The Mathematical Approach

[billy the punter]

sean's post about an open-ended straight flush draw reminded me of something I wrote a a couple of years ago or so... ---- I believe that certain people will always take the mathmatical approach. Is this the huge mistake I personaly think it is? There was a time, when I would usually take the math option at all times, I was a keen maths student all my life, I refused to see past odds etc. However, I was inexperienced at poker then and over the years my experience and skills grew and I started to totally disagree with this theory. But there can be no universal rule for all. I believe the better the player the less risks they should take - most will agree there. Ability must be a factor with these decesions, but also bankroll. Now I know a lot will say that bankrolls should be irrelevant when making such choices, and that you shouldn't be under pressure by playing higher than your should, or buying in for a tournament with money you cannot afford to lose - blah blah blah. I'm a realist. People sit in games they shouldn't - fact. I have, a lot. I've never sat out of my depth ability wise, but there were times when I have done financially - and I knew a lot of good pro players who have done the same. As a result, bankroll, as well as skill, must come into contention when making these marginal/mathmatical decesions at the table. A quick example, I'm sitting in a game I can cope with ability wise no problem, but financially, at THIS moment, I probably shouldn't be playing - I'm hoping my ability to the opposition overcomes this. It's £10/£20 pot limit, I'm sitting with £4000 which is average. It's early, I'm level. There's been a straddle, there's been a raise, there's already 4 in the pot and it's £120 to me on the button with . I call. Flop comes Raise, reraise, it's £2800 to me. Crumbs. What to do. I know I'm odds on vs nearly all hands. I'm what? 55% fav, maybe? Probably? If I was sitting with another ten large in my pocket then it's a pretty easy play - but I'm not. So I pass. Why call? I may as well go to the Vic and stick the 4g on red or black and be home in time for X Factor. Now I know many will say that is what happens when you play too big financially, and I understand this. However, say if I win 80% of the time I sit in this game, therefore there is an 80% chance of me making money if I pass here. Calling (and making the correct mathmatical decesion) I'm much less than 80% to make money. Is it still mathmatically correct to call then? After all, I'm one of those who'd be saying "Deal Noel" when offered £80,000 grand with only the 1p and the £250,000 left. I don't care about the odds, I wrote the book on odds, I'm biting his hand off for eighty large as I honestly believe there is a massive chance I can turn the eighty into a quarter of a mil anyway. Although I promise you if I was in this position I wouldn't spend the whole 45mins prior pretending I was mates with the other 21, what's that all about? Every day the same, what are they, the nicest people in the world every time? So, most will agree that it doesn't always suit certain individuals to take the slight mathmatical edges, but can it ever be correct to pass a BIG mathmatical edge, where the odds are massively in your favour? Well imagine this, you have £100 to your name, you can't pull up anything else to next week and you can't borrow. At 5pm today I will offer you 10/1 on heads when I flip a regular fifty pence piece, min bet £100. You have to take me up on that right? Well what if I'm offering 100/1 at 7pm on the same bet? How does that 10/1 look now? I know this is taking it to the extreme, but it proves for some there can always a better time to gamble, and after all, timing is everything in this game. -------- Like I say this is a good couple of years old and the game in question would be a couple of years before that even. Playing "streched" in games is something I've not done for a long, long time but I still agree with plenty of what I wrote. I don't even play in this game now by the way. This is a prime example that bankroll is important with such decisions., that said even if I was sitting comfortably (financially) I would still pass. I just don't like calling away money with marginal hands, no matter how small the % of my role.

[SteveO]

Re: The Mathmatical Approach Good write up Bill but I dont like your deal or no deal analogy. I too would take the 80K it's a one off game and it's free money I don't give a **** what's in the other box 80K for fcuk all yes thank you very much. If you are bankrolled you have to take the gamble you mentioned above if you feel that your flush draw is live as it's +EV or otherwise you're a big dog. I understand very much why you folded though.

[seanfaz]

Re: The Mathmatical Approach Good argument. I'm really torn about this at the moment. Basically, i'm surrounded by mathematicians - im at university at LSE where literally 80% of students do maths and/or economics, and i often ask my mates to work things out with regards to variance and EV for me. So on the one hand, i have all my mates who dont really understand poker, and would say its a definate call. But then i think, the game in question is so easily beatable, with players paying off large oversized value bets, and who give away their hand with their tells. So i could just make money other ways. Its a tough decision, when you step back from the game you realise that this is money and it may mean a lot to you. For example i keep my bankroll separate at the moment from my daily expenses for just general living. For my bankroll, £200 is like nothing, only about 2-3%. But for my living its very significant - im a student after all. So when playing cash poker you have to think like that as well i think

[Nade]

Re: The Mathmatical Approach Many maths people will argue NL Hold'Em is a solved game due to maths and so they say if you play by the maths 100% you should win over time even with those small edges. Re. open-ended straight flush draws i think it's easy to put the money in without considering that if you have a low draw any pair is likely not good and if you make a flush it still might not be good anyways. Re. bankroll i can totally understand someone playing under-rolled and folding likely the favourite hand if they're a recreational player and just want to stay in the game and have some fun but for all serious players it's a must to have good bankroll management so you're comfortable going in with it at marginal times.

[Samba_SamPa]

Re: The Mathmatical Approach

Many maths people will argue NL Hold'Em is a solved game due to maths and so they say if you play by the maths 100% you should win over time even with those small edges.

What do you think about that? It looks overly simplistic to me. I'd give a 'poker person' with an understanding of the maths an edge over the 'maths person' with an understanding of the poker every day. Reads, assigning hand ranges, recognising betting patterns - all have to be taken into account when deciding on whether you do have the odds or not?

[seanfaz]

Re: The Mathmatical Approach

Many maths people will argue NL Hold'Em is a solved game due to maths and so they say if you play by the maths 100% you should win over time even with those small edges. Re. open-ended straight flush draws i think it's easy to put the money in without considering that if you have a low draw any pair is likely not good and if you make a flush it still might not be good anyways. Re. bankroll i can totally understand someone playing under-rolled and folding likely the favourite hand if they're a recreational player and just want to stay in the game and have some fun but for all serious players it's a must to have good bankroll management so you're comfortable going in with it at marginal times.

But what if you could develop a strategy where you don't play these marginal sitiuations so strongly.......you concentrate on gettting the money in when you're 80% or 100% rather than when you're 52%. You would make money in the long term taking both these routes, but you're less likely to lose money in the short term playing the other way

[Nade]

Re: The Mathmatical Approach

What do you think about that? It looks overly simplistic to me. I'd give a 'poker person' with an understanding of the maths an edge over the 'maths person' with an understanding of the poker every day. Reads, assigning hand ranges, recognising betting patterns - all have to be taken into account when deciding on whether you do have the odds or not?

I agree someone with general poker skills combined with maths skills will have a bigger edge but the general point is that maths is maths. If you go in 100 times as 55% fave you'll most likely show a profit in those situations regardless.

But what if you could develop a strategy where you don't play these marginal sitiuations so strongly.......you concentrate on gettting the money in when you're 80% or 100% rather than when you're 52%. You would make money in the long term taking both these routes' date=' but you're less likely to lose money in the short term playing the other way[/quote'] (sorry in advance for another long post, basically i've learnt a new way of approaching the game by eliminating the dangerous thought that is 'it's ok i got my money in as favourite') This is actually something i have never, for my sins, considered until i read this post and the ones in the other thread. My early poker education came mostly from PL and the common themes were as long as you get your money in ahead in the long run you'll come good. This has stuck with me and i've always justified making marginal plays in the knowledge that i got the money in ahead. After all sessions i see situations where i've lost $30,40,50 in marginal situations and written them off as 'normal' because i got my money in either slightly ahead or slightly behind. The notion of avoiding these marginal situations even if i know i'm putting money in ahead makes a lot of sense instead i'll wait to get all my money in a lot bigger favourite. The key here is the games i play at NL100 are full of weak players and my hand reading is now superb at this level so i often am able to get my money in with a marginal hand as a favourite. It now all makes sense. This leads to a lot of swings up and down where my 55/60% races don't hold up one day, but do the next and explains why i'm struggling to make big profits day after day even though i nearly always know what my opponent has and i know a colossal amount about the game. I've always just taken races for granted and getting money in ahead is good even if in a marginal situation, but i now see that it doesn't have to be 'normal' and it's the reason why i have lots of swings even though i know i'm one of the best at those limits. This doesn't mean i'll rule out putting my money in in a race at all, but i'll definitely be looking to avoid those situations as much as possible from now on and see what happens. It makes so many things make sense. When i started at FTP i was a real nit only getting my money in with way the best of it and i made a lot. As i've got better at hand reading etc. my profits although still good haven't increased at the same rate my knowledge has which has baffled me for a few months (although i had pretty much november through to february away from poker) . It now makes sense that with my better knowledge i've learnt a lot more about what my opponent has which led to getting my money in as a small favourite in many situations. Which leads to swings and not bigger consistent profits. There we are, i've learned a lot today about a new way of thinking and how to maximise profits and minimise swings. This should be the start of something very nice. Cheers.

[seanfaz]

Re: The Mathmatical Approach This is quite an interesting topic which you don't see written very much, but when you think about it its evident in many top players game. If you think about phil hellmuth's tournament style ( i know this is a cash game thread but essentially its the same principle but just related to tournament survival). He (like most skilled players) hates to have to race. He looks at exploiting his edge by raising a lot of small pots in position, winning a little for low risk, trying to go through the tournament without ever being all in with risk. This is the same concept but applied to bankroll management and steady progress in cash games, especially relevant where our skill edge is clear. But there is one danger - good opponents will pick up on such play and could easily exploit it with big bets and by constantly putting us to the test. In referance to the hellmuth example, even an amateur could stop this strategy by simply moving all in every hand. So there are always factors to consider with this play.

[PGremlin]

Re: The Mathmatical Approach I think this approach of avoiding coinflips is a lot more common in Tournament tactics, where you don't want to do to many 55% vs 45% chances for your tournament life. In Cash you can always rebuy if you lose with marginal superior hands. In the long run you should make a profit as long as you can afford the downswings. But if you really are good enough to read your opponents so that you're at least something like 70% vs 30% or better on those crusial big pots then that would be more stable/less swingy. I dunno.... I think the higher you climb on the cash tables the less the edge will be between the players so they can't afford to avoid the margional superior odds without losing to much of their +EV on the long run.

[slapdash]

Re: The Mathmatical Approach

Many maths people will argue NL Hold'Em is a solved game due to maths

I think I have to stick up a bit for mathematicians, since I am one. :) I don't know if "maths people" are different from "mathematicians", but I really can't imagine many mathematicians making an obviously false claim like that. Some interesting points made in this thread. But a lot of the implied criticism (or maybe I'm just being a bit touchy :tongue2) of "maths" is not really a criticism of maths, but of imperfect applications of maths. And I think that's actually something that mathematicians are far more sensitive to than non-mathematicians. A common frustration of mathematicians is that somebody will formulate a problem in mathematical terms and ask for a solution; you'll solve the problem and say "but that's assuming X, Y and Z" and he'll ignore X, Y and Z.

[seanfaz]

Re: The Mathematical Approach I don't think anyone is criticising a mathematical approach, just that there are so many other factors to consider, alot of which are often forgotten

[billy the punter]

Re: The Mathmatical Approach

I think this approach of avoiding coinflips is a lot more common in Tournament tactics, where you don't want to do to many 55% vs 45% chances for your tournament life. In Cash you can always rebuy if you lose with marginal superior hands. In the long run you should make a profit as long as you can afford the downswings. But if you really are good enough to read your opponents so that you're at least something like 70% vs 30% or better on those crusial big pots then that would be more stable/less swingy. I dunno.... I think the higher you climb on the cash tables the less the edge will be between the players so they can't afford to avoid the margional superior odds without losing to much of their +EV on the long run.

The last point isn't necessarily true, most of the big games I've played in have many whales (50% of the runners). Lots of money, not so much ability. I played in this game for some time and it was easier than the £3/£3 at the Vic. A question for those who would be calling (or thinking about it)... Is there any difference between... a £x call knowing you're 50/50 and £x on red on the first spin when you enter the casino?

[PGremlin]

Re: The Mathmatical Approach

The last point isn't necessarily true, most of the big games I've played in have many whales (50% of the runners). Lots of money, not so much ability. I played in this game for some time and it was easier than the £3/£3 at the Vic. A question for those who would be calling (or thinking about it)... Is there any difference between... a £x call knowing you're 50/50 and £x on red on the first spin when you enter the casino?

Interesting... I never played high stakes cash tables. :$ I should learn to be a good whale spotter then if I ever do :loon But that doesn't change my idea that 55% vs 45% should be profitable on the long run on cash, even though it could have a long and nasty downswing every now and then.

[seanfaz]

Re: The Mathmatical Approach

The last point isn't necessarily true, most of the big games I've played in have many whales (50% of the runners). Lots of money, not so much ability. I played in this game for some time and it was easier than the £3/£3 at the Vic. A question for those who would be calling (or thinking about it)... Is there any difference between... a £x call knowing you're 50/50 and £x on red on the first spin when you enter the casino?

Its not quite the same......because don't forget about the pot odds......you may still be taking a 50/50 but you may be getting 1.4/1 on it or even more...... About the whales yeah there are loads of them......i've noticed a lot of players who seem to be regulars that slowly eek out a profit, but they just sit and complain about their bad luck and "fishy calls". The rest of them.......well they sem to have bottomless pockets and just throw their money away!

[Nade]

Re: The Mathmatical Approach

But that doesn't change my idea that 55% vs 45% should be profitable on the long run on cash, even though it could have a long and nasty downswing every now and then.

Of course maths is maths 55% out of 100 = favourite but the point for me is not about pushing these tiny margins because there's no need to at NL100/200. After all my hundreds of thousands of hands this could be the biggest leak to be plugged yet. Even though it defies all mathematical logic it makes a huge amount of sense to me, my game and my bank account.

[SteveO]

Re: The Mathematical Approach A 55% fav hand is the common coinflip of say JJ vs AK allin preflop, but after the flop where say in a certain hand you deem yourself a 55-60% fav and you're getting 1.5-2/1 the odds dictate that you should gamble even if you don't have a made hand.

[billy the punter]

Re: The Mathematical Approach With the coin flip vs red or black question I didn't mean this actual hand/. Hyperthetically if Joe Bloggs made a 10k call for a exact (or very close to) 50/50 then no one would really say much (it seems), yet if he stuck the same amount on red or black he'd be seen a mad gambler. Discuss. :D

[GaF]

Re: The Mathematical Approach

With the coin flip vs red or black question I didn't mean this actual hand/. Hyperthetically if Joe Bloggs made a 10k call for a exact (or very close to) 50/50 then no one would really say much (it seems), yet if he stuck the same amount on red or black he'd be seen a mad gambler. Discuss. :D

Sticking £x on red at even money for a 18/37 chance of winning is a losing bet. Calling £x to win £x+£y (i.e. odds against) with a 50% winning chance is a profitable bet. Assuming bankroll isn't an issue and your opportunity to place the wager recurs significantly enough, then you are financially mad to bet on red, but are onto a profitable thing calling your 50/50 shot (you never get worse than evens in poker if you are calling an all in). One of the bets is profitable and makes money. One of the bets is losing and costs money. They're totally different.

[SteveO]

Re: The Mathematical Approach I wonder how many PL'ers never actually calculate the pot odds when they play poker I reckon theres quite a lot.

[billy the punter]

Re: The Mathematical Approach

Sticking £x on red at even money for a 18/37 chance of winning is a losing bet. Calling £x to win £x+£y (i.e. odds against) with a 50% winning chance is a profitable bet. Assuming bankroll isn't an issue and your opportunity to place the wager recurs significantly enough, then you are financially mad to bet on red, but are onto a profitable thing calling your 50/50 shot (you never get worse than evens in poker if you are calling an all in). One of the bets is profitable and makes money. One of the bets is losing and costs money. They're totally different.

Only if there are multiple opportunities. If both are one off they they aren't totally different, in reality I mean. On a 5k stake... It's possibly for you to be taking 5003/5000 on the poker bet. The red is 5000 at 18/36.5 isn't it? So you're taking evens about a slight odds on shot. Ok so there is a difference, but are they as different as the theorists make out? If you're not repeating the bets aren't they both crazy gambles?

[billy the punter]

Re: The Mathematical Approach

I wonder how many PL'ers never actually calculate the pot odds when they play poker I reckon theres quite a lot.

Slightly different point but knowing if your opponent understands odds is pivotal in tourn play when stealing etc.

[Nade]

Re: The Mathematical Approach Made $1k today, shows what a fresh mind with fresh ideas can really do for my game. Also running hotter then the sun helps ;). Most of the big pots i won were donations but the races i got it in with 75% of it mostly. Only twice did i get involved in a race, once early in the day when i called with overpair TT vs a flush draw and lost (exact scenario i was trying to avoid but it was right at the start it's pretty hard to make immediate adjustments.) and then late on had a blind v blind battle i shoved in with K high flush draw with over card and straight draw plus fold equity felt i had a vgood chance to win the pot, he had aces but i hit the flush. In only 2 hands did i lose between $30 - $99, as i've said a few times looking to curb the amount of average sized pots i lose as they're often with the marginal hands and this is a great start.

[billy the punter]

Re: The Mathematical Approach

Made $1k today, shows what a fresh mind with fresh ideas can really do for my game. Also running hotter then the sun helps ;). Most of the big pots i won were donations but the races i got it in with 75% of it mostly. Only twice did i get involved in a race, once early in the day when i called with overpair TT vs a flush draw and lost (exact scenario i was trying to avoid but it was right at the start it's pretty hard to make immediate adjustments.) and then late on had a blind v blind battle i shoved in with K high flush draw with over card and straight draw plus fold equity felt i had a vgood chance to win the pot, he had aces but i hit the flush. In only 2 hands did i lose between $30 - $99, as i've said a few times looking to curb the amount of average sized pots i lose as they're often with the marginal hands and this is a great start.

I'm glad this thread has been recieved differently to the last one I posted on the subject when I first came to the poker section last year. ;) :lol

[GaF]

Re: The Mathematical Approach

Only if there are multiple opportunities. If both are one off they they aren't totally different' date= in reality I mean. Incredibly unlikely :unsure You'd need to be playing a $1/$2 game and someone open shoves for $5000!!! But even so - it's odds against and if you're even money it's positive ev. Going back to your point - I wouldn't say much if you called with exactly even money, because it's positive ev - that's all that matters to a (cash) poker player playing within his means. You will win (In the long run) There are 18 reds. The 37 is 18 Red, 18 Black and one zero so it is 18/37. On American roulette it is 18/38, with two zeros. (I think :unsure) It is a negative ev proposition. You will lose (in the long run) For sure - but that means you're playing outside of what you can afford and you should not be at the table! Sitting at the table was a crazy reckless gamble, not your decision on this hand.

If you are playing poker, within your bankroll, then there will be multiple opportunities

[billy the punter]

Re: The Mathematical Approach

There are 18 reds. The 37 is 18 Red, 18 Black and one zero so it is 18/37. On American roulette it is 18/38, with two zeros. (I think :unsure) It is a negative ev proposition. You will lose (in the long run)

You will lose? You think that I do not know that? Think I'd be the worst professional gambler in history if I didn't, don't you? I should've said odds and evens as it's a better bet - you get half your stack back for zero, so odds/evens is NOT 18/37.

For sure - but that means you're playing outside of what you can afford and you should not be at the table! Sitting at the table was a crazy reckless gamble, not your decision on this hand.

Dress it up all you like, but making a 50/50 call for massive amounts (even if getting slightly over evens) is a crazy, unnecessary gamble when you have a massive ability adge in a game. This is the whole point of the post.

[seanfaz]

Re: The Mathematical Approach

If you are playing poker, within your bankroll, then there will be multiple opportunities Incredibly unlikely :unsure You'd need to be playing a $1/$2 game and someone open shoves for $5000!!! But even so - it's odds against and if you're even money it's positive ev. Going back to your point - I wouldn't say much if you called with exactly even money, because it's positive ev - that's all that matters to a (cash) poker player playing within his means. You will win (In the long run) There are 18 reds. The 37 is 18 Red, 18 Black and one zero so it is 18/37. On American roulette it is 18/38, with two zeros. (I think :unsure) It is a negative ev proposition. You will lose (in the long run) For sure - but that means you're playing outside of what you can afford and you should not be at the table! Sitting at the table was a crazy reckless gamble, not your decision on this hand.

So lets say you sit in a cash game with $5k, and its 5% of your bankroll - nothing wrong with that......you can afford it. First hand this spot arises, the cards are face up. You call because you will make money in the long run - 3/5000??????? Thats bad poker, surely!! That is almost pure gambling - and for $5k!!!

[Milber]

Re: The Mathematical Approach

I wonder how many PL'ers never actually calculate the pot odds when they play poker I reckon theres quite a lot.

I think that the majority would consider this but i'm not so sure they are working them out correctly, if you consider a flush draw post flop 9 outs is about 36%. but if you believe your opponent has paired the board on the flop and you have 2 overcards to the flop that is another 6 outs or 24% that would make 60%. which is quite a good favourite there could also be odds of runner runner for a straight, or maybe you only have 1 over card to your opponents pair etc etc. Basically what I'm saying is there are lots of other things to consider rather than just basic maths not to mention table image and position and why maths is important I think it is harder to call a coin flip or a 45/55 than it is to get your money in first and give your opponent the decision.

[seanfaz]

Re: The Mathematical Approach

I think that the majority would consider this but i'm not so sure they are working them out correctly, if you consider a flush draw post flop 9 outs is about 36%. but if you believe your opponent has paired the board on the flop and you have 2 overcards to the flop that is another 6 outs or 24% that would make 60%. which is quite a good favourite there could also be odds of runner runner for a straight, or maybe you only have 1 over card to your opponents pair etc etc. Basically what I'm saying is there are lots of other things to consider rather than just basic maths not to mention table image and position and why maths is important I think it is harder to call a coin flip or a 45/55 than it is to get your money in first and give your opponent the decision.

But you can work this out mathematically. You can take factors such as table image, position, how active a player is...... etc and use them to assign a hand range. You can then see how your hand fares against that range on an odds calculator such as pokerstove and see if you are a favourite against that range. A lot of online pros play this way........the +EV method if you like. This is not the debate here, this is about always making a marginal +EV move regardless of bankroll and money etc.