Question for the theorists

[lee h]

heads up match, blinds 1/1 (never going up) starting stack 40

Player A - plays perfectly

Player B - never played poker before, goes all in every hand.


What's player A's optimal strategy?

How often does player A win the match?

[Honeybadger]

Lee I can't remember the answer to this one, but I did used to know it (it has been talked about on forums a lot before). It is not that difficult to solve. I just haven't got time to either do it or to look up the answer.

However if I remember right, with ~40bb stacks Player A is only around a 60% favourite in the match. It may even be less than this.

[dwayne110]

http://wizardofodds.com/games/texas-hold-em/2-player-game/   

The above link is helpful in breaking down the heads up statistical chances pre-flop of a hand. I suppose it depends on how high variance you wish to play, given we don't know how long the opponent will continue with this strategy. If we were playing the villain over thousands of hand then we'd want to widen our range of hands we call with close to a 51% win rate, working on the assumption villain is shoving all hands regardless. However, this doesn't take into account the unlikelihood of villain continuing to do this for long period of time if he repeatedly loses buy-ins, nor the likelihood of him learning and changing his strategy. I think I'm calling with anything at approx 53% upwards (going off hand order on the attached link, from K-4 suited upwards). Interested to hear an expert's opinion on this!

[BorntoBubble]

In these spots is it accounted for if we change the action so that if we are SB and they are BB. If we flat do they always shove.. same for if we raise do they always shove. If we shove before them to they always call?

Im not sure if this will make much difference but would definitely affect my strategy. Rightly or wrongly

[lee h]

Its a freezeout and B ALWAYS shoves

[SuuPRlim]

Yh i heard this before it's reliant on PLAYER A's calling EXACTLY perfectly  and its like 60%, curiously though iirc, player A's single win% is increased if he plays non-optimally.
s

[jgcblack]

Yh i heard this before it's reliant on PLAYER A's calling EXACTLY perfectly  and its like 60%, curiously though iirc, player A's single win% is increased if he plays non-optimally.
s

do you mean his $% winrate.. I.e. he only calls with 20% of hands but they do so well vs 100% that he wins more than calling with a perfect 54% of all hands and riding the variance?

[theprawnidentity]

Assuming that we have both have 40bb and we are facing an open shove vs a 100% range our optimal calling range (to break even) would be:

(53.2%) 22+,A2+,K2+,Q2s+,Q4o+,J4s+,J7o+,T6s+,T8o+,97s+

In a scenario where we are this deep I would assume we would be able to call quite a bit tighter than optimal as folding the first 5 hands isnt going to be too detrimental.  Assuming we call with:

(52.9%) 22+,A2+,K2+,Q2s+,Q4o+,J4s+,J7o+,T7s+,T8o,97s+    We would expect to have a 0.2 chip edge in that scenario.
(51.4%) 22+,A2+,K2+,Q2s+,Q5o+,J5s+,J7o+,T7s+,T8o,98s      We would expect to have a 0.4 chip edge in that scenario.

We would then need to work out how altering our calling ranges affects our overall equity (how much we lose by folding vs how much we gain by calling).  Given that this is 40bb and there is a ton of variables + its still 9.22am so I will hold off on this till later.

Should we have a bad run of cards and are unable to find a hand to call with, the optimal calling ranges don't really change much untill we get to a 60/20 chip opponent advantage.  If we somehow dont pick up a calling hand for 20 consecutive hands (which is so unlikely that its hardly worth mentioning), then our calling range would change to:

(57.5%) 22+,A2+,K2+,Q2s+,Q3o+,J3s+,J6o+,T6s+,T7o+,97s+,98o,87s

This scenario becomes far more interesting if we start with a 20bb or smaller stack, as folding becomes far more detrimental to your stack as a %age.

Cliffs: Im sure theres some absolute bollocks in here, ill read it again later and actually try and do some sums when I'm functioning properly.

PS: Can we change the scenario to 15bb or 10bb starting stacks?  10bb being the ideal compromise!!!!!

[SuuPRlim]

Yh i heard this before it's reliant on PLAYER A's calling EXACTLY perfectly  and its like 60%, curiously though iirc, player A's single win% is increased if he plays non-optimally.
s

do you mean his $% winrate.. I.e. he only calls with 20% of hands but they do so well vs 100% that he wins more than calling with a perfect 54% of all hands and riding the variance?

No i mean his chance of winning an individual game.