1 Minus Alpha

I’d just like to create a thread for discussing topics related to defense frequency, and leave it mostly for others to throw out and discuss ideas. Some possible topics for the thread:

  • Creating an unexploitable defense frequency, so that you are not either incentivising bluffs, or driving people to only make value bets against you
  • How to select the hands you will defend with, and those that you will not
  • How to respond to players without a balanced defense frequency
  • When not to use 1 minus alpha as a basis for your defense range (I’m specifically thinking of when your opponent is actually strong and seems to be fairly well balanced, rather than the simpler cases when they bluff far too much or far too little)
  • What 1 minus alpha means with multiple potential defenders
  • Anything else that seems to fit in well with the topics above

Oh, and just a quick definition, for those not familiar with 1 minus alpha. Alpha is the ratio of the bet faced divided by the bet plus the pot without the bet. So with a 1/2 pot bet, that becomes 1/2 divided by (1/2 plus 1), or one third. 1 minus alpha then becomes 2/3, and is the general frequency you must defend (either with a call or a raise) to avoid making bluffs of that size profitable. With a pot sized bet, alpha becomes 1/2, and so ideal defense frequency 50% (1 minus 1/2).

It’s much simpler than that… the 1 simply means a whole number.

So, an alpha of 0.05 tells you that you’re looking for a 95% confidence interval… ergo,

1-0.05=0.95. That can be calculated with 100% confidence.

I guess I’ll throw out some brief thoughts on why you might not use 1 minus alpha, or minimum defense frequency (MDF), as a basis for making call decisions. MDF tells you how often you need to call to keep bluffs from becoming profitable, but it does not tell you if you can actually call profitably. It’s important to realize that, over a large number of hands, if you almost never call, eventually any observant opponent is going to start increasing the number of bluffs they make, and they’ll be able to do so profitably. But as you face an individual calling decision, it is probably better to focus on your pot odds and the actual ratio of combinations that probably beat your current hand. There will be times you find yourself facing a range disadvantage bad enough that you simply don’t beat enough combinations, and won’t be able to call with some hands that you’d choose to call with if 1 minus alpha was your only guide.

Another way of describing this: you may need to call at a certain frequency to keep opponents from being able to bluff profitably, but you won’t always actually have a sufficient number of combinations of hands in your range that can call profitably to achieve that minimum defense rate. There’s no benefit to you by adding calling combinations that will be -EV; your individual calls need to be ahead often enough so that the money won the times you’re ahead offsets the money lost the times you are behind.