I find this one of the harder decisions to make live at a poker table, where I have a middle strength holding, and I’m trying to weigh the benefits of betting to get weaker hands to fold, against the problem that the bet seems mostly unlikely to get better hands to fold, or weaker hands to call.
So I thought I’d look at a few imaginary situations to try and see how the EV penciled out. Let’s imagine we raised pre-flop with 7h7c, and get a rainbow flop of Ad6s2h. Next, we’ll assume that we are ahead 2/3 of the time, and that the hands behind us are KQo-KTo,QJo-QTo,JTo,JTs,T9s,98s,65s, against which we have just under 26% equity, which we’ll round down to 25% for simplicity. We’ll assume that we’re losing to a few Ax hands and a small number of higher pocket pairs, against which we are almost drawing dead (we’ll round the equity up to 10%, though it is 8%). Does it make sense to make a 1/2 pot bet with one opponent?
We’ll assume the hands behind us will always fold, and that the hands ahead of us will always call, and we’ll say the pot is $100, and the bet puts us all in. This won’t quite match reality most of the time, but should still provide some useful insight. So 2/3 of the time, we’ll be getting worse hands to fold, improving our equity share from $75 to $100, for a $25 gain, and 1/3 of the time we’ll have $20 equity in a $200 pot to help offset the 90% of the time we lose a $50 bet.
To simplify visualizing this, lets run this 30 times:
- 20 times a worse hand folds, and we pick up $100, for $2,000
- 10 times a better hand calls
- 9 times we lose our $50 bet for a loss of $450
- 1 time we win $150
If it had gone to showdown 30 times, we would have had 75% of the pot 20 times, for $1,500, and 10% of the pot 10 times, for $100, for a net of $1,600 ($3,000 total pot). Above, betting half pot, we win $1,700. So in this simple test case, our protection bet does perform better than checking.
You can probably tweak this quite easily to generate a scenario where you are better off checking.