Haha, priceless!
Level 17: Hand v Range
50/100 tables here I come! I can tell I’m finally thinking less about “what hand” my opponents have, and more about the full range of hands that would make sense given the play so far.
Ummm, well I guess I’m mostly raising hands that I think will be best most of the time,
Yes, but you can mix it up a bit, depending on table factors. For example, in a tournament if you are the big stack on the table, you might want to raise with bluffing hands like small pocket pairs or suited connectors, with the intention of 1) improving your position, 2) winning the pot with a bluff at the flop, and 3) actually hitting a draw and semibluffing the flop, 4) actually hitting two pairs, trips, or something that can beat top pair.
For 1) if you raise from the cutoff with the intention of knocking out the Button, you may steal the button, and then put yourself in position, so that if a caller from the blinds leads out, you can re-evaluate before putting in any more chips.
For 2) if you have position there are many flops where a smaller stacked caller will be unable to continue against your continuation bet, since you have already represented a big hand preflop. Let’s say you raise with 8 9s. The flop comes QQ3. Now if the villain called your raise with Q3, then you are toast, but odds are that he did not. The fact that there are two Qs in the common cards reduces the odds that he has one of the other Qs.
If he has 33, then you are toast, but 33 occurs only at the same frequency as AA, so not too often. So in most cases he will not be able to call a continuation bet even if he has a flush draw, because a flush could be beaten by a boat that he does not have. And in his mind, he is going to be thinking that you could easily have raised with AQ and that he may be toast.
It is very satisfying to win a big pot when you have nothing, especially since you may pick up the mighty AA and just take the blinds and nothing more.
Similarly, you may win even bigger pots by 3-betting with midrange suited connectors from position. If the flop comes without broadway cards, who is to say that you have not 3-betted with 88 or 99, made a set, and have AA crushed?
If you are small stacked in tournaments, it is often better to shove preflop with your better hands. If you can knock out a few limpers you may pick up a nice pot, and if you are called by some suited ace, or small pair, you may well double up, at which time you can evaluate your opening strategy. Of course if you run into AA, you are probably dead, but then every single player in every tournament is knocked out, bar one.
Postscript: These kind of strategies can be difficult to implement in low-entry play money tournaments, because many players will fold to no bluff and will call any raise preflop with any hand, but they will work better if you play at levels where the players are a bit more rational and have some understanding of value and odds.
Less limping probably should be Level 6. And limping in the blinds is obviously very different from open-limping or over-limping.
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Maybe it’s me, but I find SPR to be a more complex concept that some of the subsequent levels, and probably would place it at a higher level. Levels like Table Image, 3-betting, and Less Limping are easier concepts to apply. Concepts like table image have been around a long time, while SPR relatively new. That said, your explanation of SPR is one of the most concise and accessible I have read.
Level 18: The Semi Bluff Shove
Ohhhh… here’s another tool for the tool kit. It seems that I can sometimes make big, all in bluff bets on the flop or turn thanks to something called fold equity… errr… what’s that? Oh, hmmm… the likelihood of the opponent folding multiplied by my gain in equity when they do fold.
OK, let me see if I can think through this. If I have 9 outs on the turn to a nut flush, and a pot of 10,000. I have 12,000 and shove (opponent covers me). I don’t really know my equity, because I don’t know what my opponent holds, but let’s just say that I’m behind right now, and that I have no outs other than the 9 flush cards. So I’ve got 9 river cards left where I’ll win, and 37 cards where I lose (though it might actually be better than that). So my equity would seem to be at least 9/46, or almost 20%. That’s a losing play if my opponent calls me every time, but they won’t call every time. On the flip side, if they fold every time, it is also obvious that I win.
Hmmm… what happens if they call half of the time (let’s pretend 5 calls and 5 folds)?
- 5 times they fold, and I win $10,000 each time, for $50,000 in winnings
- 4 times they call and I lose the $12,000 I bet, for $48,000 in losses
- 1 time they call and I win both the $10,000 that had been in the pot, and the $12,000 they called, for $22,000 in winnings
Wow… that’s certainly cool. Even if they call half of the time, over 10 replays, I’d probably lose $48,000 on the hands where I got called and lose, but would probably win $72,000. I wasn’t expecting that even if they called half the time I’d still be winning… I wonder how often they’d need to call before I would no longer win money…
What if they call exactly 2/3 of the time (will use 15 hands this time to make the number easy)?
- 5 folds, still with $50,000 in winnings
- 8 times they call and I lose, for $96,000 in losses
- 2 times they call and I win, for $44,000 in winnings
Wow, I lost $2,000 that time, but I can’t believe how close it was to be being break even, even then. So even slightly over betting the pot, and on the turn, when the chance of making my draw has deteriorated, they need to call about two thirds of the time before this becomes a losing play.
Yeah… I’ve changed my mind about 100 times on the order to do this in, LOL. Really level 13 is probably better titled: Wow, I think I have a 6% grasp of effective stack depth and SPR now!!!
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Yes.
To be honest I had never heard of SPR before and had to look it up, but it is one of those things that one automatically calculates on every hand when playing in tournaments, where increases in the blinds completely change the ratios.
An obvious example is that when you come to the five-minute break at the end of the first hour of a tournament, you will be restarting at higher blinds, that dramatically change the ratios.
When I’m playing tournaments will also look at the half stack pot ratio. What does that mean? Well, lets say I started with 5000 chips and am doing fairly well after 29 minutes and have 7500 chips, which is slightly above average at this point. If I am playing against a smaller stack, I have to be aware that he may well shove the flop on a bluff or a single pair.
Let’s say he has 3500 chips. If he shoves the flop and I call and lose, then I am down to 4000 chips, which is less than the starting stack with a blinds increase coming in one minute, and some other stacks in the 10,000 to 15,000 range. Being down to 4000 chips is not the end, but I will immediately have to switch to a small stack strategy.
That being the case, I am more likely to tighten my raising range when this player is in the BB, to reduce the chances of losing a lot of chips by folding when he fires at the flop.
(One thing that is never much discussed is that if you raise with an A in your hand, the very fact of you having an A somewhat decreases the probability that BB has an A, and if you both have one, then the probability of an A on the flop is significantly reduced, and if you have an A and another comes on on the flop, the probability of villain having one is reduced. Maybe this is too obvious to be worth saying.)
And as I have said here before, in the early rounds of tournaments you can play cards that only have drawing strength and no high card strength, based on implied odds, but once the blinds go up, drawing hands lose value as you probably cannot afford to play post-flop as it will be all or nothing–which is just another way of looking at pot to stack ratios.
Having said that, sometimes you just have to take a shot and get a bit lucky. In this hand I fired from the BB on the flop with top pair, no kicker plus flush draw and was called by top pair, better kicker, but luckily I made my flush and dodged another flush card on the river. In my opponent’s position here I would not have instacalled the shove on the flop bet due to pot to stack ratio. In other words, did he really want to put his whole tournament on calling that bet?
Level 19: Pot Control
Interesting… I’ve now run into this idea called pot control in a number of places. It seems like an alternative way of saying it might be that there are hands you want to play for a big pot, and other hands that you want to play for a small pot, with top pair actually being an example of the latter type. This often seems to get described in terms of “streets of value”, or how many bets you think you can make across the flop, turn and river, and still usually get called primarily by worse hands. So the notion then is, that with a hand like top pair, if you think you can’t get 3 streets of value from a given opponent, then you want to decide where you might best want to check or bet smaller to try and control the size of the pot.
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Level 20: Counting Combinations
This seems useful…
- 6 combinations of cards that can make any pocket pair
- 4 combinations of cards that can make any specific suited hand
- 12 combinations of cards that can make any specific unsuited hand
Wow, so I can use that to kind of measure the relative abundance of certain types of holdings in the ranges that I’m facing. Seems like that should help at times when I’m trying to make a tough call, and want to try and decide on the relative abundance of different kinds of hands that might be betting at me… I suppose I could also flip that, and use the same type of thinking to decide how many hands might be out there that would be likely to call a certain bluff…
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Level 21: Patience
Yay! I’ve finally started playing medium stakes, and I think a key improvement has just been staying more patient. Heads up or short handed I don’t seem to have a problem, but at full ring with most of the seats full, it seems like I’ve had a hard time waiting for the hands I’d been wanting to play (even using a range bigger than I switched to for level 9). It seems like it is one thing to raise and get called by the big blind and then fire a continuation bet, and something else to raise and get called by the cut off. I’m beginning to realize that the latter just has a much stronger range, and I can’t count on him having air after the flop as often.
So just doing a better job of waiting for the right hands pre flop, and then also not feeling like I have to win every hand that goes post flop, has helped me to avoid a lot of the spots where I was losing big pots. It seems it is not only about maximizing winnings, but also about minimizing losses?
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Level 22: Unwanted Multi-way Pots
I’ve been noticing that as people check around the table, by the turn or river it’s often possible to pick up pots with small bets. Sometimes someone has been trapping, and will fire a big raise… well that’s an easy fold. Worse is when someone has been checking with a marginal hand, and does call, as then your covert operations are uncovered. But if the bets are small enough, they don’t need to work that often to be profitable.
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Level 23: Balance 1
So much talk about balance on the internet, but I haven’t been sure what it really means in terms of how I should play, but I was just thinking about the semi-bluff shove move I started trying out with a lot of success. In the case where I had 20% equity, and was shoving for 1.2 times pot, it was surprising to realize that my opponent had to call almost 2/3 of the times that he had a better hand than me to keep the play from being profitable. But even if he realized that I’m almost always bluffing when I make that move, is he really going to be able to call with ace high or even a weak pair?
But then I wondered… what if I wasn’t always bluffing? What if half of the time I have a moderately strong hand that has 60% equity against his 2/3 calling range, and 50% equity against his calling range when he’s calling 50% of the time? Let’s also say the starting 10k pot represents 100 big blinds. Those same scenarios now:
40 hands where he calls half of the time:
- 20 times I have a hand with 20% equity
- 10 times he folds and I pick up the 10k pot for 100k profit
- 8 times he calls and wins and I lost the 12k bet for 96k loss
- 2 time he calls and I hit my draw to pick up original pot and his call for 44k profit
- 20 times I call with made hand that has 50% equity
- 10 times he folds for another 100k profit
- 5 times he calls and wins and I lose 60k
- 5 times he calls I win for 110k profit
Winnings: 354k
Losses: 156k
Profit over 40 hands: 198k
Profit per hand: 4.95 k
Profit per hand in big blinds: 49.5 bb
So I’m still crushing there… and now for the 2/3 call variant that I was losing previously (and since he’s calling with a bigger part of his range, we’re assuming the equity of our made hands went up from 50% to 60%):
- 10 times he folds: 100k profit
- 10 times he calls and I have a draw with 20% equity
- 8 times I lose and I lose 96k
- 2 times I win and pick up 44k
- 10 times he calls I have a made hand with 60% equity
- 6 times I win and pick up 132k
- 4 times he wins and I lose 48k
Winnings: 276k
Losses: 144k
Profit over 30 hands: 132k
Profit per hand: 4.4k
Profit per hand in big blinds: 44 bb
Wow… it almost feels like there is no defense. If he folds more than half of his hands, winnings overall increase further, and if he calls with more than 2/3 of hands, the equity of my made hands increases further, and what kind of hands would he need to call with to even do that?
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But surely the hands that he calls with will be more promising than the hands he folds, and perhaps he will re-reraise you with his strongest draws and some bluffs-depending, of course, on stack sizes and how many chips you have behind. You may win lots of small pots, but lose a majority of hugs pots. There is not much point calling if you cannot beat a bluff.
That the hands he calls with will be more promising than the hands he folds is already baked into the math.
It’s not possible to re-raise an all in bet, which is what this is looking at (an all in bet on the turn, betting 120% of pot).
The EV of the small pots versus the large pots is also already baked into the math.
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I’d also note that this is something of a worst case scenario, assuming that with the 50% of the time that you bluff, you are always behind, and have only the 20% equity provided by hitting your draw. In practice, you will often have additional outs that you are not counting on, and do better with this move than described, whether you balance it with value, or never play it except as a semi-bluff.
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I’m just noticing I have a correction that is needed above: “20 times I call with a made hand that has 50% equity” should have been “20 times where he calls when I have a made hand with 50% equity against his range”, as this is all spots where hero makes an over-bet shove on the turn.
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Level 24: Blocking Bets
Oh, more tricks for the tool kit. Yet another way to play a draw. Especially in a relatively passive environment like this, it seems you can often donk into the aggressor with a small bet, as many people seem hesitant to make a full sized raise, and so you get to see the next street at a cheaper price than you would have otherwise (even if they min raise you), and occasionally even take down the pot.
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Level 25: Player Type Classification
It’s really becoming quite clear that not everyone is playing in the same style. Pre flop ranges differ to an amazing margin, and with those same ranges some players are always limping, others are always raising, and others are playing a mixed strategy. Being able to quickly identify broad play types seems likely to help find the best lines against those players.
- Super Fish: plays almost every hand to the river, and will call most bets before the river with any kind of hope to improve, but then will fold on the river to almost any bet
- Trappy Fish: plays most hands, and will nearly always call with any draw, and never bets without a big hand
- Nit: very tight pre-flop ranges, and bets represent very strong value; often tends to over fold
- Maniac: loves to bet, without too much concern for the cards they have
- TAG: tight pre flop, with moderately high aggression frequencies on all streets
- LAG: plays more hands pre-flop than a TAG, and is often even more aggressive post flop
Now that I’ve been playing medium stakes for a while, I think I’m mostly seeing trappy fish and nits, a few super fish, along with an occasional maniac?
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Level 26: Bet Sizing 101
OK, I’ve pretty much always been betting 1/2 pot or pot so far. Why? Well, I suppose just because I see that they have buttons for that. But I just recently moved up to 200/400, and started to wonder if using some different bets sizes wouldn’t be beneficial.
I’m imagining a hypothetical situation where I have a value hand that is in front of 90% of a villain’s range. If I bet pot (or especially more), it feels like I might be getting called more often by the 10% that is ahead of me than the 90% that is not, and so a really big bet feels like it just loses money.
As I move my sizing down, I think the calling range gets wider and wider as my bet size gets smaller and smaller. At 200/400, $400 is the smallest bet I can ever make, and so if the pot is $10,000, let’s just imagine a $400 bet gets called by 90% of villain’s range, and so I win $400 8 times for every 1 time I lose, for a volume adjusted win rate of $2,800. Let’s imagine a bet of $7,500 is the break even point, where the villain calls with 20% of their range, so that they are ahead of me exactly as often as they are behind me. So the min bet out performs that, and all larger bet sizes in this thought experiment.
But what if I bet $4,000? I don’t really know what the call rate will be now, but let’s pretend it is now the top 30%, meaning I win twice as often as I lose. Using our initial 9 frequency brackets from the min bet, results are now {fold, fold, fold, fold, fold, fold, win, win, lose), or {0,0,0,0,0,0,+4k, +4k, -4k), for a volume adjusted win rate of $4,000 (I’m not winning as frequently anymore, because their are fewer calls).
So I’m guessing that, without a nut hand, there is usually a sweet spot for maximizing winnings that is somewhere between a min bet and a huge over bet of the pot, but not knowing how my opponent shapes their calling range in response to different bet sizes, sure does seem to make it difficult to figure out what the right size is…
But still, at least the first part seems like something I can put into effect: if I have thin value, betting big will just cause me to lose chips, while by reducing my bet size, I can expand my opponent’s calling range to the point where they are calling me with worse hands more often than they call with better.
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