Quote:
Originally Posted by Fish Sticks
Got this book a couple of days ago from amazon and it's a very good read so far. Just a quick question regarding page77, could you explain why A3s and A4s have different ranges of stack depths for shoving? Probably not useful for any real game application but it'll be interesting to know the reasoning behind it.
Glad you're enjoying the book.
Page 77 has the well-known Nash shove/fold charts. Some hands like A3s, A4s, 43s don't really have a contiguous range of stack sizes for which they should be shoved. For example, a good approximation of the stack sizes for which 43s is in the equilibrium shoving range is:
less than 2.2BB;from 4.9 BB to 7.8 BB, and from 8.6 BB to 10.0 BB
I show this graphically for the case of 43s on the next page, pg78, and give a bit of discussion there too. But the main idea is that, for the stack sizes listed, jamming 43s is +EV with respect to folding and for the sizes not listed, it isn't. This has some to do with card removal effects and how the BB's range also changes as stacks get deeper.
Something similar happens for A4s and A3s as well, and you can check for yourself that at stack sizes where the shoving ranges don't overlap, one hand is a profitable shove vs the BB's Nash calling range, and the other isn't.
I agree that worrying too much about this stuff isn't super practical. In some sense it's a pretty minor detail of a very specific situation, and I sort of went back and forth while writing on whether or not I even wanted to include Figure 3.4 and the surrounding discussion. But in the end I decided that people use the "Nash chart" often enough that it was worthwhile giving a very clear picture of where exactly it comes from and what exactly it means.