during a group sweat session yesterday MattUK asked that question of the player, but we didn't get back around to fully addressing it.
the answer obviously depends on the opponents ranges for each action leading up to and facing the 5-bet. the most important being their 4-bet and calling off ranges. if we have those accurate, exploiting any flaws should be fairly straightforward. so, here is a situation w/ approximate ranges for 'standard tag reg':
the answer obviously depends on the opponents ranges for each action leading up to and facing the 5-bet. the most important being their 4-bet and calling off ranges. if we have those accurate, exploiting any flaws should be fairly straightforward. so, here is a situation w/ approximate ranges for 'standard tag reg':
- 200bb effective stacks
- CO opens to 3.5bb w/ top 50%
- BB 3bets to 11bb w/ [JJ+, Axs, T9s+, 55-22, AQo, AJo, A5o, KJs] ~12% of hands
- CO 4bets to 27bb w/ [QQ+, AK, var1% of other hands] 4.6% of opening range for value + ~var1% as bluffs
- BB 5bets to 56bb w/ [AA, KK, AK, var2% of other hands], 15.4% of 3betting range for value + ~0.8*var2% as bluffs
- CO ships w/ [QQ+, AK], folds others
- BB calls (144bb) w/ [KK+, AK], folds others {fwiw, EV(QQ, call) = +16bb if BB knows CO range above, EV(JJ, call) = +0.2bb}
note: these ranges are easy to tweak, so let me know if they seem inaccurate.
if we then vary the amount of 'air' in both CO (var1) and BB (var2) ranges, we get the following table:
you can see that CO is unexploitable if he 4-bet bluffs w/ between 5-6% of his non-value hands (EV(4b) is inversely proportional to var2 below 5%, but increases w/ var2 above 6%; equilibrium somewhere between).
so, we see that BB would benefit from a 5bet bluffing range v. players who 4-bet more than ~11% total (4.6% value + ~6% bluffs), and only ship a value range.
so, we see that BB would benefit from a 5bet bluffing range v. players who 4-bet more than ~11% total (4.6% value + ~6% bluffs), and only ship a value range.
we then need to consider whether CO has a 6-bet bluffing range. so, we set CO 4-bet air frequency (var1 above) to 10%, give CO a 6-bet shoving range of [QQ+, AK, var3% of others], and find the EV(5b) for different values of var2 and var3. if we then use those values to make a table similar to the one above (i'm to lazy to embed it) we find that BB cannot be exploited by a 6-bet if he 5-bet/folds ~13% of 'air' hands (something like A5s-A2s, would do the trick).
finally, we can answer the original question by noticing that the EV of 5betting only for value is ~6.0bb, and the EV 5betting for value + 13% of air is ~7.7bb, to definitively prove that: YES, BB WOULD BENEFIT FROM A 5-BET/FOLDING RANGE (at least, v. this particular CO, given some assumptions and hoping that i didn't fuck it up somewhere).
response to comments:
yes, var2 is defined as a % of non-value hands, so the absolute % gets discounted
i think the discrepency you noticed was due to a tweak i made in the decision tree when i was looking for a specific group of hands that would make up that ~13% air. so, for that final paragraph i had defined the bluff hands to be specifically A5s-A2s.
also, i posted this in a forum where a question was asked about the effect of 6-bet bluffing frequencies on the EV of a 5-bet. here is a chart that shows the equilibrium points more clearly:
yes, var2 is defined as a % of non-value hands, so the absolute % gets discounted
i think the discrepency you noticed was due to a tweak i made in the decision tree when i was looking for a specific group of hands that would make up that ~13% air. so, for that final paragraph i had defined the bluff hands to be specifically A5s-A2s.
also, i posted this in a forum where a question was asked about the effect of 6-bet bluffing frequencies on the EV of a 5-bet. here is a chart that shows the equilibrium points more clearly:
Posts
Why on step 5 of the situation why do we multiply var2 by 0.8? is this because we want to account for the 15.4% that is already being bet for value. Just confused why this was accounted for here and not on step 4. My assumption is that it just became more significant so you included it...but I wanted to verify that.
ReplyDeleteThen in the final conclusion you cite an ev of 6.0 if 5-betting only for value and 7.7 w/ bluffs....on the chart the largest ev I see w/o bluffs (var2=0) is 5.4 and w/ bluffs is 6.37. Can you clarify where the numbers cited here come from?
This is cool in an academic sense, as far putting this into practice I doubt that I am good enough in the heat up battle to get this little bit of extra EV without spewing.
ReplyDeleteOne of my leaks is looking for fancy justification to gamble more.
Good post though, and BTW I found a comment that Fidodell wanted me to take down that post. I thought you locked the blog? Anyway, I took it down.