Semibluffing for implied odds
I was answering a question in private that looked interesting enough to post publicly, so here it is:
Given the nature of NLHE can it be more profitable to semibluff the turn with no fold equity purely for the extra value we gain by being able to value be the river larger when we hit? What varying amounts of fold equity yield what profitability?
against a megafish who never folds and never raises.
The board is
and we expect villain to have a set at this point. We have %18 equity.
EV is simply measured as the sum of all possible outcomes multiplied by the probability of each outcome happening.
So for events A through C, the formula would be:
Total EV = Probability(A)*Outcome(A) + P(B)*O(B) + P(C)*O(C)
Assume $100 pot on turn.
$75 turn bet, which gives us sizing for $200 into $250 on the river.
As the control, ie what we're measuring our different EV calcs against to see if they're more profitable, we have to measure the EV when we check turn and try to spike the river. Assume that when we check the turn, we value bet for $75 into $100 on the river.
EV when we check turn:
= [EV of checking turn and valuebetting when we hit river] + [EV of checking turn and missing river]
= [Probability of hitting*likelihood of getting called*outcome of hitting]+[Probability of missing*outcome of missing]
On average, we make $31.50 by checking back and value betting river when we hit.
Now let's try an EV calc for %0 fold equity and the assumption that we bet turn.
EV when we bet turn:
= [EV of betting turn, hitting river and valuebetting] + [EV of betting turn, missing river and giving up]
= [EV(turn bet)+EV(river vbet)] + [EV(turn bet)+EV(river ch)]
= [-$75+(P(hit river)*P(call)*outcome)] + [-$75+0]
= [-75+0.18*1*375] - 75
So with %0 fold equity on the turn, we clearly lose money.
Solving for least FE needed for play to profit more than checking back turn:
To find out where the breaking point for EV is vs checking back, we set our breaking point to $31.50, and solve for the fold equity needed to reach that point. Any more fold equity than that, and we have a good bet. Gets a bit complicated:
$31.50 < EV(turn fold) + EV(turn call, river hit & we bet) + EV(turn call, miss river)
$31.50 < P(turn fold)*O(turn fold) + P(turn call)*O(turn call) + P(turn call)*P(river hit)*O(river bet) + P(turn call)*P(river miss)*O(river miss)
$31.50 < X
*100 + (1-X
)*100 + (1-X
)*0.18*375 + 0
$31.50 < 100X + 100 - 100X + (18-0.18X)*375
$31.50 < 100 - 67.5X + 6750
$31.50 < 6650 - 67.5X
67.5X < 6650-31.5
X < 6618.5/67.5
X = 100.7
I redid the equations several times with this post, and as of right now I'm assuming the place where I went wrong would be in this last one for solving for X. If someone can point out any mistakes that'd be great, otherwise the conclusion is simply that a bet can't be profitable without %100 fold equity, which doesn't make any sense.