Will the OTG strategy give a positive reward if an opponent plays non-optimally?
I am 99.99999999% sure that the answer is yes. I don't have a mathematical proof, but here are two intuitive arguments:
Play many hands against the Cepheus bot. You will loose money in the long run no matter what strategy you choose.
For the following toy poker game below I will prove that the OTG strategy gives a positive reward against a non-optimal opponent. Based on this example you can then guess that the OTG strategy for the limit Hold'em also gives a positive reward against a non-optimal opponent:
Each of the two players independently uniformly at random get either a J or a Q.
They always pay 1 chip ante to play the game.
The first player can either bet 1 chip or call for an immediate showdown. If the
first player bets, the second player can either fold or call for a showdown.
Several hand play examples (p1 = player 1, p2 = player 2):
p1 hand | p2 hand | p1 action | p2 action | reward for p1
Q | J | raise | call | +2 chips (1 ante + 1 bet)
J | J | raise | fold | +1 chip
J | Q | raise | call | -2 chips
J | J | raise | call | 0 chips (pot split)
The strategy of player 1 can be summarized using these variables:
q - the probability to raise having a queen.
j - the probability to raise having a jack.
(just subtract these values from 1 to get probabilities of other actions).
The strategy of player 2 can be summarized using a single variable f denoting the probability to fold when he has a jack (if he has a queen there is never a reason to fold).
If you do the maths, you will arrive at the following expected reward equation for player 1:
(q - j)(1 - f)
What does this equation tell us about the OTG play? Note that if
j=0, the expected reward for the first player is always maximized. If you set
f=1 for the second player, his expected reward is always 0, thus he can never be exploited.
Thus the Nash-equilibrium strategy pair (i.e. the OTG strategy) for players 1 and 2 is
([q, j], [f]) = ([1, 0], 1), giving the expected reward of 0 for both players.
But what happens if a player 2 plays non-optimally and does not fold his
J all the time? Then the expected reward for player 1 is strictly positive and thus the OTG strategy of player 1 also exploits the weakness of player 2.