# Math Workbook: Answer Key Error?

Red Chipper Posts: 14 ✭✭
Making my way through CORE and SplitSuit's Preflop/Math workbook. Thanks for all the amazing content!

I have a question about the "%-pot" Answers in the "Raises" section (starting on page 106). I'm pretty sure the way %-pot for raises is calculated is not totally correct.

For instance, let's look at the example given on page 105: Starting pot is 700, I bet 400, and opponent raises.

A pot-sized raise would raise to 1900 total, giving me 2:1 odds (call 1500 to win 3000) and I'd need 33% equity to continue. The %-pot calculated for the raise-to-1900 is, naturally, 100%. I've noted here that the pot odds and equity relative to the % of the pot are unchanged from regular bets–if I had just checked and then faced a regular pot-sized bet (700 into 700, or 100% of the pot), I'd still be getting 2:1 and need 33% equity.

Now let's take a look at an opponent raising to 1200. The odds and equity required are correct (2.9:1 and 26%), but notice that all of a sudden the %-pot relationship is broken. The %-pot is calculated as 1200/1900=63%, but a normal 63%-of-pot bet (where I had checked instead of bet) would be giving me 2.6:1 and require 28% equity.

I believe the way the %-pot should be calculated to maintain this relationship is to compare the *raise sizes*, not the *total sizes*. So a 100% pot-sized raise is a raise of 1500 on top of the 400 to call (resulting in 1900, as stated before). And a raise to 1200 is actually a raise of 800 on top of 400 to call. 800 is 53% of 1500, so the %-pot here should be 53%, and this would actually keep the number in line with the odds and equity required. Now the 2.9:1 and 26% are the same whether I'm facing a 53%-pot-bet or a 53%-pot-raise.
The same applies to all of the %-pot calculations provided in the answer key for that section.

I don't know if this is an actual error in the workbook/answer key, but I thought I should bring it to your attention in case you guys meant %-pot differently here.

• RCP Coach Posts: 1,876 -
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• Red Chipper Posts: 14 ✭✭
edited May 2020
Thanks Doug!

Note I'm encountering a similar issue in the "Implied Odds: Facing Raises" section with %-pot calculations.

*Edited--an earlier version thought the 'Pot Size to Start Street' in the answer key was off*
• Red Chipper Posts: 14 ✭✭
@SplitSuit just checking in--I'm still wondering what to do about these calculations exactly.
• Las VegasPosts: 4,857 -
The issue is there's a difference between the size of half a pot raise and a half-pot raise.
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• Las VegasPosts: 4,857 -
edited June 2020
This may help:

Credit: dubakkur2
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• RCP Coach Posts: 4,082 -
@SplitSuit just checking in--I'm still wondering what to do about these calculations exactly.

The answer by @TheGameKat is solid. I would also make sure to watch this video entirely since I discuss many things including % of pot, how to do some of the questions, and "IO when facing raises" begins around 8:20

If you watch the whole video and still have questions, please let me know!
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• Red Chipper Posts: 14 ✭✭
Thanks @TheGameKat and @SplitSuit for your answers! I really appreciate y’all taking the time :)

I’m still kind of confused. Please hang in there!

I actually agree with the formulas provided by @TheGameKat. I think the answer key is in violation of those formulas, and I think the alternate approach I proposed in my original post is in line with them.

The methodology proposed by @TheGameKat presupposes that a “1/2 Pot Raise Size” corresponds to “3:1 Odds”--which is also what I was trying to keep consistent. The formulas derived are a way to ensure that, for instance, the opponent is provided with 3:1 odds when a 1/2 Pot Raise is made (I’m referring to the first table, the one that maps to a factor F).

Now let’s look at the Preflop Workbook Answer Key for the first question on p.109. The Pot Size to Start Street is 20,000. The answer for a Total Raise Size of 40,000 is listed as follows: %Pot=50%, Their Pot Odds=4:1,Their Equity Requirement=20%.

Isn’t this already in direct violation of the table provided? In the answer key, % of Pot is 50 and their pot odds ratio is 4:1. How could villain only need 20% equity facing a half-pot raise?

If we were to use the formula provided to calculate an actual half-pot-raise:
P = 20,000 (Pot Size to Start Street)
b = 20,000 (villain’s initial bet)
1/2 pot raise formula: x = 0.5P + 2b
filling in, x = 0.5*20,000 + 2*20,000 = 10,000 + 40,000 = 50,000

So with the example provided, the formula claims a half-pot raise is to 50,000 total, but the answer key lists a total raise size of 40,000 as “50% of pot”.

For @SplitSuit — thanks for the video! I think watching it in real-time pinpoints the exact difference in the calculation. You’re dividing the total raise size by a pot-sized raise to find %-pot. So in the example in the video, you divide 40k by 44k (what would be a pot-sized raise in that example).

By the video’s logic, a pot-sized raise is two times a 1/2-pot-raise. It sounds intuitive, but the formulas provided by TheGameKat prove this isn’t true:

For a 1/2-pot-raise, x = 0.5P + 2b
This would mean that 2*x = 2*(0.5P+2b) = P + 4b

P + 4b obviously does not equal P + 3b (the formula for an actual pot-sized raise). So it’s clear that two times a 1/2-pot-raise does not equal a pot-sized raise. That means we can’t say, “This raise size is half of what would be a pot-sized raise, so it’s a 1/2-pot-raise.” Does that make sense?
• Las VegasPosts: 4,857 -
Yup, makes sense.
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