Poker Math Every Player Needs to Know 

Yes! I learned I need more gin in my tonic 👍

Tombos21 is the best coach))) can he make please video about how deadmoney impact in cash game, for example rush cash cash drops (10bb deadmoney), maybe ante games etc

Quantum Physics

Loved it, I'm not sure if already has a video converting this, but I would like to know if I close my eyes and always play GTO would I be profitable in a field that plays way off the GTO, let's supose I play in a field that never bluffs, and I play GTO calling the MDF will I be profitable in the long run?

range advantage, nut adventage and that kind of stuff

Exactly my thought 😂

Then shove pre flop

@@If6wasnine when shoving all in preflop with kings the caller will have aces 125% of the time. fact.

Yah theres no math to truth

poker is not an art

it is. even if what a pure gto/math game, it's still art imo. the hard science and statistics is working in tandem with the flawed human element@@nicolasspray

If this is 101 I need a tutor and summer school

Or another way to put it, comprehension =100 / (100+101)

Like man I’m just trying to get better at poker not study theory 😭

@@elias60well that’s how you get better like

@@CasualSloth I’ve realized that lol

@@elias60 yeah it’s a big can of worms mate haha

Do them in your head, make the numbers up and practice. While playing, calculate on every street, especially when you're NOT in the hand.

found it :)) its a heads-up sim

I once had this on 888 poker. BB vs SB, I was the BB. after the flop the software decided it was my turn instead of the SB. I was completely flabbergasted. Eventually emailed support and told them I want my buy in back or i post it on 2+2. They gave back my buy in and a little extra, lol

You can define the input over-bluffing or overfolding proportionally instead, but the resulting output equation isn't as clean.

They are almost all outdated in my opinion. You will improve more watching all the videos by GTOwiz and playing with the free version that reading an old book.

Yes, you can do 5 (size of pot before villian bets) divided by 11.5 (size of pot after villian bets). But I think MDF is only useful to ensure you don't start hugely over folding over a number of hands, and not a good way to decide whether to call or not in a particular situation.

You can calculate MDF directly for the initial bet using this formula: MDF = pot / (bet + pot) -> 5 / (6.5 + 5) = 43% = MDF Facing a raise, like in example 17:56 you have to account for dead money in the pot. In this case the starting pot is (5 + 2.5) = 7.5 because SB already bet 2.5 and that belongs to the pot after we raise, and the Bet (Raise) is 12.5. MDF = pot / (bet + pot) -> 7.5 / (7.5 + 12.5) = 37.5% Or more succinctly: MDF = Reward / (Risk + Reward) I recommend calculating Alpha first rather than deriving MDF directly, and understanding the basics of risk and reward make it easier to learn EV and develop an intuitive understanding of what you're risking vs what you're getting. Hope that helps! You can check out our blog for more details: Read more: blog.gtowizard.com/mdf-alpha/

You can define percentage changes as a relative (33% * 1.1) or absolute (33% + 10%). Both are valid, and if you wanted to define an equation using a relative input you could. I chose to use absolute differences because it made the math cleaner. Here is the 2+2 thread: forumserver.twoplustwo.com/15/poker-theory-amp-gto/theory-question-technical-players-1829120

Nah you just do all your math and decision making away from the table, so when you are multi-tabling you're already studied on your position. Like chess.

how much money have you made in your career if you dont mind me asking? just curious

@@mr.annoying9453 hard to have exact amount, but i played professionally from 2006-2010, both cash and MTTs. Between 1.5 n 1.7 mil USD profit. Quit in 2011, didnt play again til sept of last year. Made every major online ft in every major MTT yearly on pp, UB, FT and stars. Best placing for 4th twice. Had couple 6figure scores live including 2 wins. Won alot of online mtts, crushed 6max NLHE on stars and ft from 2007-2009 2-4- 5/10 mainly, with occasional shot at 25/50 n 50/100. Crushed 10/20 thru 50/100 at the commerce mainly and live at the bike and would play wynn and bellagio couple weekends a month and during the series. Quit in 2010 after breaking up with my gf and moved back to Canada. She was a pro on fulltilt. Prob tmi lol i quit due to burn out as well and never enjoyed being in casinos, so toxic and depressing.

Lmao people like this why did you stop playing if you were so good

And now he is commenting on RU-vid instead of living it up

@@barygol lol who said i wasnt "living it up" there is life after poker. Just a game i was better then most at, i moved on to other things and guess what im still better then most.

Yes. The probably of one or more A on flop is the same as any other card (doesn’t matter which one you pick) . Unsure why they used Ace high flops as it’s confusing. It’s always 21.7%.

This is an interesting question, and my sense is that what really matters for the caller are the pot odds. Once villian bets, the only thing that determines whether we can make a profitable call or not is whether our hand is good 33% of the time or more. I believe MDF is not a particularly useful concept in practice.

Great question. Pot odds tells you how often your hand needs to WIN to break even, whereas MDF tells you how WIDE you need to defend to prevent your opponent from overbluffing. So if they're balanced, you'd call 37.5% of your range, and all of those hands would have minimum 33.3% equity facing the raise. However, it may not always be possible to meet MDF. For example, if villain is underbluffing, you would need to start calling unprofitable hands to meet MDF, which is a bad idea. So Pot Odds takes priority. It's ok to defend less than MDF if your opponent is underbluffing.

Maybe the problem is the lingo being used -- "you're getting 3:1" -- it would appear this means, you put in 1 and stand to win 3. But in fact it means, you put in 1 into a pot of 4. The lingo itself is confusing.

If you split the cost of a pizza with 3 friends, you'd expect to get 1/4 of the pie, not 1/3. The same logic applies to pot odds.

They can only fold a maximum of 100% of their range, so in practice your "edge" caps out. You can't have a 10% edge while risking 1000x pot, since that would likely require them folding more than 100% of the time.

Thanks for the feedback!

You're close. Alpha of a 4x raise is 66.6%. Retaining the 10% edge means they fold 76.6%, not 70%. Hard way: 76.6% (2) - 23.4% (4) = 0.6 Easy way: 10%(2 + 4) = 0.6

ace being high card is the same as an ace being shown since ace is the highest card

Yes, each card is equally likely but if you're filtering by the highest card on the flop the math changes

The Ace bit is saying the odds are over 20% that an Ace would be the highest card post flop. It is just as likely as flopping a 6 or jack, but since an Ace would be the highest card when it shows up, it has the highest probability of being the high card post flop if that makes sense.

It's a slightly misleading chart, stating what % that will be the high card on the board....but that number looks correct for A high, since it will always be the highest card (all the others should have a ~21.7% chance to appear on a flop too). The more interesting thing is that the percentage drops to (assuming the random 2p2 thread I found these numbers in is actually right) 16.88% when you have an single A in your hand (known card). So depending on the game stakes/ effective stacks, it might be more profitable to fold all your Ax hands to discourage flops (or better yet, opening some much larger bb amount to take it down without seeing a flop). It's actually a very interesting proposition, as the above mentioned play of winning preflop comes into factor. Then the reality vs probability factors that players are more likely to take flops/defend with Ax holdings. Looks profitable on paper, but closer or even losing in practice.

A23, A89 , AKQ OR 222, 234, 235. Do you see it now? If you got a deck of cards at home.. deal some flops and see how often its 5 high board and how often its A high board.

Thanks y'all, makes more sense now. I got a bit confused why he was talking about the % chance an Ace hits on the flop and then showed a chart of the chances of an X high flop. Those are the same thing but only for the Ace, so trying to apply that logic generally threw me off. Appreciate the comments!

@kylebennett4434: Your intuition is correct. The percentage is wrong as it looks at A high flops rather than chances of flop containing an A. Since A high flops doesn't take into account cases where 2 or 3 Aces show up, as well as A + pair, the percentage on screen is actually smaller. The correct one is ~23.5% and it's the same for any card in the deck, as you rightly pointed out. It can be calculated as 4/52+4/51+4/50 (assuming no hole cards).

You're referring to the geometric bet size, formula here: blog.gtowizard.com/pot-geometry/

You can also count the break even. If you lose ten and gain 20, in a 1/3 odds scenario you would lose ten twice and win 20 once in three runs of the hand, resulting in ev 0

Check out 2:27 for an intuitive explanation. The basic idea is that you want to win your call back to at least break even. So if you win 1/3 of the new pot, you do just that.

I bet is IA

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That's a fun question. The intuition is that when you bluff, you are risking your bet to win the pot. But when you're calling a bet, you risk your call to win their bet and the pot. For that reason, MDF < Pot odds for all bet sizes less than the golden ratio.

That makes sense, thank you!

Intelligence Artificial

He is most probably french - it would stand for Intelligence Artificielle

are you implying that this math is difficult? honest question.

@@jeffe2267 for me it is yes I’m dyslexic

Oh, just realised it is a heads up sim :D

​@@alexanderkornyukhin7241if you get confused by that just think "dealer acts last"

1 = 100% obviously. So it is 37,4% actually

The logic is wrong because we dont care what we already invested. We only see the pot now and what we win. So we win 5 and invest 6.5. 6.5/6.5+5= 57% it needs to work. This is the "sunk cost fallacy" you fall into.

Compare to giving up with a bluff. You still lose that 2bb that you put into the pot earlier. So, if the river decision is to bluff or give up, the money you put in earlier is a sunk cost and doesn't count towards your risk.

Probability of flopping an Ace = 1 - probability of NOT flopping an Ace =1 - (48/52 * 47/51 * 46/50) = 21.7%

There are two problems with your approach: Problem 1) You are multiplying OR logic (1st card Ace OR 2nd card Ace OR 3rd card Ace). Problem 2) You are calculating the probability of EXACTLY one Ace, rather than AT LEAST one Ace. **My calculation assumes no information about your hole cards, so drawing from a fresh deck** Convert this from OR logic to AND logic to calculate it correctly: P(At least one Ace) = 1 - P(No Ace) P(At least one Ace) = 1 - (1st card not Ace AND 2nd card not Ace AND 3rd card not Ace). P(At least one Ace) = 1 - (48/52 * 47/51 * 46/50) = 21.7% Or alternatively, the much cleaner solution using combinatorics: Total ways to choose an Ace on the flop = (52 choose 3) - (48 choose 3) Total flops = (52 choose 3) Probability of a at least one ace = [(52 choose 3) - (48 choose 3)] / (52 choose 3) = 21.7% - Here’s the same calculation assuming we hold two non-ace cards: 1 - (46/50 * 45/49 * 44/48) = 22.6% ((50 choose 3)-(46 choose 3))/(50 choose 3) = 22.6% Hope that helps!

Ace high flop not chance of an ace appearing. Ace is obviously the highest card so if it appears, it will be an ace high flop regardless of the other two cards. A 4 is just as likely to flop as an ace though.

Odds tend to be more useful in live settings.

There are three cards on the flop, not one. Probability of flopping an Ace = 1 - probability of NOT flopping an Ace =1 - (48/52 * 47/51 * 46/50) = 21.7%

Ask the opposite question. How many professional players do you know who don't understand basic poker math?

@@GTOWizard I'd be willing to bet that ANY "professional" poker player could pass an exam on the basic probability of poker hands and how they relate to successful play..

A good player would recognize that the risk is just slightly bigger than the reward, and would know that they need their opponent to fold just over half the time for this bluff to be profitable.

you can just say no.@@GTOWizard

bcs is it.

If you and your opponent is going to flop and nobody has a 2, the first card is 2 with 4/48, second 2 is 3/47, third is 2/46. If we multiply it, it is roughly 1 in 20000 that all three cards are going to be 2. However, if it is 6 or 8 player table, the probability of folded players having 2 is significant, so it is even less common. It's almost 0% for this to happen

@@torpeda8766 that almost 0% happens all fucking days.

@@modeob88 what he’s saying is it’s so low it gets rounded down to zero

@@torpeda8766 This is just incorrect there could be a 20 handed table, and the odds the flop comes out as 222 is exactly the same as if the table is heads up. The reason being that we don't care about the cards we don't know about, and we only know about our hole cards. So it would work out as 4/50 * 3/49 * 2/48 which works out as 1/4900. Or in your example where you somehow know your opponent's hole cards it would be 1/4324...

Yes, all cards are equally likely. However that chart displays the probabilities of the TOP card on the flop. Since there are 3 board cars, Ace high flops are obviously more common than 2-high flops.

@@GTOWizard thank you for the clarification.

Odds and fractions are not the same… with fractions, one of the represented numbers is the total amount… with odds both numbers represented get added together for the total amount… he’s not wrong, and if you need further proof, google this exact phrase… “4:1 odds as a percentage”

Lmao where did you get this information

What would be the point of smart contract poker? I could program it, but what’s the reason? Wouldn’t it be slow as shit?

Coin poker do it no ?

the point sir, is that poker players know that if you involve a central human authority there is always the danger of "knowing the deal" or "seeing the hole cards" always always and also collusion takes meeting at the same table or flooding the tables to by chance get together however live poker prevents some of that by the floor man sitting players (players do not decide which table they sit at). also anonymous player sitting prevents player tracking and heads up displays. you will see white papers come out professing crypto poker that does all this, and they never come to fruition...why? not enough money in it...for the house, for employees or for collusion. peace. A program that autodeals can be random enough, there are proven deal methods already in cryptoworld but and always always always...there is a human central authority? why? why no auto front to back..why why why. a smart coin and smart platform on the blockchain could do allllllll this with a human "manager" never lifting a finger and crypto knowledge already has beaten "hacking the blockchain" so...put auto poker on the blockchain with zero human interaction. have the table rake fuel the growth of the coin. have the smart contract deal the cards and the players engage with no human manager, it will be the most lucrative coin and poker "room" the entire history of humanity has ever seen. mark my words Software that is updatable or manageable by humans , and there will always be cheating...why? one word ..money. why will it be the best coin and smartcoin in the world...one word...money money money. if anyone knows crypto programmers let them know. finally we will have a fair online poker choice and an investment we will all make money from. Peace. Governments and Casinos will have a fit for sure. blockchain poker was headed in that direction..look them up...bye bye why? because it was headed there. they are probably remaking blockchain poker in exactly the way I am sayin and nobody in the world will ever see the riches this platform will produce..nobody knows the value of this except people who know both worlds..poker and crypto. this will be the most valuable crypto coin since bitcoin. they always make "coins" for poker but they always move to managing the table , software and people..why? got to get those humans involved. ridiculous @@wysonlegion5398