On Gambling X/Twitter, there is seemingly a majority of people who think early cash outs are the way. No matter how poorly priced, users will <insert argument here> as to why the bettor should absolutely take the early cash out. Today, I am going to break down the math that goes into these processes and explain why you should (almost) never early cash out a bet. Let's dig into the details...
How to Calculate If an Early Cash Out is Worth It
There are a few pieces of information that we need to know to be able to start the calculations.
1. The early cash out offer
2. The original total payout
3. The no-vig of the events that are remaining on one's parlay.
You'll notice that the one thing missing here is the previous games that have been graded. For all intents and purposes, those games have absolutely no effect on what is going to happen in the future.
With the early cash out offer and the original total payout, we can then find out what odds this early cash out converts to. Next, we find out what the no-vig odds are on the events remaining. There are a variety of ways to do this, but this is one of the purposes of GamedayMath's Nostradamus No-Vig. Now, with the no-vig odds, we can calculate the fair value payout. Concluding, we compare the fair value payout to the early cash out offer to see if it's a good deal.
I Don't Get It. Show Me an Example
We recently had a user reach out and ask us if they should cash out. The following is what they sent over...
Let's get right into the math. The remaining game is the under 45.5 in the Thanksgiving match up between the Washington Commanders and Dallas Cowboys. A quick check shows that the no-vig on u45.5 is +138 (the line moved up to 48.5).
Now, an early cash out of $72.14 compared to the original payout of $191.87 implies odds of +166. Put another way, would you bet $72.14 to win $191.87 on u45.5 in this event. With a no-vig of +138, the answer should be "OF COURSE!" as that bet would have an 11.7% expected ROI. This means that in this scenario an early cash out should not be taken.
Taking this one step further, we find the fair value payout of this bet is $81. This is calculated by converting the no-vig line into percentages and calculating expected value. Thus, with a fair value payout of $81 and an early cash out offer of $72.14, we have further proof that we need to ride this out.
How Does a Sports Book Create an Offer?
To understand why a cash out offer is (almost) never worth it, we need to figure out what a sports book does to calculate their offer. Luckily for us, this is actually very easy to figure out. Sports books are generally very good at knowing what the no-vig values are for every bet. They compute things the same way that we did above.
The sports book knows that the fair value payout is $81. They are also marketing geniuses and know that since the bettor hit his first four bets and he really wants to win something out of his five team parlay that he is likely to take a terrible offer to get out the bet. So what does the sports book do? It's simple. They take the fair value payout and multiply it by a number, which varies in range, from 75% to 95%.
In the example above, it appears DraftKings used a multiplier of ~90% to get from $81 to 72.14.
Finishing All of This Up...
Unless a sports book greatly miscalculates the no-vig (which the sometimes do, but rarely), then you should never take an early cash out. If you want bet on a parlay, then plan on being in it for the long haul. The early cash out is the most profitable tool that a sports book has at their disposal. Please do not aid them by utilizing it. If you are sweating a bet that much and feel the need to get out of it, then there are a bunch of ways to hedge against the bet that have better ROI than an early cash out!
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