As we all know, in the polarized river toy game, our EV increases the more we increase the bet-size.
I watched a RIO video by Steven Paul and he explained it like this:
This gave me the impression that our value bets gains its increased EV from when it gets called,
but when I broke it down further that doesn't seem to be the case.
Let's look at three different bet-sizes.
EV of Bluffs:
0.5x = 33.3% * 1 - 66.7% * 0.5 = 0
1x = 50% * 1 - 50% * 1 = 0
2x = 66.7% * 1 - 33.3% * 2 = 0
EV of value getting called:
0.5x = 66.7% * 1.5 = 1
1x = 50% * 2 = 1
2x = 33.3% * 3 = 1
EV of value getting folds:
0.5x = 33.3% * 1 = 0.33
1x = 50% * 1 = 0.5
2x = 66.7% * 1 = 0.667
So the EV of our value getting called remains the same, while the EV of our value getting folds increases.
I found this surprising for some reason...