[spoonitnow strategy] Back to Basics (Part 3): Semi-Bluffing in Position

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This is part 3 in the Back to Basics series. In this series, we take basic concepts and look at them in a little more depth than beginners typically do. The idea here is to fill in some knowledge gaps and play better poker on a fundamental level. In this week’s installment, we’re going to look at the idea of semi-bluffing in position, particularly in heads-up situations. Like the other installments in this series, you’ll need to have completed the EV Calculations Tutorial series to learn the quick-and-easy method for calculating the expected value of plays if you want to get the most from this article.

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There's a homework section at the end of this week's article. If less than ten people complete it and post their work in this thread, then I'll pick a random winner from those people for a free half-hour session of talking about poker with me. However, if ten or more people complete it, then you'll get a full hour question and answer session with me where I'll answer questions asked from all of the people who completed the homework. This is available to players who complete the homework by midnight on Friday, May 2, 2014.

You don't have to get the homework right to get in on this deal.

Continue Reading: http://www.flopturnriver.com/poker-s...position-21028

Note: If a mod wants to cross-post this in the small stakes forum, that would be great. It's getting a lot more views in the BC.

Good read as always, here's the homework.

Spoiler: Show

6 Outs

Semi-Bluffing
1) Our opponent folds (40 percent), we win the pot of $30.
2) Our opponent calls (60 percent), we hit our draw (6/46), we win the $30 pot and the $25 call.
3) Our opponent calls (60 percent), we miss our draw (40/46), we lose our $25 bet.

<Semi-Bluff> = (0.4)(30) + (0.6)(6/46)(30+25) + (0.6)(40/46)(-25)
<Semi-Bluff> = 12 + 4.3 - 13.04
<Semi-Bluff> = $3.26

Checking
1 )Miss our draw (40/46), no win or loss.
2) Hit our draw (6/46), no extra money goes in (95 percent), win the pot of $30.
3) Hit our draw (6/46), get stacks in (5 percent), win the pot of $30 and the $25 bet.

<Check> = (40/46)(0) + (6/46)(0.95)(30) + (6/46)(0.05)(25+30)
<Check> = 0 + 3.72 + 0.36
<Check> = $4.08

This shows that the more outs that we have to the nuts the better our EV for both checking and semi-bluffing assuming all other variables stay the same. Whilst checking is still the better option in this scenario the EV of semi-bluffing has increase by more than the EV of checking. So I would assume that there is a tipping point where <Semi-Bluffing> is better than <Checking>.

8 Outs

Semi-Bluffing
1) Our opponent folds (40 percent), we win the pot of $30.
2) Our opponent calls (60 percent), we hit our draw (8/46), we win the $30 pot and the $25 call.
3) Our opponent calls (60 percent), we miss our draw (38/46), we lose our $25 bet.

<Semi-Bluff> = (0.4)(30) + (0.6)(8/46)(30+25) + (0.6)(38/46)(-25)
<Semi-Bluff> = 12 + 5.74 + 12.39
<Semi-Bluff> = $5.35

Checking
1 )Miss our draw (38/46), no win or loss.
2) Hit our draw (8/46), no extra money goes in (95 percent), win the pot of $30.
3) Hit our draw (8/46), get stacks in (5 percent), win the pot of $30 and the $25 bet.

<Check> = (38/46)(0) + (8/46)(0.95)(30) + (8/46)(0.05)(25+30)
<Check> = 0 + 4.96 + 0.48
<Check> = $5.43

Once again we see that the EV of Semi-bluffing has increased more than that of checking but has still not caught up to the EV of checking.

Extra Credit
If x is the % of the time we hit the nuts

<Semi-Bluff> = (0.4)(30) + (0.6)(x)(30+25) + (0.6)(1-x)(-25)
<Semi-Bluff> = 12 + 33x - 15 + 15x
<Semi-Bluff> = 48x - 3

<Check> = x[(0.95)(30) + (0.05)(55)]
<Check> = x[28.5 + 2.75]
<Check> = 31.25x

<Semi-Bluff> = <Check>

48x - 3 = 31.25x
192x - 12 = 125x
67x = 12
x = 12/67 (0.179)

8/46 = 0.1739
9/46 = 0.1957

So the point at which semi-bluffing becomes better than checking in this scenario is when we have 9 outs to the nuts.

Assuming I've not made a silly mistake.

Was going to post my homework, (but I might have cheated a little).
Actually it became clearer looking at the second and third examples.
Is it really over 9 outs before it is better to semi-bluff than check?

I would also think that this is the mathematics, but that in poker it would also or perhaps more so depend on the other player's characters and ranges, determining their propensity to call or fold.

Once again though a good read, stimulating, thought provoking, well presented and logical.
Glad to see the basics back after the mind blowing advanced topics.

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Originally Posted by chemist

1)Is it really over 9 outs before it is better to semi-bluff than check?

2)I would also think that this is the mathematics, but that in poker it would also or perhaps more so depend on the other player's characters and ranges, determining their propensity to call or fold.

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1) Probably, I could have messed up on something simple though. I didn't check it at all.

2) You should note that all that changed in this example is two variables, the number of outs. Really this is only one variable because the chance we hit and the chance we don't hit are related in that they add up to one. In simple enough scenarios where we can only bet all-in the variables are all laid out for you in this situation. The things you have mentioned account for how often villain stacks off, or how often he folds to a bet on the turn, etc.

People should really post their answers because I've spoke to spoon 1 on 1 before and it's very helpful for your poker game.