It's complicated and there are some leaps of faith and assumptions ...
We've had threads on this before but my search abilities aren't really up to finding the better threads right now.
My post #12 in this thread more or less sums up my thoughts on the matter:
Starting to question military pay < civilian pay
Short version (and it's not really that short) - if you're ONLY considering the financial break even, here's how I think you should do the math:
1) Put a dollar value on the pension, if you were to stay for 20. Several ways you can do this: you could get a quote for a single premium immediate annuity for a person your age @ military retirement, with COLA adjustments, that would pay the same as the pension; you could look at your life expectancy on the Social Security actuary table and calculate the $ value of TIPS you'd need to buy as a lump sum to duplicate the pension until you die; you could divide the annual payout of the pension by the withdrawal rate of your choice to estimate the portfolio you'd need to duplicate the pension (here you can be fairly aggressive with the % since a fair comparison isn't the usual 3-4% SWR that leaves principal behind when you die). This is extremely fuzzy and uncertain math.
2) Divide that dollar value by the # of years between your ADSO is up, and your eligibility for retirement. This figure is essentially what the military is paying you in addition to your usual pay (including the expected post-ADSO retention bonus contracts), as if it's going into a pre-tax 401(k) style account.
3) Compare the income you'd expect to earn in private practice if you got out at ADSO completion, to the military income + the virtual "401(k)" pension value. If the PP value is still higher, you might come out ahead in PP.
Caveats
1) It's unlikely the PP job will include any kind of pre-tax investment vehicle comparable to the pension value.
2) Earlier entry into PP has the potential for other benefits, like establishing a referral base sooner, opening up side businesses related to your practice (we have an ex-military ENT here who makes significant money from hearing aids his practice sells)
3) PP income may escalate substantially after a few years, depending on things like partnership, profits from ancillary ventures, a growing/improving referral base, etc
4) There's a risk of becoming "institutionalized" by the slow pace and low case volume of the military if you stay too long and don't or can't aggressively moonlight - we don't really like to talk about it, but there are some military physicians who retire and really aren't fit to work in a lean private practice. If you stay for the full duration you may not want or be able to do the kind of work and hours to really earn top PP income at that point.
Regardless - in the end you're going to be Just Fine whatever you do. I think it's important to do the financial math carefully and honestly, but there's more to life than money.
If you're not working a job you hate and you spend less than you earn, you'll be happy.