6.6 Calling With Showdown Odds

Calling with pot odds is based on the immediate situation (the cost to see one more card) and is based purely on potential for improvement (for the flop and turn). It does not cover situations where Loki has both a moderate PPOT and a mediocre HS_n but neither is good enough to justify a call. For this reason, we introduce calling when $EHS >= Showdown\_Odds$ (since this is not a decision to bet, we must include NPOT, so EHS' is not used). Showdown odds is a defensive measure that ensures the opponent cannot win simply by betting at every opportunity. By calling whenever our hand is strong enough to show a profit in the long run, Loki discourages frequent bluffing by the opponent.

On the turn,

$$Showdown\_Odds(turn) = \frac{to\_call + bet\_size} {pot\_size + to\_call + 2*bet\_size}.$$ (6.7)

Expecting to face one more bet on the river, we add one bet to the cost and one to the pot for the bet we expect to be made. On the flop,

$$Showdown\_Odds(flop) = \frac{to\_call + 4*bet\_size} {pot\_size + to\_call + 8*bet\_size}.$$ (6.8)

This case is more complex. The bet size doubles going to the turn and we expect to face (on average) one more bet on both the turn and river. For this reason, four bets of the current size are added to the cost and to the pot. This is a first approximation and ignores much of the information available, such as the number of players. Additionally on the flop it would be more appropriate to re-evaluate EHS with PPOT₂ and NPOT₂. However, it is sufficient to capture the essence of the strategy.