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May 14, 2017 at 20:34 comment added domotorp I find both of these examples very interesting, especially the second one. (Which had far less poker terms that needed googling, but now all is perfectly clear.) I think what would be most interesting to know is whether you always need to go all-in in NL (unless you check). I've updated my question above.
May 14, 2017 at 14:40 history edited Douglas Zare CC BY-SA 3.0
Corrected typos. Tried to clarify.
May 14, 2017 at 12:55 history edited Douglas Zare CC BY-SA 3.0
Typos
May 14, 2017 at 9:40 comment added Douglas Zare The second example was in a limit betting structure. The bets are a fixed size of $1$. (In actual Limit Hold'em, the bets are $1$ unit in the first two betting rounds, and $2$ units in the third and fourth betting rounds.) The computation of the equity in situations $1$ through $4$ in the second round assumed a bet size of $1$, so they are not valid in a NL structure. If you assume that you can bet $3$ units in both rounds, that changes the equities. Making the pot $8$ would not mean that someone with $1/5$ equity could call a bet in the second round if that bet might be $3$ units.
May 14, 2017 at 6:02 comment added domotorp Assuming that the players know that the other player also plays optimally, in your last example isn't another optimal action to simply bet 3 at the beginning?
May 14, 2017 at 2:21 history answered Douglas Zare CC BY-SA 3.0