I believe it would, but playing hu cash at 10bb or less stacks is probably not a good idea, due to the rake and diminished edge.I'm not positive on both of those but that's how it appears to me.
Interesting question. And I'd aggree with you Ryan :-)Here's my reasoning:I don't know the exact mathematical details, but to my understanding, Nash is a mathematical strategy which has been created by people who knew what they were doing - and it can be proofed mathematically that it's correct. If it can be mathematically proofed that Nash is correct, then this strategy needs to contain all variables that are neccessary.Nash says nothing about the length of the blind levels.n -> n+1:Nash works for HUSNG's with 13 minute blinds, right ?Why 13 ? That's an arbitrary number that I just picked. Let's call that n.So Nash works for HUSNG's with n minute blinds.Does Nash fail if the blinds increase one minute later ?It doesn't say so anywhere.So Nash also works for HUSNG's with n+1 minute blinds.Well, n was some arbitrary number and for any n, is also works for n+1 => it also works for indefinite blind lengths.Proven so far:Nash works for HUSNG's with any blind lengths, including HUSNG without any blind increases.This doesn't imply that it's working for Cash Games, though ! The difference is that a HUSNG must end with a winner while you may leave any time in a cash game.However - if you neglect rake - what difference does it make whether you play an infinite number of HUSNG's with no blind increases or one single cashgame that never ends ? None that I could think of.So I think we can safely say that it also works for cash games.
However, the drastic rake effect at lower cash limits (up to at least 400NL when dealing with shortstack situations) will change the "perfect" ranges of both players.As an example, say effective stacks are 10bb and the blinds are $1/$2:The N-E chart says:Push 58.3% (AA-22,AKs-A2s,KQs-K2s,QJs-Q2s,JTs-J3s,T9s-T4s,98s-95s,87s-84s,76s-74s,65s-64s,54s-53s,43s,AKo-A2o,KQo-K2o,QJo-Q7o,JTo-J8o,T9o-T8o,98o-97o,87o,76o)Call 37.5% (AA-22,AKs-A2s,KQs-K2s,QJs-Q6s,JTs-J8s,T9s,AKo-A2o,KQo-K5o,QJo-Q9o,JTo).This is +0.91EV for the pusher and +1.44EV for the caller.*****When a 5% (max $3) rake is in effect, the numbers change:Push 50.2% (AA-22,AKs-A2s,KQs-K2s,QJs-Q3s,JTs-J4s,T9s-T5s,98s-95s,87s-85s,76s-74s,65s-64s,54s,AKo-A2o,KQo-K5o,QJo-Q9o,JTo-J8o,T9o-T8o,98o,87o)Call 27.6% (AA-33,AKs-A2s,KQs-K7s,QJs-Q9s,JTs,AKo-A2o,KQo-K9o,QJo-QTo)This is +0.78EV for the pusher and +0.89 EV for the caller.*****If you keep the same pushing and calling ranges with rake in effect, then the pusher has +0.71EV and the caller has +1.04EV.*****Notice that the effect is greatest on the caller, as not only does it take away more of an absolute percentage of his range, but also a much larger relative percentage of his range.Note that even though these percentages vary greatly, it's even more important to be able to put your opponent on a pushing/calling range than it is to blindly adjust N-E for rake.
Very good point, that is something I did not take into consideration.I think the overall premise of "don't play vs 10bb stack guys hu in cash" is probably still true, perhaps even more once you see the impact of rake.
I believe it would, but playing hu cash at 10bb or less stacks is probably not a good idea, due to the rake and diminished edge.I'm not positive on both of those but that's how it appears to me.
Interesting question. And I'd aggree with you Ryan :-)Here's my reasoning:I don't know the exact mathematical details, but to my understanding, Nash is a mathematical strategy which has been created by people who knew what they were doing - and it can be proofed mathematically that it's correct. If it can be mathematically proofed that Nash is correct, then this strategy needs to contain all variables that are neccessary.Nash says nothing about the length of the blind levels.n -> n+1:Nash works for HUSNG's with 13 minute blinds, right ?Why 13 ? That's an arbitrary number that I just picked. Let's call that n.So Nash works for HUSNG's with n minute blinds.Does Nash fail if the blinds increase one minute later ?It doesn't say so anywhere.So Nash also works for HUSNG's with n+1 minute blinds.Well, n was some arbitrary number and for any n, is also works for n+1 => it also works for indefinite blind lengths.Proven so far:Nash works for HUSNG's with any blind lengths, including HUSNG without any blind increases.This doesn't imply that it's working for Cash Games, though ! The difference is that a HUSNG must end with a winner while you may leave any time in a cash game.However - if you neglect rake - what difference does it make whether you play an infinite number of HUSNG's with no blind increases or one single cashgame that never ends ? None that I could think of.So I think we can safely say that it also works for cash games.
However, the drastic rake effect at lower cash limits (up to at least 400NL when dealing with shortstack situations) will change the "perfect" ranges of both players.As an example, say effective stacks are 10bb and the blinds are $1/$2:The N-E chart says:Push 58.3% (AA-22,AKs-A2s,KQs-K2s,QJs-Q2s,JTs-J3s,T9s-T4s,98s-95s,87s-84s,76s-74s,65s-64s,54s-53s,43s,AKo-A2o,KQo-K2o,QJo-Q7o,JTo-J8o,T9o-T8o,98o-97o,87o,76o)Call 37.5% (AA-22,AKs-A2s,KQs-K2s,QJs-Q6s,JTs-J8s,T9s,AKo-A2o,KQo-K5o,QJo-Q9o,JTo).This is +0.91EV for the pusher and +1.44EV for the caller.*****When a 5% (max $3) rake is in effect, the numbers change:Push 50.2% (AA-22,AKs-A2s,KQs-K2s,QJs-Q3s,JTs-J4s,T9s-T5s,98s-95s,87s-85s,76s-74s,65s-64s,54s,AKo-A2o,KQo-K5o,QJo-Q9o,JTo-J8o,T9o-T8o,98o,87o)Call 27.6% (AA-33,AKs-A2s,KQs-K7s,QJs-Q9s,JTs,AKo-A2o,KQo-K9o,QJo-QTo)This is +0.78EV for the pusher and +0.89 EV for the caller.*****If you keep the same pushing and calling ranges with rake in effect, then the pusher has +0.71EV and the caller has +1.04EV.*****Notice that the effect is greatest on the caller, as not only does it take away more of an absolute percentage of his range, but also a much larger relative percentage of his range.Note that even though these percentages vary greatly, it's even more important to be able to put your opponent on a pushing/calling range than it is to blindly adjust N-E for rake.
Very good point, that is something I did not take into consideration.I think the overall premise of "don't play vs 10bb stack guys hu in cash" is probably still true, perhaps even more once you see the impact of rake.