Poker Math Quiz Flashcards
(1) The pot is $400 before your opponent bets $200. What pot odds are you getting here?
ANSWER: 3:1
To call here, you would be risking $200 to win $600 (the $400 pot + their $200 bet). The pot odds ratio is essentially REWARD:RISK, and here would be $600:$200, which simplifies to 3:1.
(2) You raise preflop and just the BB calls with this range. If you cbet for $25 into $40 and suspect the BB only continues with a pair or better, is this bet outright profitable?
ANSWER: YES
Given this range and flop, villain only has a pair or better about 35% of the time and thus folds
the other 65% of the time. A bet of $25 into $40 has a breakeven-% of 38%. Since villain’s fold-% is higher than the required breakeven-%, this is an outright profitable bet. Finding outright profitable bluffs is a key way to amp up your aggression both preflop and postflop.
(3) Assuming there are zero blockers to consider, how many combos exist in a range of QQ+/AK?
ANSWER: 34
There are 6 combos of each pocket pair and 16 combos of each unpaired starting hand (12 of those are unsuited, and 4 of them are suited). As such, a range of QQ+/AK has 18 combos of
pocket pairs and another 16 of unpaired starting hands - for a grand total of 34 combos.
(4) Playing $5/$10, you open-raise to $30 total from the SB and suspect the BB only defends with this range. About how often will you pick the pot up uncontested preflop?
ANSWER: 50-70%
This range contains 37% of hands, which means the other 63% of hands would all get
folded after you raise. Being able to effortlessly parallel %-form, combos, and composition of a range is a crucial skill that all intermediate-advanced players need to be refining. Many of the exercises in the Poker Math & Preflop Workbook will guide you through this work and help you build improved intuition that you use in every single session.
(5) Stacks are $100 and you invest $10 on a preflop setmine expecting to win your opponent’s stack every time that you flop a set. What is the EV of setmining here?
ANSWER: +$3
You will flop a set or better roughly 12% of the time which means you make $100 12% of
the time, and you lose your $10 setmine 88% of the time. Plugging everything into the EV equation, that is (12%$100)-(88%$10). That simplifies down to $12-$8.8, and gives a final answer of roughly +$3.
(6) The pot is $800 on the river. What is the breakeven-% if you overbet for $1,600?
ANSWER: 67%
The formula for breakeven-% is $Risk/ ($Risk+$Reward), where risk is the size of your bet/raise and the reward is the size of the pot you are fighting for. In this case, your risk is
$1,600 and the reward is the pot, or $800. $1,600/($1,600+$800) gives us a final answer of 67%.
(7) Your opponent bets 18K into a pot of 18K on the turn. You suspect you have a 20% chance of improving to the best hand. How much extra do you need to make on the river to justify calling?
ANSWER: 36K
Facing a pot-sized bet gives you 2:1 pot odds, but given your estimated 20% equity, you
would actually need 4:1 pot odds to make continuing immediately correct. To estimate how much extra money I need to make on the next street, I multiply the gap between the odds (the gap between 4 and 2 is 2) by the bet I’m facing. So multiplying 18K by 2, we see that we need to make 36K on the river.
(8) What is the %-form of this preflop calling range?
ANSWER: 1-15%
This is a 14% range of hands when blockers aren’t considered. It may seem unnecessary to be able to closely estimate these numbers, but this is the foundation for finding extra bluffs preflop and hand reading postflop.
(9) How much equity does A♣K♥ have against a range of JJ+/AK preflop?
ANSWER: ~40%
t’s technically 39.78% equity for AK here, but who’s keeping track? Knowing the equity of common hands you play vs. common ranges your opponents might go all-in with preflop is
a HUGE benefit - especially if you play tournaments. The good news is that some practice with Equilab (even 10 minutes per day for a week) will help you make better estimations. And since equity is so important when discerning the EV of various preflop all-ins, this is 100% worth your time.
(10) You suspect MP open-raises with 20% of hands and would only continue with this range if you 3bet to $100. Roughly how often can you expect MP to fold preflop?
ANSWER: ~75%
The range shown is roughly 5% of hands, which means MP is folding the other 15% of hands
from the original range of 20%. 15/20 = 75%, and as such, we can expect villain to fold that often. This is a great example of how technical knowledge can help you find extra 3bets preflop. The exercises in the Poker Math & Preflop Workbook guide you through countless drills to internalize this skillset sooner than later.
(11) The pot is 150 on the river and your opponent bets 100. How much total would you put out if you decided to make a pot-sized raise?
ANSWER: 450
The simple way to calculate a pot-sized raise here is to multiply the bet you are facing by 3 and then add in any extra chips. In this case,
you would take 3*$100 and add in the extra $150 from the pot, for a final raise size of $450 total. You will know that your pot-sized raise is correctly sized when your opponent is getting 2:1 after you raise. In this spot, they would be calling $350 more to win $700 (the $150 pot + their $100 bet + your $450 raise)…giving them exactly 2:1 on a call.
(12) At 500/1K blinds, it folds around and the SB goes all-in for 10K total. Your 1K blind is already posted and it is 9K more to call. What is the EV of calling assuming your 22 has 45% equity?
ANSWER: 0
This is a spot where you would use the simple EV equation.
The formula would get filled in like this: EV = (45%11K)-(55%9K) and solve down to EV=0. I don’t know about you, but risking my tournament life for 0EV doesn’t make calling all that attractive.
13 You cbet 80K into 190K with this range on T♦9♦5♣ and your opponent raises. Which of these raise sizes are auto-profitable if you only continue with top pair or better and draws with at least 8 outs?
ANSWER: 180K & 220K
Given the continuance range, you are folding 47% of the time. If villain raises to 180K or 220K which both have a breakeven-% under 47%, villain can bluff us with any two cards for these sizes since we are folding too often. Of course, this doesn’t mean villain is actually adjusting properly and adding heaps of extra bluffs for those raise sizes - but it’s a serious consideration against stronger opponents.
(14) The pot is 20K on the turn and your opponent makes a pot-sized bet into you. If you raise to 80K total, what pot odds would you be offering them?
ANSWER: 2:1
Your opponent would be calling 60K to win 120K (the 20K pot + their 20K bet + your 80K raise).
This gives them exactly 2:1 on a call, and based upon what you learned in Question #11, you know that your 80K raise was also a perfectly sized pot-size raise.
(15) What is the %-form of this 3betting range?
ANSWER: ~10%
This is technically 9.5% of hands with zero blockers accounted for. Understanding the %-form of 3bet ranges can help you build that player’s preflop calling ranges AND hand read against them postflop in 3bet pots.
16 Assuming there are zero blockers to consider, how many combos exist in this range?
ANSWER: 251-400
This is a 27% range of hands that contains exactly 354 combos. If you’ve never worked with %-form and preflop combos before, when there are zero blockers accounted for there are
1,326 combos of all 169 starting hands. Meaning a 0% range of hands contains 0 combos, and 100% of hands contain 1,326 combos. Given this, you should be able to quickly calculate how many combos are in a 10%, a 20%, and a 50% preflop range…
