How much is initiative worth?

My friend Barbara emailed me a question last week, “We once talked about how much in big bets the positional advantage is worth. Have you ever attempted to work out how much initiative is worth? I'm just starting to try to quantify this and am not getting very far. It obviously much factor in the opponent's fold tendencies. Thought maybe you'd done this and had some thoughts”

I don't have an answer to this question but here are some of my thoughts:

I don't think there's an easy way to quantify what initiative or the betting lead is worth. Overall it is worth "something" because it's the only way you can win pots with the worst hand– these are generally the biggest mistakes your opponent can make. Also you can cause your opponents to mistakenly fold hands where their equity share in the pot justifies a call.

A good place to see the value of initiative is to look at how hands are faring when you raise as the first player in the pot from the small blind. Then compare the results of these same hands when the situation is reversed and you’re defending from the big blind against a small blind raise. I attached a spreadsheet below that shows this, it comes with the disclaimer that it's a relatively small sample size. Something to consider when looking at this is that when the small blind raises first in, they are normally doing this with about 60% of their entire hand range whereas the big blind is defending in this situation with about 90% of their range. Because the big blind is up against a tighter hand range, you’d expect that the hands wouldn’t fare as well on a whole. However, this should be somewhat offset by the fact that big blind has position on the small blind. Also, because the big blind is defending with 90% of their hands they are immediately forfeiting the pot 10% of the time which is included in the small blind’s results- this is part of the value of initiative though.

What the spreadsheet shows is that the player raising first in from the small blind averages .16 BB/HD compared with -.14 BB/HD for the big blind defending against this raise. It’s hard to say how much of this difference is attributable to initiative because the hand ranges are different but it undoubtedly accounts for part of the difference.

A couple other thoughts:

Initiative probably isn’t as important with your marginal hands that have showdown value. In these cases it’s often better to let your opponent do the betting for you without risking extra bets. Conversely it’s very important to have the betting lead with your draws that don’t have showdown value.

Initiative isn’t necessarily as important on early streets with your best hands. In some cases it’s better to let your opponent have the betting lead early in the hand with the intention of raising one of the bigger bet streets.

Hope this helps or at least gets you started in the right direction. As I'm about to post this, I can't figure out how to attach the spreadsheet - I will email it to you.