Indifference – Why is it important?

Indifference

How, and why, do we want to create indifference for our opponent’s bluff catchers? Why do we need a mix of value bets/bluffs, and what ratio should we use?

Example of indifference

  • Let us imagine that on river we cover our opponent, and go all-in for $300 into a $300 pot.
  • This leaves our opponent with only two options, i.e. he can call, or he can fold.
  • In order to stop us from doing this with any 2 cards, our opponent needs to calculate his minimum defense frequency. In order to breakeven, our opponent needs to call at least $300/($300+$300+$300) of the time, i.e. 1/3 of the time. That is to say he has to put in 1 pot sized bet, trying to win the 2 pot sized bets already in the pot (the initial pot and our bet).
  • Thus, from our point of view, to make him indifferent to either calling or folding, our value betting to bluffing ratio should be 2 to 1. That is to say we should be:
    • Bluffing 1/3 of the time
    • Value betting 2/3 of the time

If we do this, our betting range on the river is balanced. Our opponent will be indifferent between calling or folding with his bluff catchers.

We will likely arrive on the river with a range consisting of hands we want to bet for value, hands we want to bluff, and hands we want to check. Our opponent will have some hands that are easy calls or folds, however a large number of hands in his range are likely to be bluff catchers – they only win if we are bluffing.

What does our opponent do with his bluff catchers if we bluff too little?

  • If we only value bet (and never bluff) we win $300 (if he folds) or $600 (if he calls)
  • Once our opponent catches on that we never bluff, he will always fold his bluff catchers to our river bet. This means we never will be paid for our value hands (except when up against a less strong value hand from our opponent – often a cooler situation).
  • Similarly, if we bluff too little (and our opponent catches on), he will not get paid enough for our value hands – in low stakes live poker, strong players can often find unbalanced folds when it is obvious their opponent is almost never bluffing.

What does our opponent do with his bluff catchers if we bluff too much?

  • Once our opponent catches on that we bluff too much, he will call more often with his bluff catchers to our river bet.

What if we use the correct ratios?

  • We bluff 1/3 of the time, and value bet 2/3 of the time
  • If our opponent folds 100% of time: We always win the $300 already in the pot, before our bet.
  • If our opponent calls us 100% of the time: the 1/3 of the time we are bluffing we will lose $300, however the 2/3 of the time we are value betting we will win $600.
  • That is to say on average we expect to win (2/3 * $600) – (1/3 * $300) = $400 – $100 = $300
  • Indifference: We have made our opponent indifferent between calling and folding.

Benefits to having an appropriate value bet to bluff ratio

  1. You will get paid off appropriately on your value hands (as if you bluff too little, you opponent will start to not pay you off with his bluff catchers).
  2. You get to bet with a larger range of hands (as you will usually get to the river with not just value hands), and your opponent will be indifferent between calling and folding, and thus you make more profits on average. A strong opponent should respond by making us indifferent to bluffing, by calling with an appropriate range of hands, especially hands that block our value hands – however, at low stakes poker your opponents are unlikely to be calling appropriately in many situations.