Small Stack vs. Big Stack

[Mathemagician]

[ QUOTE ]
This is what I suspected you meant and it is just ridiculous. If I have a $10,000 bankroll in a game with $2 and $4 blinds in which I am a reasonable favorite over you, then my risk of ruin is certainly negligible, no matter what your stack size is.

[/ QUOTE ]
If his stack size is infinite your ruin is guaranteed. Also, as the ratio ofhis stack size to yours increases towards infinity, your risk of ruin increases towards certainty.

M

[pzhon]

[ QUOTE ]
pzhon,
You're missing my point,

[/ QUOTE ]
That's possible, but it is more likely that I'm dismissing your point as trivial and irrelevant.

[ QUOTE ]
I'm not arguing that me setting you all-in is +EV for me (in the long run),

[/ QUOTE ]
To be clear, the plays you were suggesting are massively -EV, particularly when overused. Someone who likes money should not open-raise to 25 BB. If some fish is going to throw a party like that, it's not a threat to me. It means I am going to average several times my usual win rate.

[ QUOTE ]
my point is that if you don't have enough money, when I stack you, you're through and you and your +EV will be on the rail hugging your nuts.

[/ QUOTE ]
First, that's trivial. Come on, who do you think doesn't understand this?

Second, no one is advocating playing while underbankrolled. At the highest level I play, I have hundreds of buy-ins in my gambling bankroll. I still sometimes buy in short in smaller games where I have thousands of buy-ins. Recent polls have suggested that most 2+2 forum posters are overbankrolled, too.

Third, if someone were underbankrolled, it would be better to stay short-stacked to decrease variance, so you put a smaller fraction of your bankroll at risk at a time. In fact, this is the advice given in the SSNL forum to those who fall to under $100 on a site where the lowest level is NL $25.

So, you are arguing that underbankrolled short stacks should be worried... about something that should tell them to buy in short if they are underbankrolled. That's hardly an argument against playing with a short stack in general. Others are not assuming the short stacks are underbankrolled.

[ QUOTE ]
The problem with your reply is that it assumes that you have an infinite bankroll, if your SS is all of your money when I break you, you're done.

[/ QUOTE ]
I made no such assumption, and once again, it is ridiculous to assume that the short stack represents someone's entire bankroll. The player buying in for $200 was assumed to have $1000 in his pocket, and you can bet that $1000 did not represent his entire bankroll, either.

Proper bankroll management does not mean you have to avoid all risk. You can accept variance if it comes with an edge. The edge for a small stack against a bully can be huge, greatly exceeding the edge:variance ratio of playing normal winning poker. Not only can you win a lot from a bully, but it may be safer than taking money from opponents who are trying to win money on average.

[ QUOTE ]
Also I wasn't saying that the 20x raise was to steal the blinds, it isn't.

[/ QUOTE ]
I don't care what the intent was when making such a grotesque overbet. If I have 40 BB, I will push over that with anything significantly ahead of the range you are raising, and give up the blinds with anything lower. This simple strategy is enough to make you regret raising so much, if you like money.

[ QUOTE ]

And the deep stacks aren't lessening their raising values, they're just playing regular poker. The other deep players will be calling or re-raising at the same level, since these raises are proportionate for their stacks, it's the 'normal stacks' and SS that will have problems.

[/ QUOTE ]
They won't be having problems. They will be enjoying the party.

Suppose you saw someone with 1000 buy-ins who was moving in preflop every hand. Would you run screaming in terror because you don't have an infinite bankroll, or sit down with glee? I would sit down. If I were underbankrolled, I would sit down and buy in short. I would expect to win at many times my normal rate.

[ QUOTE ]
His +EV would be useless to him if he had to spend his Vegas trip on the rail and that is why he stayed in Ed's limit game.

[/ QUOTE ]
You seem to love imagining someone is "hugging his nuts on the rail." Here is something to think about: Suppose you have $1000, a tiny fraction of your bankroll, in your pocket. You are offered a great opportunity: You can double up or go bust as a 60:40 favorite. Would you take it? Of course. Wait! An hour from now, you will be offered a chance to double up or go bust as an 80:20 favorite, and you definitely want to take advantage of that. Should you wager everything now? Wager $500? Wager $0? I have put your expected balance after each choice in white:
<font color="white">
Wager $1000 now, and let it ride: $1920
Wager $500 now, and bet everything later: $1760
Wager $0 now, and bet everything later: $1600
To risk busting out is the best way to take full advantage of the opportunities. That the first opportunity was +EV was not useless.
</font>

[jason1990]

[ QUOTE ]
If his stack size is infinite your ruin is guaranteed.

[/ QUOTE ]
I'm not going to play an infinitely long session with the guy. I'm not going to play until one of us is broke. I'm just going to play my normal game for a while and try to win some money off him (after all, I assumed I am a favorite over him). I imagine, as usual, I would stop when I got tired or had something better to do with my time. If I'm properly bankrolled for an "ordinary" game, wouldn't I also be properly bankrolled to play against him? Should I really be worried about going broke in this situation? Should "hugging my nuts on the rail" really be a concern for me here? I don't see it.

[pzhon]

[ QUOTE ]
[ QUOTE ]
This is what I suspected you meant and it is just ridiculous. If I have a $10,000 bankroll in a game with $2 and $4 blinds [and $200 maximum buy-in] in which I am a reasonable favorite over you, then my risk of ruin is certainly negligible, no matter what your stack size is.

[/ QUOTE ]
If his stack size is infinite your ruin is guaranteed.

[/ QUOTE ]
While that is technically true, it is not true in a useful sense. It is true if, having doubled up so many times that you have millions of dollars on the table and only a few thousand dollars left in your pocket, you are compelled to try to double up the money on the table again as a slight favorite. It is more reasonable to assume that you are following the Kelly Criterion or something similar, and will quit when the amount of money you have on the table is a significant fraction of your bankroll.

Suppose you have the ability to get all-in as a 3:1 favorite. The Kelly Criterion (maximizing the expected logarithm of your bankroll) suggests that the optimal amount of your bankroll to wager is 1/2, and that you should walk away if asked to wager more than about 84% of your bankroll. You only need to double up 8 times to have $51,200 on the table, which will represent enough of your bankroll that you should quit.

The probability of doubling up 8 times is about 1/10. The probability that you double up 8 times in a row in your first 25 attempts (without cutting your $10k in half) is about 92.8%, at which point you have $56,200-$61,000 and quit.

The 7.2% of the time your bankroll gets cut in half, you should lower your sights, and should quit after you have $25,600 on the table, doubling up only 7 times. You succeed about 1/7.5 of the time, and have 13 attepts before your bankroll is cut in half again. You end up with $28,000-$30,400 84.5% of the 7.2%. You fail again only 1.1% of the time. At that point, you should continue, but suppose you quit.

By using the Kelly Criterion, which many people find too aggressive, your bankroll is cut to $2400 only 1.1% of the time. 98.9% of the time, you end up with at least $28,000, and your average ending bankroll is over $57,000. This is a great deal.

The amount your opponent has over $100k is irrelevant because you will sensibly quit when you have 5/6 of your bankroll on the table.

[pzhon]

[ QUOTE ]
the SS is likely to get broken ... and that it creates difficulties for a SS, that if you play with a larger stack you won't have.

[/ QUOTE ]
You seem to be erroneously assuming that a short stack is underbankrolled. Do you mean to say that if you have a big stack, and you are set in, you don't have a problem? So, having a big stack guarantees that you are not underbankrolled? In fact, the mathematics says the opposite: You may have a proper bankroll to handle a short stack while you are underbankrolled to have a big stack.

When I have accumulated several buy-ins, I don't feel I can bully short stacks with a half buy-in. If they bust out, they can rebuy for the exact same amount. I feel I can threaten someone who has multiple buy-ins, since they don't want to lose what they have worked so hard to achieve, and those buy-ins represent many hours of expected profits for a good player. If they bust out, they can only buy in for the table maximum.

[jason1990]

Thanks for this informative post. You mentioned some people find the Kelly Criterion too aggressive. Are there any commonly used alternatives?

[Ed Miller]

[ QUOTE ]
They're not setting them in before the flop with these hands (that would be stupid), but rather calling SS raises with them and setting the SS in when they hit something better than TPTK. My point is that this kind of player will do these things to a SS, but not to a larger stack, who if it hits against him could cripple him.

[/ QUOTE ]

The implied odds simply aren't there for the big stack. Say we're playing $2-$5 blind, and I have a $100 stack. You have a $2 bazillion stack. I make it $20 to go and turn over my hand... AA. You have 76s. You call the $20. My strategy on the flop is to bet $80 no matter what.

You have to fold almost every time. You only get to call when you flop two pair or better (something over 20-to-1 against... not sure what the exact number is) or a big draw (straight/flush draw, or a pair and a straight or flush draw). That means you are folding nearly 9 times out of 10. Hell, I'll give you 8 times out of 10, 1/10 with two pair or better, and 1/10 with a big draw because I'm too lazy to do the real math. And I'll give you 100% winrate on two pair or better, and 50% winrate on big draw. I'm spotting you a lot of equity there, but you'll still get hammered:

EV = 0.8(-20) + 0.1(100) + 0.1(0) = -16 + 10 = -6

You keep talking about how the SS won't know if he's beaten or not. He doesn't care. He stacks off EVERY TIME and shows a healthy profit. That's the whole point of the SS strategy... stacking off EVERY TIME is profitable. Big stack can't bully small stack. Small stack just calls.

[soah]

[ QUOTE ]
[ QUOTE ]
You seem to be oblivious to the very basic gambling concept of Expected Value.

Let's say you start with $3000 and your opponent starts with $200, and you bully him around by constantly setting him all-in when you're a 2:1 dog.

1/3 (27/81) of the time he will lose the first hand and go home. You end with $3200.
2/9 (18/81) of the time he will win the first, lose the second, you end with $3200.
4/27 (12/81) of the time he will win the first two, lose the third, you end with $3200.
8/81 of the time he will win the first three, lose the fourth, you end with $3200.
16/81 of the time he will win all four times. Now he has gone from 200 -&gt; 400 -&gt; 800 -&gt; 1600 -&gt; 3200 and you end with $0.

So assuming that you will continue bullying him until one of you goes broke, at which point the game ends, you will make a $200 profit 65 times out of 81, and lose $3000 16 times out of 81. (65/81 x 200) + (16/81 x -3000) = 160 - 593 = -433

You lose an average of $433 to each person that you try to bully. So congratulations. You're one of the millions of fish that make the games good.

[/ QUOTE ]This is not quite right. He still has $200 left at the end, not $0.

M

[/ QUOTE ]

3000 - 200 = 2800
2800 - 400 = 2400
2400 - 800 = 1600
1600 - 1600 = 0

[soah]

[ QUOTE ]
[ QUOTE ]
This is what I suspected you meant and it is just ridiculous. If I have a $10,000 bankroll in a game with $2 and $4 blinds in which I am a reasonable favorite over you, then my risk of ruin is certainly negligible, no matter what your stack size is.

[/ QUOTE ]
If his stack size is infinite your ruin is guaranteed. Also, as the ratio ofhis stack size to yours increases towards infinity, your risk of ruin increases towards certainty.

M

[/ QUOTE ]

I have a five-figure bankroll to play 2/5 NL. There are hundreds of 2/5 NL games available, each of which is played at various times by hundreds of different players. Each of those players has thousands of dollars they can afford to lose at poker. Their combined bankroll is somewhere in the tens or hundreds of millions of dollars. I can play 2/5 NL every day for the rest of my life and still never run out of opponents. This does not mean that my ruin is a virtual certainty.

There are two reasons for this. The first is because I am only buying in for a small portion of my bankroll. Once a day, I quit and go home, and the next day I buy in again for just a small portion of my bankroll. So I might briefly have $2000 on the table, but at the end of the day, $1500 goes into the bank and the next day I start over with $500 on the table. I have a significant skill advantage over my opponents so my bankroll is growing continuously. Each day my risk of ruin gets smaller. How much money my opponents have is irrelevent. It does not matter at all to me if I play against the same guy every day who has $10 million on the table, or if I play against thousands of different opponenents who each have $1500 on the table. I'm never putting my entire bankroll into play. If it were true that a player was certain to go broke if their bankroll was drastically smaller than their opponents', then there would be no such thing as a professional poker player, because all poker players would be broke. This is obviously not the case.

The second reason is because I am not playing infinitely long. If I have a million dollars, and I flip a coin for one dollar, then I would eventually go broke, if I played infinitely long. However, if I only flipped the coin 999,999 times, then my risk of ruin is exactly zero. As a poker player, I am dealing with a finite amount of playing. I will play until I don't want to play anymore... not until I've bankrupted every single opponent I can find, or lost my own roll in the process.

[grimel]

The "real" question is can a SS bully the big stacks?