Well we already have an opportunity to arb out of our bet on Rampage/Rashad. We put our bet on Jackson at -122, and as of right now Rashad is +137. I am going to hold off though until much closer to fight time to see what the final odds will be, as it may get even better. I will ponder this fight a little more and decide if I want to take the arb opportunity, but I am just letting you know it is there if you want it.
At the current odds, a bet of 1.536 units on Rashad will give the maximum arbitrage opportunity and deliver .104 units regardless of the outcome of the fight. So if your unit size is 100 bucks, you will win $10.40 no matter who wins.
One thing I have been thinking about with regards to arb bet is the fact that most of the time it is done to give an equal result regardless of outcome. In the above calculations for example, the bets are placed so that the amount won is the same no matter who wins the fight. This is pretty much the standard way to use an arbitrage opportunity.
This is curious though, because we have already determined through our own handicapping that the there is not an equal likelihood of each fighter winning. Meaning, we view Rampage as more likely to win, hence the original bet.
For this reason, it seems more reasonable and profitable for the advantage player to use the arb opportunity simply to eliminate risk, as opposed to guarantee a equal return regardless of outcome.
If you are really an advantage player this should theoretically be more profitable in the long run (if you are not an advantage player you will lose money over the long term regardless).
To further explain, take the above example again. If we are a good handicapper, and view Rampage as more likely to win, why would we set up our arb opportunity to favor each outcome equally? it makes much more sense to structure the bet sizes so that if Rashad wins you just push. You don't win anything, but you don't lose anything either. That maximizes the profit for the outcome that we have already decided is more likely, but it eliminates any risk.
So for this fight you would bet 1.46 units on Rashad at the current odds. This would give you .18 units ($18 assuming a $100 unit) if Rampage wins, and you would push if Rashad wins. May not seem like much better at first, but it is giving you about 80% more profit if Rampage wins (which we had already decided is more likely anyway)
Obviously you can structure the arb bet to distribute the guaranteed profits however you wish between the two outcomes, based on how likely you view each.
Something to think about.
-The Wise Guy
That's interesting. I agree. If you have an advantage it makes more sense to just eliminate the risk and put all the opportunity with your favorite.
ReplyDeleteBasically, this is an optimization problem that can be solved in the same manner as the standard Kelly wager. In these situations, you are finding the mathematical solution to optimize expected (long term) growth.
ReplyDeleteFor a case where you bet on both sides of a line for arbitrage, your expected growth is:
EG = (1 + (D1 - 1)*X1 - X2)^P * (1 - X1 + (D2 -1) *X2)^(1-P) - 1
Where P = probability of fighter 1 winning, D1 = (original) decimal odds on fighter 1, X1 = fraction of bankroll bet on fighter 1, D2 = (new) decimal odds on fighter 2, and X2 = fraction of bankroll that you bet on fighter 2, at the updated odds. Draws are ignored here.
This function should have its maximum at:
X2 = (1-P) * (1 + D1*X1 - X1) - P * (1-X1) / (D2-1)
Awesome work svino, I like the formula.
ReplyDeleteto translate for the non math-inclined,
It would allow you to adjust your arb bet based on how likely it is that you think your fighter will win. So you determine the percentage chance that your fighter will win (your personal handicap) and then plug in the rest of the variables which would all be givens based on your bet.
If your personal handicapping odds are good you will win the more money this way over the long term, as opposed to a normal arb bet.