned $400.91 returned $420
Result: Staight bets are always a better deal.
This table you made is right, but it ignores the chances of you hitting a game.
IF you have a 50/50 chance on any game, then any row in your table is as equally likely to occur as any other, and then you are right to say that straight bets are better. Imagine if you had 2 LOCKS, and I mean that literally, they were 100% to come in. Then you would obviously want to parlay them. The closer you are to 100% the more profitable the parlay becomes for you.
If you can pick games correctly 54% percent of the time, then ROW 1 in your table will come up about 30% of the time, rows 2&3 about 25% of the time each (50% total), and row 4 will come up about 20% of the time. In that case, parlays are better because row 1 is the row where the big payout comes from the parlay.
To acehistr8, the easiest way to think about parlays (and most sports betting) is just like playing drawing hands in poker. So, if you want to parlay a dog getting +130 with a dog getting +160, you're getting paid about 5-1 on that (2.3*2.6 = 5.98 = your return on a 1 dollar bet). So, basically, you play that parlay if you think it is better than 5:1 against (a 1/6 shot, about 12%). If you think each team has a 50/50 shot at winning, then the chance of hitting them both is .25, and a fair price would be 3:1 (.75:.25).
Of course, any bet you make can be thought of like this. A lot of times if I play a ML dog, it will be a game where I think the outcome is truly 50/50 but the dog is getting +140 or something. Better than even money on an, in theory, even money propostition. Or as an example, last weekend, I was getting 3-1 on the Rams straight up. I might not have thought that they were even 1:1 to win that game, but I thought they were much better than 3-1 to win it, maybe 2.5-1. I was getting good odds on my "call".
Notice that betting the point spreads can be thought of like this. They, supposedly, make a bet a 1:1 propositiion, but you only get paid 10:11 on it. You're not getting proper odds on your "call", unless you are >52.4% sure that you hit that game. 52.4 being the magic, break-even, pecentage. Not-coincidentally, 52.4% is the break-even point of playing parlays too. Anything above that, it is more profitable to parlay. Anything below that, it is less profitable to parlay. This jives with what I said about ALB's table.
A 4-team parlay is no different. It might be like drawing to your one-outer (45-1 against) when the pot is $500 and the bet is $10. You're not going to hit many of them, and you could go a LONG time without hitting one but if you actually have an edge when playing them, in the long run they can be profitable.
Anyway, to sum up a bit:
Parlays are not necessarily profitable or unprofitable. Basically, if you KNOW you have an edge, they are more profitable, but more variable (higher risk, higher return). If you hit games at 50% or less, then they are less profitable, as ALB wrote up. Considering that most people betting are probably 50/50 or worse, it's no wonder a lot of people think they're bad bets.
A lot of what I wrote assumes you could possibly know something like "I have a 54% chance of hitting this game". That's difficult to know. The thing is with parlays, you might have a 54% chance of hitting a game, but by the time you get to the 4th team in your parlay, you're probably looking at a 50% chance, pushing the parlay into negative expectation.