Quote:
Originally Posted by irenicus24
Hello Mathew; Question
In a mixed strategy, I understand that the two actions have the same ev, but, What do means they have different frequencies? It is the action with the highest frequency that we would take by default if the opponent were unable to exploit us and the action with less frequency only a defensive line in case the opponent is enough good to exploit us?
In the example you give in Chapter 2, ask 1: 10s 8s in 9h7c4d, assuming the optimal strategy was a mixed strategy of bet 97% of the time and 3% check of the time; The ev of both lines would only be the same if the frequencies are respected, so it is true that you say that no line is superior to the other, but only if the frequencies are respected.
Therefore we will make a minor mistake if we bet 100% which is almost the same as betting 97% than if we check 40% instead of 3%. So in practice, by our inability to balance exactly could appear that one line is superior to another, or it is less likely to make a mistake when its frequency is higher in a mixed strategy. Do you think this is correct?
I think if there was a mixed strat between betting 97% and checking 3%, then I'd just always bet against an unknown (unless I knew the general tendencies of my opponents, and the 3% line was exploitatively better).
A mixed strat doesn't really mean one line is defensive, it just means there are two (theoretically) equally good lines. That's it. And just because two lines are equally good, doesn't mean you need to take them both at the same frequency.
For example, perhaps chocolate ice cream and strawberry ice cream are equally good. I still may prefer a 70% strawberry/30% chocolate mix, because I want to feel like I'm eating chocolate covered strawberries, not strawberry covered chocolate (gross). But that doesn't mean one ice cream is better, it just means we eat one a little more often than the other to get the ratio right.