You have one sportsbook that lets you make 3-team 6-point teasers at +180. They have spread blow (1). Assume you can also bet any moneyline at Pinnacle (2) or from (1). Finally, assume you can also get +3000 on "Will this team win by exactly 1", and can also bet "Will this team win by exactly 2" at +3000 at matchbook.
You have exactly $1000 you can risk, however you want among these books. What is the most you can GUARANTEE via arbitrage, if none of these odds change?
(1) from Bookmaker
301 PITTSBURGH -7½-110 o44-110 -360
302 ST. LOUIS +7½-110 u44-110 +300
NFL First Half Lines - Dec 20
5:15 PM12 /20 /07
337 NY JETS +8½-110 o37½-110 +330
338 TENNESSEE -8½-110 u37½-110 -400
1:05 PM12 /23 /07
339 TAMPA BAY -7-110 o36½-110 -300
340 SAN FRANCISCO +7-110 u36½-110 +250
NFL - Dec 24
NFL
MONDAY, DECEMBER 24TH
5:00 PM12 /24 /07
# Spread Total Money Line
343 DENVER +8-110 o47½-110 +315
344 SAN DIEGO -8-110 u47½-110 -375
(2) from Pinnacle
Sun 12/23 337 New York Jets +9 -112 +335 OVER 37 -106
01:15 PM 338 Tennessee Titans -9 +104 -365 UNDER 37 -104
Sun 12/23 339 Tampa Bay Buccaneers -7 +102 -300 OVER 36.5 -109
01:05 PM 340 San Francisco 49ers +7 -110 +270 UNDER 36.5 -101
So after conferring with Professor RickySteve we came up with the following:
If the only goal were zero variance then (assuming no tie games) by taking each of the following teasers and hedging as appropriate you'd net the following guaranteed returns (as a percentage of the teaser wager):
PIT-TB-SD => 3.55%
PIT-TEN-SD => 1.48%
If the NYJ vs. TEN and TB vs. SF were not contemporaneous then you'd also be able to choose from:
PIT-TEN-TB => 1.93%
TEN-TB-SD => -1.48%
But that's not the case and so that's irrelevant to this question.
So the highest possible risk-free return would be 3.55% of the notional teaser value. This would be achieved by taking the PIT-TB-SD teaser and hedging as appropriate.
If limited to a $1,000 bankroll then the highest possible zero-variance return using the PIT-TB-SD teaser would be $12.83 (a $361.73 bet on the teaser).
In keeping with Justin's wishes I won't divulge the hedging strategy that produces these results unless he gives the go-ahead. Feel free to PM if you need the answer now.
Of course the more interesting (and labor-intensive) problem would involve determining the Kelly-optimal allocation given these available bets and some assumed W/L/P probabilities.
Since no one's answered and Justin's 24-hour period's expired:
PIT/TB/SD Teaser
Initial Bets:
<style> .GANCH { font-size: 12px; font-family: Verdana, Arial, Helvetica, sans-serif; }</style> <table border=0 cellpadding=1 cellspacing=2> <tr> <td align=left class=GANCH> TEASER +180 </td> <td align=right class=GANCH> $361.73
</td> </tr> <tr> <td align=left class=GANCH> STL +300 </td> <td align=right class=GANCH> $130.47
</td> </tr> <tr> <td align=left class=GANCH> PIT BY 1 +3000 </td> <td align=right class=GANCH> $16.83
</td> </tr> </table> Only If PIT by > 1:
<table border=0 cellpadding=1 cellspacing=2> <tr> <td align=left class=GANCH> SF +270 </td> <td align=right class=GANCH> $196.08
</td> </tr> <tr> <td align=left class=GANCH> TB BY 1 +3000 </td> <td align=right class=GANCH> $7.56
</td> </tr> </table> Only If PIT by > 1 AND If TB by > 1:
<table border=0 cellpadding=1 cellspacing=2> <tr> <td align=left class=GANCH> DEN +315 </td> <td align=right class=GANCH> $244.06
</td> </tr> <tr> <td align=left class=GANCH> SD BY 1 +3000 </td> <td align=right class=GANCH> $32.67
</td> </tr> <tr> <td align=left class=GANCH> SD BY 2 +2940 </td> <td align=right class=GANCH> $10.60
</td> </tr> </table> Only If PIT by > 1 AND If TB by exactly 1:
<table border=0 cellpadding=1 cellspacing=2> <tr> <td align=left class=GANCH> DEN +315 </td> <td align=right class=GANCH> $166.40
</td> </tr> <tr> <td align=left class=GANCH> SD BY 1 +3000 </td> <td align=right class=GANCH> $22.28
</td> </tr> <tr> <td align=left class=GANCH> SD BY 2 +2940 </td> <td align=right class=GANCH> $10.82
</td> </tr> </table>
In this manner the player will risk at most $1,000 (only if both PIT and TB cover the teased spreads) and will, regardless of outcome (save a tied game), have guaranteed himself a $12.83 profit (that's 3.55% of the $361.73 notional value of the teaser).
<hr>
(The PIT/TEN/SD teaser is inferior to PIT/TB/SD teaser as far maximum zero-variance profitability goes, but for the sake of completeness, however, the solution follows.)
In this manner the player will risk at most $1,000 (only if both PIT and TENN cover the teased spreads) and will, regardless of outcome (save a tied game), have guaranteed himself a $5.33 profit (that's 1.48% of the $359.04 notional value of the teaser).
Arbitrage challenge
Linear Mode
