You can see there's an inverse relationship between transaction size and the success rate. The bigger the payment, the more often it fails. The idea of breaking up a large payment into smaller payments sounds good, but for a group of multiple payments to atomically succeed, every payment in the group has to succeed. If we look at this from a probabilistic perspective, the odds of independent events occurring is calculated by multiplying the probabilities together. Think of rolling a die. You have a 1/6 chance to roll a 1, but you have a 1/216 chance to roll three 1's in a row. Generally, different payments would be independent events since the route going from Alice to Bob doesn't depend on the route going out from Alice to Carol. So, while the chances to route a smaller payment have gone up, the chances to route all of them might not be higher. They could actually be lower.

There's a lot of interesting things that can happen with this probability distribution; for example if you go slightly above expectancy (say an 11% win rate with 10% of the trials requiring success), you'll approach a limit of 100% (certainty) that the overall experiment succeeds as the trials become large...and you'll approach 0% if you use 9% win rate on the same experiment. It can get a little confusing to think about, but the basic principle is unchanged: You can increase the probability of success on a single event, but increasing the number of successes required has an opposing effect on the probability of the experiment as a whole. If you want a way to formally express this idea, we can look to the generalization of the binomial distribution in the normal, or (in the case when p is relatively small), the poisson.

There's a lot of interesting things that can happen with this probability distribution; for example if you go slightly above expectancy (say an 11% win rate with 10% of the trials requiring success), you'll approach a limit of 100% (certainty) that the overall experiment succeeds as the trials become large...and you'll approach 0% if you use 9% win rate on the same experiment. It can get a little confusing to think about, but the basic principle is unchanged: You can increase the probability of success on a single event, but increasing the number of successes required has an opposing effect on the probability of the experiment as a whole. If you want a way to formally express this idea, we can look to the generalization of the binomial distribution in the normal, or (in the case when p is relatively small), the poisson.