Quote:
Originally Posted by hu4food
that is very interesting.
I am surprised to learn that this chart is only meant to achieve a slightly better result than sitting buttons out.
I am a very steady winner long run 20% ROI over 40k husng games or more so I am in real shock at these news.
where have you seen that the chart is just looking to top -0.5bb/hand?
thank you
A lot of people interpret NASH as some way of "never losing" but that kind of thinking won't turn a profit. You have to remember that shove/fold places a huge restriction on the game, such that above certain stack sizes (8-13BBs are often quoted as where people start playing pure shove/fold) it isn't representative of real play - you have far more strategic options with which to exploit your opponent. When the game IS restricted, as in shove fold, we want to shove as much as possible in order to win the 1BB, & villain then needs to find the calling as much as possible such that we, the pusher, profit as little as possible. At this happy medium is the NASH equilibrium which has definitely been computed correctly!
Example at 20BBs:
Our range is 22+, A2s+, A2o+, K4s+, K9o+, Q5s+, Q9o+, J7s+, J9o+, T6s+, T9o, 96s+, 86s+, 75s+ , 65s, 54s, or 39.37% of hands.
So we fold 60.63%, & push the rest of the time.
{Fold% * 19.5 + 0.3937 * (Villainfold% * 21 + 40 * Villaincall% * EQ} where EQ is our equity vs villains calling range.
vs NASH call range at 20BB (21.72% of hands, vs which we have 44.16% EQ):
0.6063 * 19.5 + 0.3937 * (0.7828 * 21 + 40 * 0.2172 * 0.4416) = 19.8BBs
So at 20BBs NASH is guaranteed to be at least + 0.3 BBs better than folding (but notice it's still a losing play!). As we get shorter stacked the SBs NASH strategy becomes slightly more profitable (our profit is non-negative below 7.8BBs & highest ~4BBs) but it's certainly not emphatic!
I re-crunched the numbers for a tighter calling range of 44+, A2s+, A7o+, KTs+, KJo, QJs (17.95%):
0.6063 * 19.5 + 0.3937 * (0.8205 * 21 + 40 * 0.1795 * 0.4251) = 19.808BBs
Even if you're playing a spastic monkey who calls 100% your average total BBs is only 20.1. The point is that if you're playing NASH at these higher stack depths you're never gaining much advantage even if your opponent is deviating heavily from NASH. That is why someone who realises that you're pushing 100% can just sit back and wait for a hand. You're never profiting a great deal no matter what strategy they employ & you leave yourself no room to exploit someone.
So why then are you still losing? Simple, because you are only ever winning small from the SB at best, but when you're OOP you can only play NASH when villain plays it. And SB will always have an advantage at this depth.