Poker Math Every Player Needs to Know

[@GTOWizard]

Did you learn something new? What would you like to see Tombos21 cover next?

[@stevefillier6951]

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

[@postmur625]

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

[@zeouhu7345]

Quantum Physics

[@luizfelipeap]

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?

[@modeob88]

range advantage, nut adventage and that kind of stuff

[@kelvinlee7550]

This is a comprehensive video on the science behind poker. Mastering both science and art is what makes any poker player greater than having only one, good job

[@nicolasspray]

poker is not an art

[@AtGame7]

For the first question I need more information? Am I holding Kings? If I'm holding Kings the correct answer is the flop will contain an Ace 100% of the time. Fact.

[@schwarzer0se463]

Exactly my thought 😂

[@If6wasnine]

Then shove pre flop

[@mikecheckov5365]

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

[@MrCEO-1]

Yah theres no math to truth

[@ColeCleveland1]

fold kings

[@jakestern298]

If this is 101, i need 100

[@ryangiglio7784]

If this is 101 I need a tutor and summer school

[@ACE-sx8mo]

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

[@NoahAlston]

He has another video on Pot Odds that is really good and will help better understand these concepts

[@peternguyen1911]

If this is 101 I need preschool

[@sentimenta1664]

cool video and all but i think i'll stick to flopping royal flushes every hand

[@SpaceFortunaa]

Poker is as much a game of skill as it is about reading people. One of the key concepts to master is understanding pot odds-the ratio of the current size of the pot to the cost of a contemplated call. Knowing your pot odds helps you make better decisions about whether to call, raise, or fold based on the likelihood of completing your hand. For example, if you're on a flush draw (needing one more card to complete your flush) and the pot is offering you odds that match or exceed your chances of hitting that flush, it might be worth continuing in the hand. However, if the pot odds are low compared to your chances of making the hand, it’s usually better to fold. Mastering pot odds, along with reading your opponents’ tendencies and controlling your emotions, can significantly increase your chances of long-term success in poker.

[@Mr.Muckington]

Cool story Phil hellmuth. This like every trash book from the 90s lol.

[@fisher00769]

>start watching the video as a beginner >10 seconds in: "what do these 5 things I've never heard about have in common" >bruh 💀

[@elias60]

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

[@CasualSloth]

@@elias60well that’s how you get better like

[@elias60]

@@CasualSloth I’ve realized that lol

[@CasualSloth]

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

[@Drtydeeds]

Please keep playing poker.

[@rileygibbs3128]

I must be the first person watching this video! I should go play poker with all this run good.

[@JakGruen]

Please help, I'm crazy confused by the calculations at about 25:38 How is EV Bluff Raise = Edge (Risk+Reward)? Wouldn't that mean that the more I risk, the better my EV? So if I raise to 1000 pots, it's EV Bluff Raise = 100.2 pots? I can't make sense out of it. It seems way more profitable to just call, because I put less risk into the same amount of possible profit. So what's off with my thinking here? Where am I going wrong with my logic?

[@GTOWizard]

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.

[@raijin5280]

Do you have a longer video on how to apply the math to your strategy? Kind of how you touched on the BB changing strategy based on value-to-bluff ratio at 11:06

[@HaerinAU]

20:18 Can I say that we use MDF when having medium-strength hands and use outs vs pot odds when we have strong draws?

[@shrankai7285]

18:10 with a 33% pot odds, and a 37.5% defending percentage, how does that work? Does that mean that 37.5% of SB's hands have a 1/3 chance of winning against BB's raise? Do you start calling once you reach the 33% win chance with your hand, or do you call with worse hands to protect against BB's bluffs?

[@jambojack]

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.

[@GTOWizard]

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.

[@bojan10]

Do the calculations only make sense against decent poker players or also against first-time players or absolute fishes?

[@FlexxXlife]

Man thanks a lot for this ! this is very good material

[@josyvan7680]

I love how in 21:28 "% of hero calling after raise" just ties in perfectly with you guys' True MDF video lol where we defend more than MDF suggests vs a raise suddenly the pieces of the puzzle fall into place ✅

[@DirusSC]

I have a problem with Method 2: The Easy Way at 25:38. Would increasing the raise to 4x initial pot increase the EV if we assume no influence on the edge to EV = 10 % (4 + 2) = 0.6? At the same time Method 1: The Hard Way at 24:47 calculates EV = 70 % (2) - 30 % (4) = 0.2. The two methods seem to give different answers. Am I doing the math wrong?

[@GTOWizard]

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

[@kylebennett4434]

Can someone explain to me the flopping an ace bit? I don't understand how flopping an ace would be so much more likely than flopping a 6 or jack. It just seems like simple math that any card is just as likely as any other

[@benjaminbereznak8588]

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.

[@mad1337nes]

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.

[@kezman82a]

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.

[@kylebennett4434]

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!

[@LectiidePokerRo]

@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).

[@johnsoleiman4088]

how do we use this video when most of decisions will also be heavily driven by "these people, this player" tends to do xyz more/less often and we don't know this information or how to obtain it?

[@sagekita1042]

I am confused on how the Ace on flop bet is profitable. The percentages in the video are referring to an ace-high board. An ace-high board occurs more frequently than any other card because it is the highest card in the deck, i.e. lower cards have a chance of flopping with a higher card. However, that does not mean it is more likely to flop an ace than any other card. Are all cards not equally likely to come out on flop?

[@smfreeze]

Don't know what you're on about, but the odds of picking an ace out of a deck is 1/13 and on the flop you pick three cards, if you get 4:1 returns, on average you will profit. I don't know why he used that table to demonstrate it, it was kinda confusing lol.

[@TooMuchInternetTMI]

4:47 ace high flops occur 21.7% of the time, if you win more than 20% of the time because of the 4:1 odds given its profitable, since 21.7% is higher than 20% it's a profitable bet

[@scorpinex_twitch]

You can just calculate it as 1/13 of ace propability for a random card on a flop. This way, around 0,92% is a chance of having a non-ace card. ~0,92^3 = ~0,78% is a chance of not having any aces on the flop. Thus, 1 - 0,78 = 0,22% of times you will face an ace. 22% (our calculations) > 20% (100$:400$ ratio), so the bet is profitable

[@Ohrami]

Bunching could make A-high flops in effect

[@TFFYoutube]

Hi can someone tell me why do we count our chips in pot odds ? Like in 16:40, vilain asks us to put 10 chips on a pot of 20 (10 chips in the pot + vilain bet), how do we end up with a calculation of 10 / 30 = 1/3 ? Why isn't it 10 / 20 = 1/2 ? Thanks a lot

[@hungjon]

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

[@GTOWizard]

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.

[@mcc1200]

Hi @GTOWizard! Excuse me but I am very confused in the example @19:04. I don t understand why OTF, BB checks before SB, and SB checks behind. Why does BB is first to speak? Anyway great content, love the simple way you put it. Thanks

[@mcc1200]

found it :)) its a heads-up sim

[@ArtificialBeethoven]

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

[@MajorBaker710]

Im confused about the Ace high flop 4:35. How is it not a even 1/13 like all other cards? Is it because an ace out ranks all other cards thus discounting any sub ace high board? (AKx vs Kxx)

[@GTOWizard]

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

[@royalflush8173]

No.its not 1 in 13 because by the time you spread the flop it's less than 13 cards, further more 3 cards come out on the flop instead of 1 so the chances of an ace hitting is greater than 1/13

[@tkjyeung]

Me too.

[@naesone2653]

At 25:42 why is the reward suddenly 1 for calling and not 2 ?

[@lvzee]

Perhaps it is a technical quibble but if someone overfolds or over bluffs by 10% their frequency doesn’t go from 33% to 43% but to 36.3%. 10% of 33%. Imagine a limit game where the river bet is 10% of pot. The bettor should bluff about 8% of the time. If he underbluffs by 10% he only bluffs 7% not the impossible negative 2%

[@GTOWizard]

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

[@lucabossi7253]

It is possible make alla this maths and calculation multitabling on 6 max cash game or zoom tables? I don't think so. There must exist a shortcut or easier way to do this

[@doktordiklegz]

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.

[@NicheNiches]

4:42 is confusing me. I must be missing something. How does an Ace come on the flop 21.7% of the time?

[@GTOWizard]

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

[@hectorlopez4075]

Here I was just expecting a 4X, 2x outs calculation vid and got a intro to stats class.

[@wolfcake34]

Bit confused… you showed the chance of an ace being high card, not an ace being shown on the flop. Otherwise the odds would be same across all cards

[@ryanpark1219]

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

[@omqbrown9041]

Money is not meant to control people, rather it is meant to be put to work producing more money for you. You cannot build wealth without putting money in its rightful place.

[@orange_caesar]

Hello GTO Wizard! Is there a way to compute for MDF without getting the alpha? For the example in 14:47 I tried doing 6.5 / 6.5 + 11.5 = 36% which isn’t the 43% of 1-alpha Not sure if I’m understanding this correctly.. Thank you in advance! And love the videos. Cheers!

[@jambojack]

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.

[@GTOWizard]

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/

[@Dmanz67]

How does knights move?

[@moviemaster5425]

The Knights lose their Aura so they take the 'L' route.

[@matheusstotti]

Any tips off contents that I can practice these maths concepts more deeply?

[@dylanrobbins1245]

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.

[@akantorman1]

4:45 well… yes… but… no… Usually you‘d do these calculations assuming you have an Ace already in your hand, otherwise why would you hope for an ace on the flop? If you’re holding an ace that would be a massively losing bet. If that‘s just a bet between two spectators I don‘t really get the point of this example already but yes ofc then the math checks out

[@Alexandertygreat]

I shared this exact same theory of raising over calling in these exact same spots back when i was purely a pro poker player in 2009 and all the other pros at the time thought i was insane and just plain wrong. Didnt stop me from using it and crushing though. Especially in mtts, i made every online major Final table on every major site and won a ton of MTTs

[@mr.annoying9453]

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

[@Alexandertygreat]

@@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.

[@mike8771ify]

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

[@barygol]

And now he is commenting on KZbin instead of living it up

[@Alexandertygreat]

@@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.

[@schlauLern]

Very nice video! Thank you. I watched it just now so not sure if the question has already come up but I was wondering about the 10% over-bluffing and over-folding. Why is it additive? I would have intuitively thought that if the bluff frequency is 33.3% and they are bluffing 10% too much, they are actually bluffing 33.3 % * 1.1 = 36.63 % and NOT 43.3 %. But maybe this is more clear if you get the numbers out from the data base? Can you maybe share the discussion on 2+2?

[@GTOWizard]

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

[@DJDonkeytron]

Patrik Antonious is definitely not thinking about any of this beyond pot odds vs hand odds. Good video except over complicating the easiest part to understand (pot odds)

[@RobertoMacedaPanta]

I got the doubt, if the probability of seeing an Ace on the flop is 21.7% is the same for a 2 or a 3 right?

[@reisr4171]

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%.

[@TooMuchInternetTMI]

​@@reisr4171 little things that should be the probability of any of those cards coming but if a 3 comes it's rarely ever going to be a 3 high flop

[@S8david]

Aces would only be a 21% chance if you have an ace already in your hand with 3 remaining in the deck?

[@gallagherk11]

Is there any good intuition for why MDF > Bluff %? For example, if villain makes a pot-sized bet on the river, they should be bluffing 33% of the time but MDF says we should defend at least 50% of the time, which means we should be defending against a portion of their value bets. What's a good way to think about why that is?

[@GTOWizard]

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.

[@gallagherk11]

That makes sense, thank you!

[@11Brawlman]

@@GTOWizard Tool listeners be like

[@lucianozaffaina9853]

Best poker books? I want to improve at heads up play, and single table tournaments. I would really appreciate if someone could give me a short list

[@simonep3443]

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.

[@TooMuchInternetTMI]

Books are outdated, solver work is what everyone is doing

[@DayOfVictory007]

Err in short, Great breakdowns! Subbed.

[@lwuquh6732]

I don't understand how you calculated whether the bet is profitable or not. I would calculate profitability assuming the opponent has bullets in which case there is only a 12% change (assuming heads up) of the flop containing an ace. This therefore makes the best unprofitable

[@TooMuchInternetTMI]

If you assume they always have aces most bets will be unprofitable lol

[@paataa5886]

How do you bet an amount on the flop to get stacks in on the river? I remember seeing a simple formula before but I can’t remember it.

[@GTOWizard]

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

[@wevertonsoaresdossantos1405]

Nice video !

[@FloydMaxwell]

Your first example: 3:1 pot odds/how often do you need to win. Let's say you invested $1 in a $3 pot. Three times. You need to win one of those 3 pots to win back the $3 you invested. 1 in 3 (not 1 in 4).

[@FloydMaxwell]

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.

[@GTOWizard]

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.

[@loco4dogg]

Liking the content so far except for one thing. Math is funny in that there are many ways to get to the same conclusion or at least many ways to wrap your brain around it. The graphics need some work though, even on my 27 inch screen the smaller text is difficult to read. It can all be better the smaller stuff I left guessing is that 57% or 64%.

[@GTOWizard]

Thanks for the feedback!

[@virtualjoker9036]

Teach me having pk KK 23bb , raise and then get shoved on, I have to call and I'm up against a donk a4 rags and he hits the ace and now I have 3 bigs left, quit or just keep rebuying

[@TooMuchInternetTMI]

Rebuy if u arnt tilted

[@mur_do]

Saben donde puedo tener esta información en español?

[@justsomeguy1671]

8:09 i got 9.1 for some reason not 8.1 but ill double check that.

[@LinusK500]

It seems like the way you're calculating MDF is wrong. If you know your opponent will sometimes give up, when he reaches the river without a made hand, and he sometimes gets to the river with a made hand, then that ratio is the one you need to be calculating, not how often the opponent thinks you will fold.

[@AlessandroOrlandi83]

Such an interesting video.

[@garnetbelik4190]

A really great video tutorial

[@Oque.Nos.Somoss]

Amazing content guys! Thank you!

[@emkrisp11]

Im confused when you say 1 minus 62.6% is 37%. Can you explain?

[@soghotze]

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

[@sahar3870]

I think you explained pot odds wrong, from what i learned youre supposed to put you bet into the calculation means that you win you bet also, if you do win .

[@AAZFortnite]

No friend they are 100% correct. This is because in the pot odds example we are the CALLER therefore the bet has already been accounted for. If we are the aggressor then yes we need to factor our bet into the odds are are laying our opponent. But no you do not factor your CALL as well, in with the pot odds. It is simply your opponents bet + the pot vs what the bet itself is. Your call is not part of the pot yet, and the term is POT odds. Hope this helps, let me know if you need any further clarity!

[@sahar3870]

@AAZFortnite thanka for explaining, i still dont understand something, lets say the pot is 100 and villain bets 50, now pot is 150, if i pay the 50 and win lets say i had a flush draw and hit it, now i win 200 not 150 so why dont we calculate that in?

[@x78963xx]

i need more dozes of these Math. love it!!

[@diogopelaes2218]

100 pages of poker gto fundamentas that you would suffer to understand in a book summarized in a 30 minutes video. Impressive!

[@elias60]

I was under the impression this would be for people (like myself) who struggle with math lol

[@jeffe2267]

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

[@elias60]

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

[@MrVeenrok]

Hello guys! I didnt understand Alpha concept. If we bet 6,5 in 5 pot. We risk to lose 6,5(bet) + 2(already in pot) = 8,5 And if we win we get only 3bb, because 2 in the bank is ours What is wrong with this logic?

[@schalke0494]

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.

[@GTOWizard]

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.

[@tommymeister9543]

@GTOWizard can you tell me where i can get those cool images from this video)

[@BenjaminK18335]

I bet is IA

[@GTOWizard]

These were generated with DALLE 3, and some editing from our Graphic team. Glad you liked them! Feel free to reach out to our discord server to get the pics.

[@joshuabowkley3490]

I just follow my gut instinct, and also try to not run garbage without supporting community cards sequences. THANKY!

[@karthage3637]

The comment of other player about how holding an A reduce the probability to see this flop make me think that if you want learn to play you Ax well you should first look at Kxx board (most probable board you will see holding an A)

[@alexanderkornyukhin7241]

Why in GTO Wizard Example BB acts before SB? I am very confused with that tbh

[@alexanderkornyukhin7241]

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

[@SilenceDogood999]

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

[@nawhead]

I really love the art style in this!

[@G33wee5h]

No hand is safe hand, every hand is winnable hand, and nothing beats luck. Chip count can dictate how you play each hand.

[@justinbyrge8997]

🤔 🙋 Just so you know, the probability of seeing at least 1 ace on the flop is 21% only if you haven't seen your hand. And it can be expressed like this: 1 - ((4 C 0 * 48 C 3) / (52 C 3)) Once you're dealt a hand though, you've seen 2 cards and now you have to update your information. Assuming you don't have an ace in hand then the probability is expressed like this: 1 - ((4 C 0 * 46 C 3) / (50 C 3)), which is 22.55%. Small difference but I like math. Have a great day. Okay bye. 😁

[@coryaw95]

Could someone explain exactly how aces have a higher chance to land on the flop? All cards should be equally statistically weighted, so how in the hell can Ace flop 21% while other cards flop with less than 10%?

[@berdyderg900]

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.

[@conorkleitz6837]

no longer providing us with the power point file!??

[@AimeeGirl]

I'm too stupid to follow this, but thanks for trying to explain it to me.

[@ErnestBaillie-h3i]

Thank you very much for sharing your experience and knowledge about trading.

[@MrNicePotato]

I just don’t get why people often start with x:1 as an odds. The bets are rarely given in a simple ratio anyway. I just skip that step.

[@GTOWizard]

Odds tend to be more useful in live settings.

[@toppace]

I learned implied odds was something else.

[@rvoykin]

Did anyone else wish they only had to listen to this one time to understand it lol has a total beginner it’s not so common sense but I know a couple weeks it’ll be more and more

[@pedroarthurdutrahuning]

Bro this is so confusing 😢. I'm gonna watch one more time

[@lucasdesiqueira6122]

Excelent video

[@modeob88]

The image on the presentation are too good, some IA there :D

[@sky_rokit]

Intelligence Artificial

[@jynx619]

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

[@Luke-q4o]

Thanks for the video. but idk what calculation you used to get a 21% chance of flopping an ace!? That would mean close to 1 in 5 cards in the deck are aces. I get an average of 8.5% chance roughly.. assuming there are none in your hand; 4/50, 4/49, 4/48 = 8.0, 8.1, 8.3 % for each card on the flop respectively.

[@GTOWizard]

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!

[@11Brawlman]

oh yeah clear as day now

[@mr8966]

How can you flop an ace 20% of the time when aces are 1/13th or 7.7%

[@GTOWizard]

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%

[@FirstLast-zy6wv]

Science and the tools produced by science can help those who are not chosen to feel for a while as if they are.

[@jimz1024]

about 57% of the time, it works every time

[@austinmurphy8932]

all poker math = 25%. that's what I learned.

[@pwnd785]

Why does gto wizard not consider a 222 flop to be 2 high

[@modeob88]

bcs is it.

[@torpeda8766]

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

[@modeob88]

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

[@pwnd785]

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

[@weare2iq376]

@@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...

[@realchicagophill]

My lord! If you aren’t a tournament player, I’ll eat a deck of cards. Long division with decimals and remainders on the fly? That’s why tournament players take 20 minutes for each hand they play?

[@attackhelicopteridentifier7343]

All this math assumes your opponent is playing this way. If they’re just firing random bluffs with random bets it doesn’t work

[@parabellumCH]

thank u

[@stefenleung]

wait. would human being really calculate 6.5/(6.5+5) on the table?

[@GTOWizard]

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.

[@stefenleung]

you can just say no.@@GTOWizard

[@davidpotter1476]

Common Core Poker Math?

[@bradycrockett3403]

I just can't get it. I must be stupid.

[@joshuapatrick682]

Why would I hit like or subscribe before Ive seen the video?

[@joeblunt6126]

awful. Why use 2.7 and 5.4 when you could have used 2 and 1?

[@williamhoudersheldt7076]

Sounds very confusing, a lot of math to do at the table. I never see anyone pull out a piece of paper & pencil, I don't believe everyone can do (and remember) all these calculations in their head, while playing. Even if you could do all that math in your head, it still doesn't tell you what the other players are holding or what the rest of the cards (to come) will be.

[@11Brawlman]

i cant believe you really think you know more than these guys, they train the best in the world.

[@williamhoudersheldt7076]

@@11Brawlman Never said I did, I don't think that at all. Way beyond my mental compacity.... lol

[@DystopianMonkeyMan]

Isn't the probability to get at least one ace on the flop 23.5% (not 21.7%). (4/52) + (4/51) + (4/50) = 0,23535... If you don't know your hole cards that is. Why do I get a different answer if calculate it as: (all possible flops - flops with out an ace = flops with ace : all possible flops) which is the 21.7%?

[@fragslap5229]

So the UKTIMATE question comes down to how MUCH did all this "knowledge" INCREASE the PERFORMANCE of a REAL poker player.

[@GTOWizard]

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

[@fragslap5229]

@@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..

[@stefkleij3891]

8min in and i’m lost on the next one

[@ayezakmi-w2d]

2hard

[@gargdye1924]

I find it hard to believe that any of the players I sit across from at local casinos do anywhere near this kind of analysis during play. In fact, I would bet that 95% of players don't go beyond pot odds. Don't see myself ever sitting at a WSOP table with math geeks, so I just don't see the value in this amount of analysis. Then you factor in variance and just sheer donk magic on a daily basis and what your selling is a life tied to a chair squeezing out a living based on statistics that can mean nothing when it matters. Sure, you can call yourself a "PRO" but what does that even mean in reality? I understand every aspect of probability and can tell you exactly what percentage of the time I should win, but that won't stop me getting busted out by a complete noob who goes all in with 2/4 offsuit all night long if lady luck is sitting in his lap. Not dogging your effort, just an observation from a player who's been playing for better than 4 decades.

[@ResonNL]

I always hated the math side of poker cause its really boring. To be honest, I have never known any of this stuf but I've been a winning poker player for over 20 years.

[@davidrebocho2093]

The beginning of your video is all black, dark nothing going on

[@radleywilks9371]

I've never felt more stupid