Module 23: Graduation. One paper, twenty-four questions, and no help until you submit it.
Module 12's paper checked that you had picked things up as you went. This one is different in kind. Nothing is marked until you submit, so you cannot feel your way through one question at a time. Several questions need a number typed in rather than a box picked. Several have more than one correct answer and give no part marks. And most of them deliberately put two or three modules into a single decision, because that is what an actual hand does to you.
Every figure has already been established somewhere in this course, and every answer names where. Nineteen out of twenty-four is a pass. If you do not get there first time, the breakdown at the end tells you which modules to sit with again, which is more useful than the mark.
Blinds are 0.5 and 1. Under the gun folds, and you want to make the largest legal raise. What is your total bet, in big blinds?
Answer: 3.5. Call 1, the pot becomes 0.5 + 1 + 1 = 2.5, so you may raise 2.5 more: 3.5 total. Module 0 lesson 3, and it is why every pot in this course starts at 3.5bb.
The board is a full house on its own and you hold four broadway cards. What do you have?
Your hand: Ace of spades, King of hearts, Queen of diamonds, Jack of clubs
Board: 7 of spades, 7 of hearts, 7 of diamonds, 2 of clubs, 2 of hearts
Answer: Three sevens with ace-king.
The pot is 90 and your opponent bets 60. What share of the time do you need to win for the call to break even? Give it to the nearest whole percent.
Answer: 29%. Call 60 into a final pot of 90 + 60 + 60 = 210. 60 divided by 210 is 28.6%, which rounds to 29%: the two-thirds-pot price from Module 3 lesson 2.
You hold bare aces on this flop against one opponent who could hold anything. Which of these are honest reasons to bet? Select every one that applies.
Your hand: Ace of diamonds, Ace of clubs, 3 of hearts, 2 of clubs
Board: King of spades, 9 of hearts, 8 of spades
It is the turn and your opponent bets the pot. How many outs do you need for a call to be correct on price alone? Give the smallest whole number of outs.
Answer: 15. A pot-sized bet asks 33%. Fourteen of 44 is 31.8% and falls short; fifteen of 44 is 34.1% and clears it. Module 6 lesson 4, and it is why a 13-card wrap cannot call a pot-sized turn bet on price.
You hold top set on a monotone flop with three opponents still in. What is the honest description of your hand?
Your hand: Jack of diamonds, Jack of clubs, 4 of diamonds, 3 of clubs
Board: Jack of hearts, 7 of hearts, 3 of hearts
Answer: A drawing hand that is already behind 53% of the time and needs the board to pair.
The flop pot is 100 and the effective stack is 400. If the whole stack is going in on this flop, what share of the pot do you need to break even? Nearest whole percent.
Answer: 44%. At an SPR of S the commit price is S divided by (2S + 1). At SPR 4 that is 4 over 9, 44%. Module 9 lesson 1, and Module 16 uses the same formula to explain why 3-bet pots are commit-or-fold pots.
Which of these hands are favourites over top set, all in on the flop? Select every one that is.
Board: King of spades, 9 of hearts, 8 of spades
You flop the bottom end of a straight and your opponent turns over the top end. Over the remaining two cards, your equity is:
Your hand: 6 of diamonds, 5 of clubs, 3 of hearts, 2 of clubs
Board: 9 of spades, 8 of hearts, 7 of diamonds
Answer: Exactly 0%.
You hold a pair of kings and the money is going in before the flop. What share of the pot do you need to break even on the 100bb stack-off from Module 14? Nearest whole percent.
Answer: 44%. 43.7%, which rounds to 44%. Bare kings hold 25% against bare aces and so lose 37.2bb by getting it in; connected double-suited kings hold 43% and lose about one big blind. The question was never whether kings can fold, it was which kings. Module 14 lesson 5.
A tight opponent 4-bets 3% of the time, which is close to the frequency of a pair of aces alone. You hold bare kings. What does the arithmetic say?
Your hand: King of spades, King of hearts, 8 of diamonds, 3 of clubs
Answer: Fold: bare kings need them to be 4-betting more than about 6% before a stack-off is right.
You bluff three quarters of the pot on the river. How often must everybody fold for the bluff to break even? Nearest whole percent.
Answer: 43%. Bet divided by pot plus bet: 0.75 over 1.75 is 42.9%. A pot-sized bluff needs 50%, which is why pure bluffs are rare in a game where almost every hand has something. Module 3 lesson 4.
Three players have limped in front of you on the button. You hold bare aces. What does Module 13 say, and why?
Your hand: Ace of spades, Ace of hearts, 7 of diamonds, 2 of clubs
Answer: Raise, but expect company: a large raise does not fold Omaha limpers, and bare aces want the pot heads-up.
On which of these flops is at least 13% of the field already holding a straight or better? Select every one.
Single-raised pot: the flop pot is 8.5 with 96.5 behind. You bet two thirds of the pot on all three streets and are called every time. Roughly how much of the 96.5 stack has actually gone in? Nearest whole number.
Answer: 50. 49.7 of 96.5, so about half the stack is still sitting there at the end of a hand you wanted all in. Getting it in over three streets takes bets of about 94% of pot, not two thirds. Module 20 lesson 2.
Top set and bottom set on the same flop, both against a hand that holds no pair. Which is true?
Answer: They are exactly equal, at 40.98% each.
Everybody folds to the small blind, who raises the pot to 3, and you call from the big blind with 100bb stacks. What is the SPR, and who has position?
Answer: SPR 16, and the big blind has position.
In the published six-handed solver set this course cites, roughly what percentage of hands does the button open when it is folded to it? Nearest whole percent.
Answer: 49%. 48.6%, close to three times the 17.6% opened under the gun. The ladder matters more than the digits: if you open the same range from every seat you are folding far too much on the button and playing far too many hands early. Module 13 lesson 1.
You bet the pot with top set on a wet flop and get raised. Under Module 11's stated assumption, which statements about the raiser's range are correct?
A pot reaches 40 big blinds at 5% rake capped at one big blind. How many big blinds does the house take?
Answer: 1. 5% of 40 is 2, but the cap is one big blind, so the house takes 1. The cap is why rake as a share of the pot is worst in exactly the small pots that limping creates and mildest in the big pots that raising creates. Module 17 lesson 1, and Module 13 lesson 8.
You move from four-card Omaha to five-card Omaha. Which single number best captures what changes?
Answer: Somebody holds the nuts about 1.6 times as often.
Which of these are true of a 100bb 3-bet pot at an SPR of about 3.5? Select every one.
On a three-flush river you hold the second-best flush and face a pot-sized bet from a player who has bet every street. Which reasoning is sound?
Answer: Count the flushes that beat you and the bluffs that could be betting, then compare the count with the 33% the bet asks for.
You flop a 20-card wrap. What share of the time do you get there by the river? Nearest whole percent.
Answer: 70%. 70%, not the 80% the hold'em times-four shortcut predicts. The shortcut works up to about 12 outs and overshoots badly above that, which in Omaha is most of the interesting draws. Module 10 lesson 3.
However that went, the useful part is the breakdown rather than the mark. A module you scored badly in is a module whose numbers have not settled yet, and rereading it with the questions in mind takes twenty minutes.
And then the obvious thing, which no course can do for you: none of these figures earns anything sitting on a page. Go and play some hands, take the grade on every decision, and read the explanation on the ones you got wrong.