the dog parlay project

**atakdog** · 09-20-07, 02:28 PM

Maybe I'm missing something, but I think you are missing something: many of the results you list are not possible.

There must be six qualifying games to come up with 15 two-team parlays. There are only seven possible results, corresponding to the number of those 6 teams that win:

Indiv . Parlays . . Payoff
0-6 . . . 0-15 . . . -1500
1-5 . . . 0-15 . . . -1500
2-4 . . . 1-14 . . . -1130
3-3 . . . 3-12 . .. . -390
4-2 . . . 6-9 . . . . +720
5-1 . . . 10-5 . . +2200
6-0 . . . 15-0 . . +4050

It'd be a simple matter to calculate the respective probabilities of these outcomes, given your estimate of your edge in each game. Note that I doubt it is OK simply to ignore the most favorable outcomes, as these will provide a lot of the expected value of the strategy.

Incidentally, in another thread I think Ganchrow has said that optimal bankroll strategy does involve playing the parlays in which you have an edge, but that your single-play bets will be larger than the parlays. Essentially, your strategy eliminates what theoretically should be the largest bets.

But then, I could easily be wrong...

**atakdog** · 09-20-07, 03:01 PM

OK, I tried a case or two (spreadsheeting it is best). Plugging in a pre-vig edge of 54.5%, which seems reasonable (incidentally, why'd you eliminate the home dogs?) gives and expected value of $148, versus $67 for wagering the same $1500 total on single games. Interesting; I'm surprised.

Indiv . Parlays . . Payoff . . Prob . . . . EV
0-6 . . . 0-15 . . . -1500 . . 0.9% . . . -$13.31
1-5 . . . 0-15 . . . -1500 . . 6.4% . . . -$95.65
2-4 . . . 1-14 . . . -1130 . .19.1% . . -$215.78
3-3 . . . 3-12 . .. . -390 . . 30.5% . . -$118.94
4-2 . . . 6-9 . . . . +720 . . 27.4% . . .$197.26
5-1 . . . 10-5 . . . +2200 . .13.1% . . .$288.78
6-0 . . . 15-0 . . . +4050 . . 2.6% . . .$106.13

Total EV = $148.49. EV of $1500 in straight bets = $66.75.

Minor changes to the edge per game had little effect on the result, in that the parlay strategy tends to be 2 to 4 times better, in terms of expected value, than straight betting for all reasonable edges (i.e, from 53% to 60% win rate).

I suspect this still isn't Kelly-optimal, because of the high variance.

I also have a sneaking suspicion I'm doing something wrong, maybe in calculating the frequencies -- I used P(event) = P(win)^wins * (1-P(win))*(losses) for each outcome, times number of combinations giving that outcome (1,6,15,20,15,6,1).

**pokernut9999** · 09-20-07, 03:17 PM

First there are 30 non home dogs this week. So if he is saying 15 parlays, he is just pairing them up on a random basis not a roundrobin.

**atakdog** · 09-20-07, 03:24 PM

Ah -- misinterpreted. Oddly, I think that doesn't change the calculations: if you think non-home dogs have an edge greater than the vig, the EV of playing (even random) parlays is better, though the variance is higher. In fact, I think the EV is the same as that shown above.

It does, however, add in all those cases I thought weren't possible; sorry 'bout that.

It also seems a bit unlikely that non-home dogs have an edge that great...

**Crayzee** · 09-20-07, 04:22 PM

exactly random pairing-by the official schedule

i eliminate the home dogs because i dont think there is any value there

**Crayzee** · 09-20-07, 04:25 PM

i have the pairings figured out ahead of time
the problem is if i wait til gameday i might want to layoff some of the teams
thus messing up the pairings

obvious big decreases in the line would make me want to layoff a team such as

syracuse going from +37 to +35

**curious** · 09-20-07, 06:33 PM

I made a ton using a similar strategy with baseball. Then gave about half of it back. then stopped using it while still up.

Now the strategy doesn't work at all with baseball, but my straight bets continue to be strong on baseball. Can't explain why.

I didn't use a random pairing though. I gave each game a weighting using my best estimation of expected value, then I sorted the games in descending order from the highest expected value to the lowest expected value, then I paired the games starting at the top of the list and going down. This way each game was paired with the next best expected value.

I found that to be far superior to both round robin pairings and random pairings.

**durito** · 09-20-07, 06:57 PM

Why not the home dogs?