Spoony Exercise 8: Semi-Bluffing

In Exercise 7 we took a look at how to analyze pure bluffing scenarios in a vacuum. We noted that a pure bluff has no equity in the pot when called, and that we'll rarely be pure bluffing at the tables before the river because it's fairly rare to be drawing dead. Additionally, you'll often have plenty of hands with some equity that you could bluff with on early streets, so it doesn't make sense to bluff with hands that have little or not equity at all. Here we're going to think about analyzing semi-bluffing situations.

Suppose we have 7s6s on a board of Ac8s5d heads-up out of position against one opponent and the pot is 9bb. If we bet 7bb, analyzed as a pure bluff our opponent would need to fold more than 7/16 = 43.75% of the time for our bet to be profitable. However, suppose that when our opponent calls, we have 8 outs to make a better hand on the turn. There are 47 cards left in the deck, so our chance of hitting is 8/47 or about 17%. So about 17% of the time our opponent calls, we win the pot PLUS the amount he called on the flop anyway. (Note that to keep this simple, we're going to ignore any future betting and redraws and all of that).

Now a cool thing about this is if he's folding more than 7/16 of the time, we know we're +EV anyway as a pure bluff, so adding our equity the times he calls can only make us more +EV. If your bet is +EV as a pure bluff, you don't need to analyze any further. If your bet is about even as a pure bluff, and you have equity when he calls, then you know your bet is +EV then too.

But let's look at an example of the power of having this extra equity. What if we put our opponent on a range, and decide that from that range he's going to fold 30% of the time on the flop, call 60% of the time on the flop, and raise 10% of the time on the flop (to which we have to fold). Then look at each of the possible outcomes:

1. 30% of the time he folds and we pick up a 9bb profit
2. 10% of the time he raises and we have a profit of -7bb
3. 60% of the time he calls, and 83% of that time we miss and have a profit of -7bb
4. 60% of the time he calls, and 17% of that time we profit the 9bb on the flop plus his 7bb call that we win too for a total profit of 16bb

Even if there's no more future betting, we're +EV in this scenario (our EV will be 0.146bb). And he's only folding 30% of the time!

For this exercise, go back to your hands from Exercise 7 and take a look at how much equity you think you will have when you are called. This is a short exercise that's fairly easy to do with the help of PokerStove. Just check your equity against his calling range and post your findings.

Unless this is supposed to be just an exercise practising basic arithmetic, I'm not convinced that considering semi-bluffing whilst ignoring implied odds has that much value. I know you want to keep things simple, but I can't help thinking if people haven't got a grasp of how to do these kind of simple calculations either by themselves or after quite a number of carefully explained examples by yourself then they're not going to get it this time. It seems a shame to talk about semi-bluffing without discussing how it affects your opponent's range, your implied odds and basically all the interesting stuff.

Originally Posted by knaplek

Unless this is supposed to be just an exercise practising basic arithmetic, I'm not convinced that considering semi-bluffing whilst ignoring implied odds has that much value. I know you want to keep things simple, but I can't help thinking if people haven't got a grasp of how to do these kind of simple calculations either by themselves or after quite a number of carefully explained examples by yourself then they're not going to get it this time. It seems a shame to talk about semi-bluffing without discussing how it affects your opponent's range, your implied odds and basically all the interesting stuff.

Well then I'll expect you to write out a 1000-1500 word post explaining all of the intricacies of semi-bluffing. Until then, maybe you should give less excuses and do more work.

Originally Posted by spoonitnow

Well then I'll expect you to write out a 1000-1500 word post explaining all of the intricacies of semi-bluffing. Until then, maybe you should give less excuses and do more work.

lol. Chill.

I may just do that sometime though, could be an interesting exercise

3bet bluff-

weaktight | Hand Poll | KTo - $0.02/$0.05 No Limit Holdem

He's continuing with: {99+, AQo+, KQs}

PokerStove has me as at 30% vs this range.

1.) 82% of the time he folds netting us .82*15bb = 12bb
2.) 5% of the time he 4bets and we fold netting us -9bb
3.) 13% of the time he calls, of that 70% of the time we miss and have a profit of -9bb
4.) 13% of the time he calls, of that we hit 30% of the time we profit the 13.5bb already in the pot plus his 6bb call for a total of 19.5bb.

C-bet bluff-

weaktight | Hand Poll | KQs - $0.02/$0.05 No Limit Holdem

He's continuing with: {55-99, AT-AJ, 89s}

PokerStove has me as at 12%.

1.) 66% of the time he folds netting us .66*14.5bb = 9.5bb
2.) 4% of the time he raises and we fold for -9bb
3.) 30% of the time he calls, 88% of the time we miss netting us -9bb
4.) 30% of the time he calls, 12% of the time we hit netting us the 14.5bb on the flop plus the 9bb call for a total of 23.5bb.

i intend to try both this exercise and number 7 once my database is a little more heavily populated. for my study in the meantime, however, how do you calculate the overall EV of the bet as you did in the OP? im assuming its the sum EV in big blinds of all the possible outcomes (correct me if i'm wrong) but i'm not sure how to work out outcome number three (60% of the time he calls, and of that 60% he calls, we miss the turn 83% of the time, profiting -7bb). i am obviously quite terrible at math so i could never do this on the spot at the table but hopefully with enough drilling into my head i can start remember some basic formulas, or i might attempt to draw myself up a chart relating to 0 EV and different required amounts of raw equity, fold equity, and bet : potsize ratios. thanks. and sorry for having to ask about such basic maths.

actually, don't answer yet. i think i know a thread where i can find the answer.

so villain calls 60%, and we bink the turn 17%, the EV of that particular outcome is:

0.6 (how often he calls)* 0.17 (how often we hit when he calls) * 16bb (our immediate profit when we hit) = 1.632 bb?

Originally Posted by rpm

so villain calls 60%, and we bink the turn 17%, the EV of that particular outcome is:

0.6 (how often he calls)* 0.17 (how often we hit when he calls) * 16bb (our immediate profit when we hit) = 1.632 bb?

Yes, and to find the EV of the play we add up the EV of each possible outcome.

Bump

still strugglin'. all this math seemed so pointless when i learnt it in grade ten haha.

Originally Posted by dranger7070

3bet bluff-



1.) 82% of the time he folds netting us .82*15bb = 12bb
2.) 5% of the time he 4bets and we fold netting us -9bb
3.) 13% of the time he calls, of that 70% of the time we miss and have a profit of -9bb
4.) 13% of the time he calls, of that we hit 30% of the time we profit the 13.5bb already in the pot plus his 6bb call for a total of 19.5bb.

i may be wrong but do you really count it as a 15bb pot at that point? thats including your bet in there, in spoons example he had the pot already being 9bb and said 30%of the time he wins 9bb, not 16..

idk sorry, not trying to be a dick, just trying to clarify it for myself

Full Tilt No-Limit Hold'em, $0.05 BB (9 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

UTG+1 ($1.77)
MP1 ($5.03)
MP2 ($2.72)
MP3 ($5.73)
CO ($1.33)
Button ($5.26)
SB ($7.11)
Hero (BB) ($6.20)
UTG ($4.03)

Preflop: Hero is BB with Q, 6
4 folds, MP3 bets $0.20, 3 folds, Hero raises to $0.62, 1 fold

Total pot: $0.42 | Rake: $0

he is continuing with (tt+,AJs+,AQ+) (like i said in 7)

against that range i am 28.5% equity according to stove

so
1.) 80% of the time he is folding netting me .8* 8=
2.) 5.4% of the time he is 4betting and i lose 12bb= -.68bb
3.) 14.6% of the time he calls and i have 28% equity
and a. lose 12bb 72% of the time= -8.64bb
b. i win 20 bb 28% of the time= 5.6bb
meaning .8 (8) (cause 80% of the time i win 8bb) + .054 (-12) (5% of the time i lose 12 bb) + .146 (-3.04) (14% of the time i lose 3.04 bb) = 6.4 - .648- .44384= 5.308bb

i hope i did this math correct...but i think i am making 5.308bb where as if this was a pure bluff

it would be .8 (8) (win 8bb 80% of time) + .2 (-12) (i would assume everytime he bet or called i was beaten and lose 12bb)=6.4- 2.4= 4bb so my equity in the hand when i semi bluff increases my EV a whole bb.....can someone let me know if i did this math correct, i want to make sure before i do the the same thing for the cbet

bump: this is such a powerful equation beyond comprehension