Many on this forum have asked "should I hedge" when confronted with a potentially large payout with one or a few legs to go on a parlay (accumulator) ticket.

In this thread I will pose hypothetical hedging questions which I will answer in the context of expected growth. So, each question will rely on the player's bankroll, and some idea of the edge(s) the player may have for the wagers in question. Generally speaking, I believe expected growth is a fair way to compare different betting approaches.

Also, each question will be answered "in a vacuum", that is with no consideration to other open bets the player may have.

QUESTION 1: I played a 10 team parlay ticket with 6 games played Sunday morning, 2 games played Sunday afternoon, 1 game played Sunday night, and the final game played Monday. I wagered $4 on my $5,000 bankroll, with odds of 799 to 1 if all 10 selections win. I estimate my win rate per leg at 54%, due to the odds printed several days prior to purchasing the ticket. I expect to take the opposite side of any of the non-morning games at -105, with a 4% chance of winning both the opposite side and the parlay side. When should I hedge assuming (a) I win the first 6 games, (b) first 8 games, (c) first 9 games?

ANSWER: With no hedge wagers, your expected growth on this ticket is a paltry 0.024%. The optimal bet size is $4.30 resulting in a fractionally higher EG. The proper hedge wagers should be the following:
(a) $70 on either of the 2 Sunday afternoon games;
(b) $650 on the Sunday night game;
(c) $1,400 on the Monday night game.

Doing so will result in an expected growth of 0.037%, almost double what you get without hedging.

If you had known you should be hedging, then your parlay wager should be $12, and your hedge wagers should be the following:
(a) $375 on either of the 2 Sunday afternoon games;
(b) $2,100 on the Sunday night game;
(c) $4,500 on the Monday night game.

With the above bet sizing your expected growth increases to 0.066%.

In the ideal case you would hedge each leg after the first 6 wins, which you cannot do here because there are 2 games played simultaneously Sunday afternoon. This results in an expected growth of 0.095%, about 4x the original non-hedged wager.

Not starting with the most basic/common example (one leg to go on a future/parlay/teaser etc) is a mistake.

I chose the above parlay example because waiting until the final leg of a parlay to hedge is often a mistake.

That was an absurd example to use

I forgot to mention that the above parlay was setup with no ties. I'll try to be clear with that in the future, because the possibility of ties will impact hedging tactics.

Could we please start with something simpler?

Fk the haters. You just made my top 10 power ranking. Then again every other team massive disadvantage against clear #1 overall n00b.

Yes, your example was kinda dumb, but you actually posted real content. That already makes you a 1%er. And I don't think its regurgitated. (BTW Poogs that post recently was quite good and I was impressed. Your English skills have really made it. Congrats.)

If I was to transport myself back in time years ago, lets assume I somehow end up with a large edge + large size position. (IE the synthetic you end up with on a non-simultaneous event with a parlay or teaser.) Obv I wanna eat everything up at 0EV or better. And there are no reasonable solutions for derivs. But what would one do if they simply had +900 for a -300 fave for 18% of their BR. How would I go about solving that?

Not that its useful anymore really, but

For your simple situation (solving for one variable) I suggest MS solver or its open source equivalent as the easiest method.

You can find an exact solution by setting up an EG equation, taking its 1st derivative, then set to zero.

But with foreknowledge that you can later hedge into a position, you are probably better off wagering more than Kelly tells you, which was my point above. The calcs for that require numerical methods which I'm guessing go beyond what most here want or care to understand.

A good example would be properly sizing a futures WS bet, understanding that there will likely be decent (i.e. +EV or short price) hedge opportunities in individual series games going forward.

if you're gonna hedge then don't make the late bets

Hey look, more terrible advice from someone who doesnt know a thing about the subject

What a bull**** is this? If you want hedge after the first 6 wins why You dont bet only six games? You will always losing on parlays hedging.

Maybe because the odds on 6 games is -EV.

I don't think you understand the primary reason for hedging.

whether to hedge or not depends on several factors.

Your edge with the open bet
Your edge after the hedge
Your aversion to risk.

A scenario I get myself in quite often would be as follows

bankroll $10k
open bet; Team A win $500 at even money
hedge is an arb; Team B win at $2.20

(assume 1.90/1.90 is even money, and assume the current bookies line is perfect, so Team A will win 56.8%)

So if we take could the unhedged bet 100 times we would win 57 and lose 43 , assume we always bet 5% of roll.

Our bankroll would become

ROLL_no hedge = 10,000*(0.95)^43*(1.05)^57 = $17,779

hedging the position to build an arb guarantees 0.4545% bankroll growth each bet

ROLL_hedge = 10,000*(1+0.0045)^100 = $15,737 (with no chance of ever losing)

if you only risk 2% of your roll each trade, the end result becomes;

ROLL_no hedge = 10,000*(0.975)^43*(1.025)^57 = $13,754
ROLL_hedge = 10,000*(1+0.0027)^100 = $12,457


now if you assume the new price for team B is a little too high and team A is only expected to win 54%, at 5% roll we get.

ROLL_no hedge = 10,000*(0.95)^46*(1.05)^54 = $13,167
ROLL_hedge = 10,000*(1+0.0045)^100 = $15,737

so........ not too suprisingly
Hedge if you have too much skin in the game
Hedge if you think the hedge you can take is value

Your numbers are not correct. The formulas you used are confusing, and are most likely wrong. I'm not going to bother showing you the proper formulas, as it would likely lead to more confusion.

Assuming 56.8% win rate your non-hedged EG is 0.557%. You should have bet $1,360, not $500. Your EG would then be 0.932%. With the $500 bet your hedge bet should be $39, with EG increasing slightly to 0.558%. With the $1,360 bet your hedge should be $818, resulting in EG of 1.340%.

Assuming 54% win rate your non-hedged EG is 0.276%. Your hedge should be $555, with EG increasing to 0.461%.

You missed my point stated above which is how much should you bet on team A assuming you will be able to hedge.

$500 is the right amount, because I said it was, I never mentioned maximising growth.

My formulas are correct, median return for proportional betting.

you point regarding betting on team A is irrelevant, my hedge is an arb, so clearly roughly 50% of your roll would go on it.

And you sound like a dick, take care

Since you appear uninterested in maximizing growth that rules me out for providing any worthwhile info to you.