You’re three weeks into a pilot with a mid-market logistics company. Your AI agent is meant to cut their invoice reconciliation time by 70%. In the demo, it looked flawless. In week one of the pilot, it hit 70% on the easy invoices and choked on anything with a currency conversion. Now your Head of Sales is on the phone, and the customer wants to talk about pricing.
You have two numbers in your head. The first is what the outcome is worth to them if your product actually delivers: a genuinely large number, because reconciliation is a nightmare for them today. The second is a nagging uncertainty about how often, in production, at their scale, with their edge cases, you’ll actually hit that 70%. There is that risk of choking. Somewhere between those two numbers is a price. Quote too aggressively on the outcome and a bad quarter of edge cases wipes out the deal, and possibly your relationship with the customer. Quote too conservatively and you leave money on the table that a more confident competitor will happily take.
This is a bet-sizing problem, and it turns out someone solved the general version of it in 1956.
“The Maths Behind the Business” is a series where I look at how mathematical and behavioural theorems can help explain and address the strategic and operational challenges facing B2B software companies. We’ve talked about pricing before in this series: a few editions back, we looked at pricing negotiations as positive-sum games rather than zero-sum fights over a fixed pie. This edition is about a narrower and, for AI companies specifically, more urgent question: when you genuinely don’t know your own win rate yet, how much should you stake on the outcome you’re promising?
Let’s start with the basics: What is the Kelly Criterion?
In 1956, a Bell Labs scientist called John Kelly was working on a problem that had nothing to do with betting: how to think about signal and noise in long-distance telephone lines. But the maths he developed turned out to answer a much more popular question: if you have a genuine edge in a repeated bet, what fraction of your bankroll should you actually risk each time?
The intuitive but wrong answers are the two extremes. Bet nothing, and your edge is worthless. Bet everything every time, and you will eventually go bust, no matter how good your edge is, because one bad outcome and you’re finished, with nothing left to bet with the next time. The Kelly Criterion finds the fraction in between that maximises the long-run growth rate of your bankroll.
The formula is:
f* = (bp − q) / b
Where:
- f* is the fraction of your bankroll to stake
- p is your true probability of winning
- q is the probability of losing (1 − p)
- b is the net odds — how much you win per unit staked, relative to what you lose
Let’s go through a worked example. Say you have a genuine edge on a bet: you reckon you’ll win 60% of the time (p = 0.6, so q = 0.4), and the payout is even money, meaning you win £1 for every £1 you risk (b = 1). Plug it in:
f* = (1 × 0.6 − 0.4) / 1 = 0.2
Kelly says stake 20% of your bankroll. Not the instinctive 60%, because your edge is real but not certain. And not something as low as 5%, because that would be unnecessarily leaving growth on the table. The size of the bet should track the size of your edge, precisely, not your gut feel about how good the edge “sounds” (🤓 the formula is doing exactly what your instincts are bad at: translating a probability into a number).
Two things are worth highlighting:
First, the formula punishes overconfidence brutally. If your true p is 0.5 but you believe it’s 0.6, Kelly tells you to bet a fraction of your bankroll on a bet with no edge at all, and you will slowly bleed out.
Second, most serious practitioners don’t bet full Kelly anyway; they bet “half-Kelly” or “quarter-Kelly”, deliberately under-staking relative to the formula’s answer, because their estimate of p is itself uncertain, and the formula is unforgiving of a bad estimate.
But what does a 1956 telephone-line formula have to do with pricing your AI product today?
Every AI company selling outcome-based or consumption pricing is, functionally, sizing a bet. The “bankroll” is your company’s capital and reputation. The “stake” is how much of the deal’s value you commit to delivering, or how much revenue you tie to an outcome you don’t yet perfectly control. The “edge” is your genuine, current, honestly-assessed probability of delivering that outcome in production for this customer.
Founders routinely get this backwards. They price as if p were 1 (the demo worked, therefore it always works) or they price so conservatively that they leave significant money on the table. And Kelly’s real contribution here is the discipline of separating “how good is my edge” from “how big should my bet be”, and insisting the second follows mathematically from the first.
That distinction between edge and bet size isn’t academic. It shows up directly in how today’s AI companies price, and in what happens when they get the calibration wrong.
Let’s take customer support as an example. It is where AI has delivered some of its clearest early value, and it’s instructive to see how differently three companies serving that market have chosen to set their pricing strategies.
Outcome-based pricing with no floor: Sierra, the enterprise customer service agent company, sells almost entirely on outcome-based pricing. Customers pay when the agent resolves something, not for seats or licences, and reportedly around $1.50 per resolution. It’s a strong go-to-market wedge precisely because it looks like Sierra is betting on itself: the vendor only gets paid if the outcome lands. But the pricing only works, and only stays defensible at scale, if Sierra’s internal estimate of its own resolution rate, per vertical, per customer complexity band, is genuinely well-calibrated. A generic, blended p across all customer types could be the overconfident-Kelly-bettor mistake, because if your real p varies wildly by segment and you price off the average, you’re overstaking on your worst segments and understaking on your best ones.
Outcome-based pricing with a floor: Intercom’s Fin runs the same play as Sierra: it charges per resolution too, at $0.99, so the fee is still tied to the outcome landing. But Intercom layers that outcome fee on top of separate per-seat helpdesk pricing starting around $29 a user a month, so the customer pays a base subscription regardless of what the AI resolves. In Kelly terms, Fin stakes a smaller fraction of its revenue on p than Sierra does: the seat fee is a guaranteed floor Sierra doesn’t have, and a rational hedge if your estimate of p is less certain, or your buyer is more price-sensitive.
Outsourcing the bet-sizing decision. Decagon offers two pricing structures. Per-resolution pricing charges a higher unit rate, but only for tickets the AI closes without human help, so, in other words, a Kelly bet structurally identical to Sierra’s and Fin’s. And per-conversation pricing charges the same flat rate whether the AI resolves the ticket or not, with contracts typically opening on a platform fee alone around $50,000 a year before a single conversation is billed. Apparently, most Decagon customers choose per-conversation. Given the option to stake the vendor’s fee on p, most buyers choose the flat rate instead, likely less a verdict on Decagon’s resolution rate than a preference for a bill that doesn’t hinge on a contested definition of “resolved.”
Why enterprise buyers demand pilots, and what that’s really about. This is the flip side of the same maths, from the buyer’s chair. A CFO evaluating an outcome-based AI vendor is implicitly asking “what’s your real p, and how do I know you know it?” A vendor with no published rate card and a custom enterprise sales process is asking the buyer to trust an internal p they can’t inspect. That’s precisely why pilots exist: they’re the buyer’s way of generating their own independent estimate of p before they’re willing to accept your bet size. A vendor that resists pilots, or refuses to segment pricing by observed complexity, is behaving like the overconfident gambler in the example above, and sophisticated buyers, like sophisticated pit bosses, don’t seem to appreciate it.
| Confidence in your p (by segment) | What Kelly logic implies for pricing structure |
| High — large sample, stable resolution rate | Outcome-based pricing, priced close to true value created |
| Medium — early data, some variance by use case | Metered/consumption pricing with volume tiers, revisited quarterly |
| Low — new vertical, new customer complexity | Capped pilot pricing or seat-based fallback until p is observed |
The uncomfortable implication for a lot of AI pricing decks is that “outcome-based pricing” is a bet size that should shrink and grow, segment by segment, exactly as your evidence for p does, rather than a maturity milestone you graduate to once. Pricing the same way across every vertical because outcome-based pricing “is where the market is going” is Kelly-betting a flat 20% on every hand regardless of whether you’re actually holding an edge.
If there’s one number worth writing on a whiteboard before your next pricing conversation, make it your honestly estimated p, not your target ACV, broken down by the segment you’re about to price for, and whether the deal you’re about to sign is staking more of your company on that number than your actual confidence in it can justify.
Sources for the prices:
