Hello,

I'm new to these forums and I'm wondering if anyone could help me find the optimal bet sizes for these NFL futures bet for superbowl 52. If I were to use the generalized Kelly in this regard, how would I do it? Here are the odds and the teams which I'm interested on betting on:

New England 3-1
Dallas 8-1
Green Bay 10-1
Pittsburgh 12-1
Oakland 12-1
Seattle 12-1

If my bankroll is $1,000 what would be the optimal bet sizes on these teams if I wish to use the generalized kelly instead of regular kelly?

I imagine you realize that you need to "evaluate" each team's betting odds versus how likely you think that team is to win next year's superbowl. Of course, you only bet on a team in which you think you have an edge (i.e., your assessment of the team's probability of winning exceeds that team's winning probability implied by the odds-makers' odds).

So, at a minimum, you have to come up with your assessment of the probability of each of the teams you listed winning next year's superbowl.

Only then can you make use of the Generalized Kelly machinery.

For the above odds, I have used the implied probabilities based on the american odds:

New England 3-1 33.3%
Dallas 8-1 12.5%
Green Bay 10-1 10%
Pittsburgh 12-1 8.3%
Oakland 12-1 8.3%
Seattle 12-1 8.3%

If I added all the probabilities together, this would give me an 80.7% chance or that (1-80.7)=19.3% that the other teams will not make it to the Super Bowl. Here, we are are looking for 1 winner out of all the possibilities. An 80.7% converted to decimal odds would be about -418 and a 19.3% probability impliesodds of +418. Do I need to maximize the logarithm of my bankroll to find the optimal bet size x of each f(x) above?

The most important step in maximizing the logarithm of your bankroll is making sure the logarithm stays defined.

You're not calculating the implied probabilities correctly (What do you get for a bet that pays 1:1? What should it be?). You haven't given what YOU think the odds are of any of these teams winning, and you've kind of missed that point twice, which is important since it's the reason you'd want to bet to begin with. I'd highly recommend not gambling on this, or on pretty much anything else, for years if not forever.

The way how I figured the probabilities was that I looked online for an odds converter for decimal odds and implied probabilities. I wish to use kelly to optimize my bets to each of the 5 teams which I have listed. Since Kelly is equal to betting a fraction of one's bankroll to an event, we know the this is equal to bp-q/odds -1. However, this formula is used for an event with 2 outcomes. How do we define an outcome like futures betting, where 1 team of 32 will will the trophy?

Just to make sure everybody is talking the same language, using the example that the odds-makers have made the New England Patriots 3-1 to win the superbowl next year (assuming just for the moment that this yes/no bet is the only one you are considering), what are the "b", "p", and "q" in the above single Kelly formula?

I don't know what b is there, but it and the -1 are unnecessary. The formula is simply p-(q/odds).

You've again missed the point being made by whosnext and TomCowley. The only time to wager is if you yourself have calculated/estimated the chances to be better than the implied probabilities. But also, you haven't factored in vig. If the Pats are +200 then the oddsmakers aren't implying they're 33% to win, because 33% would mean they're not making any money by taking your bet. They're implying something less than 33%. For you to profitably bet, you need the chance to be >33% (which you'd have to determine on your own, obviously).

Taking the example of just betting the Pats, if the chance is exactly 1/3 then it's a break-even bet, and the kelly fraction is (1/3) - (2/3)/2 = 0, meaning the optimum wager is no wager.

If the chance is <1/3 then the optimum wager is negative. Since that's unfortunately not possible (unless you can be the bookie), that also means zero (no wager).

The same will be true for your portfolio of teams. Since Kelly tells you each individual team is a non-wager, it will also tell you that the entire portfolio is a non-wager.

Kelly isn't magic, it won't turn losing or break-even bets into profitable ones. You don't seem to have found profitable bets to begin with.

If you do come up with your own probabilities, post them and then I might be able to help with the Kelly allocation (though I've never had to try it for a correlated portfolio like this one). Of course, since I presume your probabilities will be based entirely on hunches, I wouldn't bet full kelly if I were you. Quarter kelly at most.

As a tip, maybe estimate probabilities for all 32 teams so that you can tweak your percentages until they add up to 100%. Then the percentages for your 6 teams might be more accurate, because you'll have eliminated contradictions in your thought process.

b is the payoff in b:1 format

Then his formula is plain wrong, or he wrote it wrong.

And is b different than "odds"? A variable shouldn't go by two different names in one equation.

By nature I am typically willing to give members, especially new members, the benefit of the doubt when it comes to asking questions that don't appear on their face to make much sense. (The Probability Forum attracts very few trolls after all.)

Until proven otherwise, I hope that they actually have an understanding of the situation that, for whatever reason, may not have been fully reflected in their OP. Perhaps they are not facile with probability or betting concepts, perhaps english is not their first language, perhaps they are not adept with algebraic formulations, perhaps they rushed when posting, etc.

Here OP appears to not fully understand (i) the fundamentals of betting and/or (ii) the fundamentals of the kelly criterion. On the other hand, OP came to this forum to ask a specific betting question and referenced regular and generalized kelly. So there is clearly a disconnect somewhere.

At the risk of continuing a conversation with myself, the formula for the fraction of bankroll to wager on a single binary bet according to the kelly criterion can be expressed in several equivalent ways:

f = (bp-q)/b

f = p-(q/b)

f = [p(b+1)-1]/b

f = p-[(1-p)/b]

etc.

As of now, I am not 100% sure that OP understands what each of the terms "b", "p", and "q" in the above formulas represents (and the expression s/he posted didn't really make sense).

More importantly, OP has not definitively demonstrated that s/he understands the fundamentals behind betting. For example, if I offered 2-1 odds that Steph Curry will make his first 3-point attempt in a Warriors game, how would you decide whether to accept or decline my offer?

In summary, I'd rather we confirm that OP is sufficiently knowledgeable about such things before we do a deep dive into the generalized kelly framework.

Sorry for all the misunderstanding. I would like to reference an article made by PlusEVAnalytics.

https://www.pinnacle.com/en/betting-...iterion#height

At the end of the atricle, it says that we can use the generalized form of the Kelly Criterion to "find the optimal bet sizes for a set of futures bets on several different teams to win the same division or championship" which is mentioned at the end of the article.

How would I go about optimizing my bets on the teams mentioned earlier using the generalized Kelly as stated in that article?

Do you see how that article has both the odds of winning (which is up to you to determine) and also the payout? That's how you determine your edge and is the key to figuring out how much to bet.

Your OP I assume contains payouts for each team, but not your estimation of them winning. If you chose one team and wanted to place a bet on them, you wouldn't have enough information to use the single/basic kelly criterion. Do you see what I mean?

I just did the Calcs for you seer8, a bit of hard work, but im happy to do it for you.

Unfortunately, kelly says you should bet $0 on each of those bets.

Lucky for you, you can keep your money.

Kelly say bet $0!!!!!!

Keep your $$ and buy some sports betting books!!

Okay, to make it perfectly clear, besides the odds offered by the odds-makers, your bet sizes surely must depend upon how likely you think each team is to win next year's superbowl.

Obviously, if you are near positive a specific team is a mortal lock to win the superbowl, you would want to bet a lot on that outcome. And, conversely, the less likely you think a team is to win the less you would wager on that team. Right? (Hopefully, this is obvious.)

Here is a simple hypothetical table showing the minimum relevant information you would need to assemble for betting in this situation. For each team listed in OP, I show the odds-makers' payout odds listed above and my own hypothetical subjective probabilities I think each team has to win next year's superbowl.

Team	Odds-Makers' Payouts	My Hypothetical Probs Team will Win Super Bowl
New England	3 - 1	40%
Dallas	8 - 1	20%
Green Bay	10 - 1	25%
Pittsburgh	12 - 1	10%
Oakland	12 - 1	3%
Seattle	12 - 1	2%

Of course, you should fill in your own personal subjective probabilities that each of the above teams will win next year's super bowl in your own table.

From that information and the kelly criterion formula for the single binary bet case (several equivalent versions of which were given above in post #10), you can work out what fraction of your bankroll single kelly recommends you should bet on each team, under the assumption that each team's bet is taken in isolation.

Once you work those out, then you can apply the more complex generalized kelly framework which reflects the fact that these events are mutually exclusive (at most one of these teams can win the superbowl). Of course, the generalized framework is based upon the same information contained in the above table: odds-makers' payouts and personal subjective probabilities of winning each bet.

People here would probably be happy to help you work through the generalized kelly case.

Hope that helps.

Thanks whosnext. I have found out the optimal bets for the futures bet for next year's Superbowl.