MATH BASED PLAYING STRATEGY

1326 possible two hand starting combinations. Ring game, ten players. Odds are at least one player will have a starting hand in the top 132.6 starting hands. So if I only played hands in the top 5%, or 66 combinations, I would be playing only one out of twenty hands. However, mathematically speaking, in a never ending game, if I just called down every bet to the river, wouldn't I win more than half of the time, regardless of the flop, turn or river, because I am probably starting with the best pre-flop hand? Remember, we are assuming a never ending game. My reasoning is that if I have a hand ALWAYS in the top half of the best 10%, my opponent will have hands in the bottom half of that top ten half the time. And that is only IF ANYBODY has another hand in the top ten. Even if I get six callers preflop and some of them hit, I have just as good a chance of hitting as they do, and most wont hit. Distributions of flop, turn and river cards will be equal for both of us, so starting with the probably best preflop hand should do it. Disregard the cash loss of lots of blinds, making believe it's not a factor for the purposes of this question.

"Figures never lie, but liars sometimes figure." What you've said may make sense mathematically, but is not practical on many levels:

1) That would be exceedingly boring rarely ever playing a hand.
2) If you played "Dan Harrington" tight, people will notice that and not call you or give you any action when you do play your 1 in 20 hands. This will probably be one of your biggest problems. If you just call to the river? What if they realize you're only playing the best hands and always check to you? Then do you have to bet? What if they all fold to you? I hope you see how this is mathematically a good idea, but practically not a good one at all.
3) There's a LOT more to poker than the math. I started as a math based player but then found I was really good at putting the story of how people play hands together, reading people, etc. The math is a MUST know for any decent player, but I truly believe HALF of the game is non-math related things such as tells, tendencies, current ranges, current levels of tilt, positioning, etc.
4) If you start with the #1 best possible hand, AA, and you get 6 callers pre-flop, you are NOT the favorite. You will have the biggest advantage over any ONE person, but if you look at it from the proper perspective, you're a huge dog. Say you have AA and have 6 callers, you're 30% to win let's say... That means COMBINED the other 6 have 70% chance to win. Individually you have each of them crushed, but at the end of the day it doesn't matter to you if player 2 or player 3 beats you. All that matters is if you win or you don't win with your #1 best possible starting hand.

I encourage you to go to a multi-hand simulator and run AA vs 6 other "random" hands... AA will always have them crushed individually, but will never hold the edge over all of them combined. This should just exemplify the point that the best math starting hand doesn't mean much, let alone the "top 5%." Add this to all the other problems listed above (and there's more I'm sure, this is just off the top of my head) and a purely math based strategy will never work.

Quote: mansherman

if I just called down every bet to the river, wouldn't I win more than half of the time, regardless of the flop, turn or river, because I am probably starting with the best pre-flop hand?

No.

If there are 10 players at the table, I read it as you have a 1/10 chance of having the best pre-flop hand. Stated another way, 90% of the time, you don't have the best pre-flop hand. (It's actually slightly different, because two people could have the same hand, and there's a possibility of a tie. I don't feel bad about approximating this one.)

My observations of poker suggest that successful play is about 1/3rd playing the cards, and 2/3rds playing your opponents.

Your proposed style of play would open you up to getting played, a lot, and hard.

If you play all, as soon as they figure you out, they'll call you every time, and you'll usually lose.

If you only play great hands, again, as soon as they figure you out, they'll fold whenever you raise.


Caveat: I'm not a poker player.

The fact is I'm already a slightly successful holdem player at 2/5 no limit. My main weakness is bad memory due to my age. I live in Vegas. Presently, I have the following rule. Play no more than 1.5 hours at any one table. Run out of tables, move to another casino. I play only later in the day when there are mostly tourists at the table. Getting hit hard because they know me is a very minimal factor. I'm successful now because I know what to play in what position, when to be aggressive, never go on tilt and always keep moving. The question I asked is purely mathematical. Boredom, as one of you suggested, is not an issue. I only play about 3 hands an hour now anyway. Thanks to all of you for your input. I would just like to be shown, why, mathematically, my hypotheses is incorrect.

First, while there are 1326 possible two card starting combinations, there are not 1326 distinct starting hands. There are 6 ways you can have a pair of 3s, etc.
Question 1: How many actual distinct starting hands are there?

If you were to order those starting hands in terms of strength, based on quantifying how likely each starting cards were to win the pot in a ring game with 10 players, you would find that the strength does not decrease linearly.
Question 2: What is the probability of each distinct starting hand winning a showdown against one other player?
Question 3: How do those probabilities change against N players where N = 2..9?

There are software packages available to help you answer these questions. I think the answers may surprise you.

Remember that the number of hands you win in poker is almost meaningless. It is how many chips you win.

So in your example where you call down every bet, 5% of the time, people will bet the strength of their hands. You will certainly lose pots where you arr a big underdog, and win small pots.

Now, if you put together a strategy where you are not calling, but you are the aggressor, you may be on to something, and it may be similar to the "Kill Phil" system.

I would suggest dealing out some face up hands and simulate what the play will look like. You'll see how the best hand, calling down to the river, is a mathematical nightmare. At relatively low cost, weak hands see the flop, and at relatively high cost, they make you call down with your now-weak hand.

MathExrtremist, allow me gently to point out that I believe you have confused the numbers 169 and 1326. If you are dealt two cards, there are 52 x 51 possible ways to obtain them, but since we don't care in which order they came, there are 52 x 51 / 2 = 1326 possibilities. If we ignore suits, except for identifying if the two cards have the same suit or not, then there are 169 possibilities.

No, I have not. There are 1326 WAYS of making hands. 132.6 is ten percent of the WAYS, and if I use an EV chart I can just go down from the top until I reach 136 WAYS, which I guess is the same thing, using a different scale.

As for the commonality of one particular response from a few of you, it is true that some people will hammer me with great hands. But it is also true that some will hammer me with bluffs. The point is, in my admittadly unmathematical mind, that inan ENDLESS game, it doesn't matter if I get hammered with a bluff that I call or a set of 3s agains four aces. In the LONG term, starting with the best 5%, calling EVERY hand down, I can't see how I wind up losing more often than I win. Remember, in an ENDLESS game, the size of the bets don't matter; only the percentage of times won. I will call down small hands and big hands, and I will never be in one place long enough for them to catch on. In vegas I regularly visit 14 casinos, never going to the same one again
until I've finished them all, and I usually switch tables once or twice. I play at night, which is tourist friendly. I'm retired and it keeps me busy, so I don't mind the travel. Most of it is just walking a block or two anyway.

Also, one of you mentioned a software program where I can pick any hand I want and then run ten hands RANDOM handsagainst it. Can you point me to it?

Thank you, everybody, for taking this serously.

Quote: mansherman

...Thanks to all of you for your input. I would just like to be shown, why, mathematically, my hypotheses is incorrect.

It's an interesting discussion that many have had prior... Your hypothesis is incorrect because you're comparing apples to oranges. Poker, as agreed by several already in this thread, isn't just a math game (regardless if you want it to be or not). Other players will form opinions about you and it will effect your hands later. Thus, you can't beat it with a math equation because you can't even form the proper equation. There are variables that must go in to the equation that you're not accounting for, such as table image, reads, other players figuring out you're a tight player, etc. There are no ways to quantify these situational variables. At one table they think you're tight. You move tables and get lucky to get a few hands in a row, so you start betting the first few hands at the new table and suddenly they all think you're a loose betting player. You can't quantify these variables in to an equation, thus you can not prove your equation has any merit, mathematically.

I don't doubt you could be successfully playing only premium hands. Hell, Dan Harrington is exactly that. Successful, and a well known/famous tight player. Most games, especially in Vegas, are basically wiffle ball where you can play what we call "ABC poker" and win. There's enough bad players to give you money.

People openly mock players that are so amateur that they can't fold AA. Imagine being the guy that can't fold KQ(suited), when there's a four card flush on the board(other suit), and you didn't hit anything.

It's impossibly negative EV. I'd say that in a 10-handed no limit hold 'em game, at any limit, there's a 95% chance of being broke within 3 hours, with a max buy-in.

What I'm trying to point out is that in this situation I should be treated as a new player at the table who is only there for 90 minutes, playing only 1.5 hands an hour, average. Tell me how, without a crystal ball, they'll get a read on me in that period of time. I keep my mouth shut at the table, wear different clothing all the time, and don't repeat casinos for around three weeks, since I dont' go ever single day. So take the getting a read on me factor out. This is just a thought exercise. In reality I play a tight aggressive game, with false moves here and there to keep them guessing. In the long run I have always been moderately ahead. Never had a losing year. However, I will tell you this: If you watch Poker After Dark reruns, or any of the shows where you can see their hole cards, experts fold winning hands all the time BECAUSE THEY HAVE BEEN WRONG in putting a player on a hand or range of hands. THEY ARE WRONG MORE THAN THEY ARE RIGHT. If you don't believe me, do what I did. Bet a friend a hundred bucks and then sit in front of the TV, watch and count. WRONG WAY more times thant they are right, and I certainly am not as good a player as they are. I put much more stock in the relative value of MY hand, that I DEFINITELY HAVE, than what the other guy MIGHT have. Poker is a game of bluffs, mistakes and incorrect play. I have lost TONS of big hands I WOULD have one if the guy on the other side only did what HE should have done.

Quote: mansherman

...in a never ending game, if I just called down every bet to the river, wouldn't I win more than half of the time, regardless of the flop, turn or river, because I am probably starting with the best pre-flop hand?

Quote: surrender88s

Now, if you put together a strategy where you are not calling, but you are the aggressor, you may be on to something, and it may be similar to the "Kill Phil" system.

My biggest issue is the passive approach of calling bets and not making bets/raises. You can't win with a weaker hand unless they fold. They can't fold if all you do is call.

Very good point. I cheat myself out of easy pots that way. So maybe I'll take five grand and do this: Get aggresseive if I improve on the flop, just get out if I don't. I've won more than five grand in my lifetime, so there will be really no loss overall. I don't depend on this money.

Can anybody out there point me to a program that will allow me to set it up so it randomly picks my hands out of the parameters i give it, then randomly gives nine more hands out over the entire deck and then allows me to play with it?

Thanks.

It's called buy a deck of bicycle cards and deal them out the old fashioned way :-D. this is how I would do it.

If you want to do 100+ trials, I could probably make an excel worksheet for it, but that would take time. Just PM me if you want a spreadsheet version. I don't know of any software that does this.

I would recommend playing for free in online poker rooms to practice.

Quote: mansherman

In the LONG term, starting with the best 5%, calling EVERY hand down, I can't see how I wind up losing more often than I win.

Against nine other players, being dealt a pair of aces means you will win less than 30% of the time.

I can anticipate the next question, which is basically isn't that what you do now? Yes, but not the same. Now I play a larger range of hands, and I sometimes bluff with nothing. So now I'll just play the top 5%, which will be about half the hands I call now, and I will do no bluffing. Just as an experiment, and see what happens to that five grand. I'll keep you all posted. I'm going to play AA-99, AK, AQs, AJs, KQs, and no more. I will only bet or raise on the flop if I hit at least an overpair. I will call on the flop with a 4 flush or openended straight. If I don't hit the striaght or flush by the turn it will depend on pot odds at that point to draw or not. No other plays. Those specific hands equal almost exactly 5% of starting combinations. Therefore, statistically, I will be startiing with the best hand on at least half the hands I play. Then since drawing odds are the same for all players we're all just as likely to improve. Since I started with the best half the time and only play sets or overhands, if I hit I must still be better. The hands where I lose my preflop bet should be made up for by the pots I take with no opposition post flop. Now, I fully realize that I could be dead wrong, but until I see mathematical proof I'll never know for sure, and neither will anybody else with an OPINION. Thanks again.

Free online is not the real world. When money is involved people play DRASTICALLY differently. Thanks for the offer, but it's too much work for you.

I've heard that, but never seen mathematical proof. Also, that depends on how aggressively you play those aces. Against nine players with a big preflop raise you are rarely going to get more than one caller,and with one caller you are MILES ahead and won't lose anywhere NEAR 70%. Show me where that's wrong. By the way, I am not saying my theory in this thread is right. It could very will be dead wrong and my five grand is toast already. I'm just looking for mathematically sound arguments.

Having everyone call your AA would actually be the ideal result, because even though you'd lose the pot slightly over 68% of the time in a ten-handed ring game with nine callers, every additional caller increases your expected value by more than what is lost from reduced win probability... but that is true if and only if one assumes that there is no further action after the flop and therefore only the value of the the pre-flop round is considered.

If you want a math/statistical treatment of that, you can get it right here:
https://wizardofodds.com/games/texas-hold-em/10-player-game/
and compare calculations of pre-flop EVs for varied numbers of opponents from the links here:
https://wizardofodds.com/games/texas-hold-em/

But. That is too simple. Among other things, that is only relevant pre-flop, and even then imperfectly so for a variety of reasons. Even assuming no pre-flop adjustments from others, as most often played, the money going in to the pot increases exponentially post-flop while that initial calculation becomes less and less relevant on each subsequent round.

In actual live play, I believe the closest one can come to implementing that line is in "short-stacking" a NL game. This involves buying in for the absolute table minimum with the intention of getting all-in almost immediately with your pre-flop premium starting hand range, such as putting $40 on the felt at a table that typically has average stacks of > $200-ish. But it is still not going to be identical to the relatively simple arithmetic of starting hand probabilities, as even then there are still going to be a multiplicity of some other factors that pull results in both directions, with both additional advantages and disadvantages that are beyond the scope of a discussion board post.

And by the way, even though this simple tactic (which exploits a fundamental flaw in the NL structure which is partly why NL was rightly very uncommon until the recent & fading boomlet of TV induced poker kiddies) is really not all that unusual now, and you can often see several doing it in almost any poker room if you know how to identify intentional short-stacking, you can also expect to be despised by those at the table who want to play deep stacked NL poker with all the significant post flop decision making and increasing bet sizes and implied odds to consider through each round. Though if it is at the most commonly spread small stakes such as 1/2NL or 1/3NL I doubt you'll find many altering their play appropriately, even among those who've seen this done before. Responding effectively just doesn't fit with the little psychological/emotional dramas many recent pokerati are there to act out, or want to imagine they are. If you want to explore that short-stacking tactic in more depth, Ed Miller has written quite a bit on the subject and I'd recommend you look into his books that deal with this and related poker topics before putting your money on the felt with this kind of plan in mind.

Quote: mansherman

I can anticipate the next question, which is basically isn't that what you do now? Yes, but not the same. Now I play a larger range of hands, and I sometimes bluff with nothing. So now I'll just play the top 5%, which will be about half the hands I call now, and I will do no bluffing. Just as an experiment, and see what happens to that five grand. I'll keep you all posted. I'm going to play AA-99, AK, AQs, AJs, KQs, and no more. I will only bet or raise on the flop if I hit at least an overpair. I will call on the flop with a 4 flush or openended straight. If I don't hit the striaght or flush by the turn it will depend on pot odds at that point to draw or not. No other plays. Those specific hands equal almost exactly 5% of starting combinations. Therefore, statistically, I will be startiing with the best hand on at least half the hands I play. Then since drawing odds are the same for all players we're all just as likely to improve. Since I started with the best half the time and only play sets or overhands, if I hit I must still be better. The hands where I lose my preflop bet should be made up for by the pots I take with no opposition post flop. Now, I fully realize that I could be dead wrong, but until I see mathematical proof I'll never know for sure, and neither will anybody else with an OPINION. Thanks again.

What about the pot odds on the flop? You Shouldn't auto call a flush and straight draw.


Don't forget implied odds that's very important.

Quote: mansherman

Against nine players with a big preflop raise you are rarely going to get more than one caller,and with one caller you are MILES ahead and won't lose anywhere NEAR 70%. Show me where that's wrong.

You're wrong because you aren't playing against nine players. You are only playing against n number of callers.

You are allowed to make a big pre-flop raise with any cards and rarely get more than one caller.

But your original "Math based playing strategy" didn't allow for raises anywhere. Once you start adding those into the equation it moves completely away from some math problem about what your winning percentage will be as you approach an infinite number of hands. It moves into what most of us simply call "Playing poker."

What about the strategy of never even looking at your cards, but once every 100 hands bet the table max? I'm pretty sure you could win well over 90% of hands that way

Very interesting answer. You know, I play 2/5 500 cap, so while a few guys are sitting with money, most of the players are in the 2-400 range. Maybe I've beeen wrong, but I LOVE to see the guys who sit there and keep buying in for 100 after 100 after 100. Mostly - maybe always - I see them playing it down to 20 or 35 bucks and then making a hail mary. NEVER see them recoup. Haven't noticed anybody playing that low stack theory, but think about this. If you try that and play only hands that are likely to win, that's maybe 10% of hands. That means at 35 hands an hour you're going to get 1.5 hands per hour, but you're going to pay 3.5 blinds for sure, that's $24 gone, first hour, and don't forget straddles. So if you sit down with 200 (minimum allowed most places, except california), your first exposure is $200. Go all in and lose that, THEN you can keep buying in for $100, and because of the blinds you'll never actually win 100 heads up, and will rarely win multi-way, but still are all in as if it's a heads up on all future levels. Also, the potential win over all is always going to be low. I'll tell you what. I'm just going to try my theory live with a 5000 bankroll and see how it works. Play only the top 5%, raise or call from any position preflop. If I get reraised preflop I'll have to judge the strength of my two and make a decision. I'll keep you all posted.

RE: "The guys who sit there and keep buying in for 100 after 100 after 100 after 100." Players who are steaming because they are stuck and are short stacked due to losing usually do exactly the opposite of what someone should be doing with an intentionally planned short stack tactic in NLHE. They tend to widen their range and gahmboool, chasing their losses with speculative hands trying to 'get lucky' without having a stack that's deep enough to offer enough post-flop implied odds to rationally do anything but turbo-muck those.

You can't set-mine with small pocket pairs or sensibly play suited-connectors in a cash game when short-stacked, or when head-up against someone who is. Much of the potential value of those comes from the prospect of taking someone's large stack who can't fold their AA, KK, QQ, AK, etc. as doing this assumes that the contesting stacks are deep enough to build a post-flop pot that's many times more than the initial pre-flop cost. When you see someone showing down 4c4d or 6s7s while short stacked, they are not playing a rationally planned intentional short-stacking strategy, or are not aware of the underlying math of it, or just suck at it.

I'm not necessarily wanting to advocate short-stacking to you in what I posted earlier. Just saying that given your stated intentions it is the approach that emphasizes relative starting hand values the most, due to the underlying math, and therefore rewards tight (but hyper-aggressive) play of only premium top 10% starting hands relatively more than other approaches, partly by eliminating much or nearly all of the implied odds value of others' more speculative hands that are derived from their expectation of much more post-flop play against deep stacks.

If the starting min-max buy-in of your game is $200-$500, you can't really short-stack in this way. You will still be making decisions for most of the chips post-flop. Eliminating that is most of the point of intentional short-stacking.

Quote: mansherman

...and play only hands that are likely to win, that's maybe 10% of hands. That means at 35 hands an hour you're going to get 1.5 hands per hour, but you're going to pay 3.5 blinds for sure, that's $24 gone, first hour, and...

This is an error. Contesting pots with only top 10% hands results in playing an average of once per orbit at a ten-handed table, or 3.5 hands at 35 hands per hour, not 1.5 out of 35.

EDIT to add:

If you really want to get a grounding in the math of the game, here you go:

King Yao - Weighing the Odds in...
Mathew Hilger - Texas Hold 'em Odds and...
Bill Chen - The Mathematics of...

If I understand correctly what you're planning on doing, I think the result you'll get is to win small pots, and lose big ones. Which is about what others have said in different ways. Good luck.

OP, the biggest problem with your strategy is that they'll figure you out and then only bet/call when they're beating you. They'll never try to bluff you, and if you bet, they'll never call with a hand you're beating. So you'll lose all the big pots and win the small ones. If you play passive it's even worse because then they'll just check for free cards when behind, but they'll shove when ahead. At least if you bet your hand you'll get more equity.

Preflop, unless you raise real big or are shortstacked, they'll have easy implied odds to setmine with 22. They hit they get your stack piece of cake, they miss they fold and lose the one preflop bet. If you do raise big pre, they'll only battle you with AA or whatever is beating your range. So you'll either pick up 1.5bb or get it in as a 20-80 dog. Meanwhile you'll be losing most of your blinds when they come around to you.

Postflop, if you miss with a premium unpaired hand, there are boards where you're actually losing to a random hand. Depending on the pot odds it would be bad to call a shove even if you know the guy is betting any two cards. Your preflop equity is no longer relevant.

In short, there's nothing mathematical about your strategy. Real-life opponents aren't betting completely at random and they do adjust to you.

Quote: mansherman

What I'm trying to point out is that in this situation I should be treated as a new player at the table who is only there for 90 minutes, playing only 1.5 hands an hour, average. Tell me how, without a crystal ball, they'll get a read on me in that period of time. I keep my mouth shut at the table, wear different clothing all the time, and don't repeat casinos for around three weeks, since I dont' go ever single day. So take the getting a read on me factor out. This is just a thought exercise. In reality I play a tight aggressive game, with false moves here and there to keep them guessing. In the long run I have always been moderately ahead. Never had a losing year. However, I will tell you this: If you watch Poker After Dark reruns, or any of the shows where you can see their hole cards, experts fold winning hands all the time BECAUSE THEY HAVE BEEN WRONG in putting a player on a hand or range of hands. THEY ARE WRONG MORE THAN THEY ARE RIGHT. If you don't believe me, do what I did. Bet a friend a hundred bucks and then sit in front of the TV, watch and count. WRONG WAY more times thant they are right, and I certainly am not as good a player as they are. I put much more stock in the relative value of MY hand, that I DEFINITELY HAVE, than what the other guy MIGHT have. Poker is a game of bluffs, mistakes and incorrect play. I have lost TONS of big hands I WOULD have one if the guy on the other side only did what HE should have done.

1) You neglected my example... Say you sit down to start a fresh 90 minute session. Say you get AA first hand, AK second hand, and KK 3rd hand, betting and winning all 3. Your table image for the next 80+ minutes is LOOSE because you've been betting since you sat down. Poor players, which I think we all agree there's an abundance of, make snapshot table images like that. Regardless if you think you're 'unreadable' that doesn't stop people from branding you based off of your current SITUATIONAL events.

2) Pro's are right and wrong all the time, yeah, so what is your point? They're quite often right more than they're wrong. That's why they're the pro's. You also are joking about watching Poker After Dark, right? There's been wild conspiracies that it's not even real, let alone it's a ton of big named players with bottomless checkbooks looking to make good TV. They're not playing their 'absolute best' and perhaps not wanting to even show some of their real moves. Saying you watched this show so you can now draw a conclusion is the EXACT SAME as someone putting a table image on you when they have little to no data. You're proof that people do this.

3) So you're saying you'd never play 9d-8d (with your proposed 'strategy')? How do you think people like Daniel Negranu, whom to them this is a STAR hand, became pro's? If you want to look at any kind of evidence I'd say look at the average hands people play. ABC poker does fine and well against amateurs, but you would get murdered with this strategy against pro's, and yes, they WOULD figure you out in under 90 minutes.

4) It's quite evident that you're a semi-educated player... but that you clearly have a lot to learn. Just from your posts alone I can make a read about your level of play and understanding of the game. I'd be willing to bet a very, very, large sum of money that in a "best of 100 series" heads up games I would best you, and I haven't even see you play a hand. Like the motto of the game says: Poker takes a second to learn, but a lifetime to master. The more you learn the more you see how far along the path others are. I remember when I would have made the same arguments as you, but then I learned more about the game and why your "math theory" (which neglects tons and tons of variables) is incorrect.

Lastly, you keep saying "prove my math wrong." In any science/math community it's not our duty to prove you wrong until you've given some kind of mathematical proof for us to review and check your work. You've proven nothing yourself. All you've given is a hypothesis (because you can't account for all of the variables to do the math proof yourself). I hope I'm not coming off too harsh, just trying to give you some advice from experience; I hope you can learn from it.

He's not trying to be the next Daniel N. though. He's basically wondering if a simple, robotic, ultra-tight approach would win at a decent rate. I think it would do fine. I think he'll beat minimum wage. Especially if he's only on a given table for an hour and a half.

Being an older guy hurts the cause a bit as people will assume you will play tight. If a twenties DB in a hoody and headphones did this, it would fare better.

He's talking about never folding K high, or Q8 in a heads-up pot, and always calling down 3 streets with it for his entire stack no matter the board. I don't see that profiting regardless of his age, appearance or time spent at each table. To do worse than this strategy, you'd have to be trying to lose.