This should result in different betting strategies.
Probabilities are not strategies. Strategy development may make use of probabilities, but only according to models that link various probabilities to outcomes, risk, and heaps of other factors. You can often formulate exactly the same strategies using different models employing different probabilities. Sometimes there is a single simplest model that employs an obvious probability space to yield a clear winning strategy, sometimes there is not.
Depending upon how the payoffs are structured in your bets and how results affect future states, I might or might not enter into any of those bets. You also use the term “thirder” and “halfer” as if this is a fixed personality trait, and not a choice of which probability space to employ in each particular scenario.
Probabilities are not strategies. Strategy development may make use of probabilities, but only according to models that link various probabilities to outcomes, risk, and heaps of other factors. You can often formulate exactly the same strategies using different models employing different probabilities. Sometimes there is a single simplest model that employs an obvious probability space to yield a clear winning strategy, sometimes there is not.
Depending upon how the payoffs are structured in your bets and how results affect future states, I might or might not enter into any of those bets. You also use the term “thirder” and “halfer” as if this is a fixed personality trait, and not a choice of which probability space to employ in each particular scenario.