So this article is about why paying more rake is better!
I’m joking. Please don’t hurt me.
Or am I?
At face value, all-in cash out is an additional way for PokerStars to generate extra rake from the variance averse players. If that’s all you use it for and you use it all the time without questioning why, that’s what will happen. However, I am here to tell you that under certain circumstances this feature can be helpful, especially in the context of Short Deck/ 6+. Why I can hear you ask?
Compared to regular No-Limit Texas Hold’em:
- Equities run very close.
- The game plays much more shallow than it appears.
- Players are all-in much more often, both preflop and on the flop.
Now I know what you’re thinking: „All this means is that the game has higher variance! We’re using all-in cash out to reduce variance and paying more rake! More rake is bad so all-in cash out is bad!“
Sighs.
If that’s how you think I doubt I’ll be able to change your mind. If I’ve made you curious enough by telling you it’s not that simple, read on.
All-In Cash Out: Surprisingly Simple
See what I did there?
I wasn’t lying though. It’s just that the all-in cash out feature by itself is actually pretty simple. All I’m going to do here is use the PokerStars page on cash out and make it a bit easier to understand. First off, you and at least one other player must be all-in. Your hand must have at least 1% equity. This means that if you’re drawing dead or on the river this feature cannot be activated even if you are all-in.
Once those conditions are met and hands are revealed, PokerStars will ask you if you want to use the all-in cash out feature. This will only happen if you do not have the option disabled in the PokerStars lobby settings.
„That’s great but you still haven’t told me what it actually does.“
Getting there. Don’t worry.
Put bluntly, it lets you cash out your equity in the hand immediately. After rake of course.
That’s it? Sadly…No! For giving you the privilege of immediately taking your money out of the hand, PokerStars will keep 1% of that money as a fee.
Let me give you a step by step, easy to understand example:
- You and another player are all-in. You both have exactly 50% equity in the pot.
- Pot is 100$ and the rake is 3$.
- We remove the rake from the pot: 100$ 3$ = 97$.
- We multiply the pot by our equity in the pot: 97$ * 50% = 48.50$.
- We remove the 1% fee for using all-in cash out: 48.50$ * 99% = 48.02$.
- We immediately receive 48.02$ and our involvement in the hand is over.
If you want the quick and dirty formula:
- Cash out value = (Pot Rake) * Equity * 99%
Easy as pie right?
What happens to the other player? If they also used the cash out feature, same result. If they didn’t use the feature, then the hand goes on as usual. If they have the best hand once all cards are dealt, they win the pot. If we have the best hand the money goes directly to PokerStars and is taken off the table.
Now you know how the all-in cash out feature works!
Armed with this newfound knowledge, let’s take a deeper look at how this actually affects variance and winrates.
Variance: Card Distribution, EV Winrate, Standard Deviation And Risk Of Ruin
Now this part is a bit more of a primer on how variance works normally and what changes when using all-in cash out.
I’m going to keep this article as simple and easy to understand as I can. As such, I’m not going to bore you with dry mathematical definitions. You don’t need to know the mathematical definition of variance to understand how it works.
What you do need to understand though is that variance is affected by many things.
What is card distribution?
The first one we need to look at is card distribution. If you’ve asked another player how many hands you need to play before you even look at your winrate and got an absurd answer: this bad boy here is a big part of the reason why. There are skill factors as well but here that’s not what we’re interested in.
What’s important here is that card distribution variance will never go away. The all-in cash out feature has no effect on this type of variance. This means that even if you used cash out every time you would still be at the mercy of card distribution.
Besides skill, card distribution is going to have the biggest impact on your EV winrate. You should note that card distribution variance is not just the hands you are dealt. It also includes the cards your opponents are dealt as well as the cards dealt on the board.
Now once we have a big enough sample we can start talking about our EV winrate. I’m going to be blunt: Your EV winrate means nothing below at least 50,000 hands. Even then 100,000 hands as a base is preferred.
What is EV winrate?
Your EV winrate is your winnings in ante if you won exactly the amount of equity your hands have when all-in at any point in the hand or at showdown. Hands that you win without showdown are also included in this.
What’s the difference between your EV winrate and regular winrate?
The EV winrate takes luck factors that aren’t card distribution related out of it. Example:
- You and another player are all-in. You both have exactly 50% equity in the pot.
- Pot is 100a. You have 50a invested in the pot. No rake.
- Your regular winrate will go up or down by 50a.
- Your EV winrate will not change after this hand.
- Your opponent’s winrate will go up or down by 50a.
- Your opponent’s EV winrate will not change after this hand.
Another example but this time with different equities:
- You and another player are all-in. You have 80% equity and your opponent has 20% equity.
- Pot is 100a. You have 50a invested in the pot. No rake.
- Your regular winrate will go up or down by 50a.
- Your EV winrate will go up by 30a.
- Your opponent’s winrate will go up or down by 50a.
- Your opponent’s EV winrate will go down by 30a after this hand.
Quick and dirty formula:
- Change to EV winrate after a hand = Pot * Equity Player Investment
As you can see, your regular winrate will change by the same amount in both cases. Your regular winrate doesn’t take your equity into account when all-in.
Know what does though? Your EV winrate.
Your EV winrate in the first example doesn’t change. You win or lose 50a 50% of the time.
- 50% * 50a + 50% * 50a = 0a
In the second example, you will win your opponent’s 50a more often than you will lose yours. Your EV winrate goes up by 30a.
- 80% * 50a + 20% * 50a = 30a
In short, EV winrate is what you get if you could use the cash out feature without paying PokerStars their 1% fee.
When talking about EV winrate we typically convert to ante per 100 hands (a/100). If we played 99 other hands after the two examples above and didn’t win or lose a single EV chip, then we would say our winrates are as follow:
- Example 1 would have an EV winrate of 0a/100.
- Example 2 would have an EV winrate of 30a/100.
This is very important to know. It is also VERY IMPORTANT to know your EV winrate before thinking of applying some of the concepts described later in this article.
Now we finally get to the meat of the matter. The kind of variance that using all-in cash out does affect: Standard deviation.
What is standard deviation?
Again, I won’t go into the dry mathematical definitions. I’ll give you a brief description of what they are, what they do, and what affects them.
In this context, standard deviation is how much your regular winrate will deviate from your EV winrate on a given sample of hands.
If you played 100,000 hands with an EV winrate of 10a/100 you will almost never make exactly 10a/100 after those 100,000 hands. You could have a regular winrate of 12a/100 or 8a/100 after those 100,000 hands. If we use a poker variance calculator and we know our standard deviation, we can calculate how likely it is that our regular winrate stays within a certain margin of our EV winrate.
Standard deviation gets affected by a few things. This includes the format of poker you’re playing as well as your playstyle.
The more high variance the format of poker you’re playing, the higher the standard deviation is as a baseline. For comparison, Short Deck/6+ Hold’em has a higher expected standard deviation than PLO overall. Short Deck/6+ has equities that run as close if not closer, plays relatively shallow, and is no limit.
In terms of your playstyle, standard deviation is affected by how tight or loose you are playing as well. Playing too loose will increase your standard deviation thus how often you can expect your regular winrate to deviate from your EV winrate. The same can be said from playing too tight. It is a balancing act that you have to figure out for the games you are playing.
What is risk of ruin?
Now we get into how standard deviation overlaps with bankroll management (BRM).
I’ll be honest. I hate this statistic for poker.
Risk of ruin is the likelihood you will go bust given a certain EV winrate, standard deviation, and bankroll size when not considering card distribution. Card distribution is NEVER taken into account because statistically it is already included in your EV winrate.
The flaw of this stat is that it is only relevant if you refuse to move down in stakes.
Respect your bankroll management strategy, move down in stakes when necessary, and this stat becomes useless to you.
What you should account for when making a bankroll management strategy:
- Your EV winrate.
- How bad is short term card distribution variance in your chosen format.
- How high you expect standard deviation to be in your chosen format.
Here are the reasons risk of ruin is only relevant if you choose to go bust at the limit you are playing at:
- As you go down in stakes you reset the amount of buy-ins you have according to your planned BRM strategy. Example: you use a 100 buy-ins BRM strategy and move down as soon as you hit 100 buy-ins remaining of the next lowest stake.
- As you go down in stakes the games become softer and your EV winrate goes up, further altering the likelihood of ruin.
- If you are a winning player you will eventually drop back down to a stake where you have a high enough EV winrate that the risk of ruin becomes insignificant.
„Okay! Okay! That’s all well and good but what does standard deviation and risk of ruin have to do with all-in cash out?!“
Well I’m glad you asked!
It negates both of them. Entirely.
If you used the all-in cash out feature all the time your regular winrate would be equal to your EV winrate minus the 1% fee that PokerStars keeps. No more standard deviation thus risk of ruin is no more applicable as a statistic. The only variance we are now subject to is card distribution.
Let’s go through both of our previous examples and see what it looks like when we use all-in cash out.
Example 1:
- You and another player are all-in. You both have exactly 50% equity in the pot.
- Pot is 100a. You have 50a invested in the pot. No rake.
- You use the all-in cash out feature when prompted.
- Your regular winrate will go down by 0.5a.
- Your EV winrate will not change after this hand.
- Your opponent’s winrate will go up or down by 50a.
- Your opponent’s EV winrate will not change after this hand.
Example 2:
- You and another player are all-in. You have 80% equity and your opponent has 20% equity.
- Pot is 100a. You have 50a invested in the pot. No rake.
- You use the all-in cash out feature when prompted.
- Your regular winrate will go up by 29.2a.
- Your EV winrate will go up by 30a.
- Your opponent’s winrate will go up or down by 50a.
- Your opponent’s EV winrate will go down by 30a after this hand.
Now, I’m not going to lie to you, the 1% fee that PokerStars keeps is actually a lot higher than it sounds when used in practice. The problem with it is that it’s not really easy to calculate just how much it affects your winrate without an all-in cash out only sample. What I’m going to do though is make some assumptions to show you how to roughly calculate it.
The True Cost Of Using All-In Cash Out
Now that we know how to calculate EV winrate and how all-in cash out takes it’s fee, it’s time to see how expensive that 1% is.
Before we dive deep you should know that giving a flat accurate cost of the feature in a/100 isn’t easy. Some of the members on the 6+ discord channel theorized a while back that if you used it every time preflop the cost would be around 3 to 4 antes per 100. If used all the time that cost would climb to 7 or 8 antes per 100.
That’s pretty expensive.
Now they didn’t show any of the math they used to get that those results but there’s a simple way to get an approximation. The tricky part is figuring out how often you go all-in per 100 hands and what your equity is when you do.
Here’s another quick and dirty formula:
- Cash out fee = Pot * Equity * 1%
From knowing this we can figure out the cost of using cash out at certain equity points.
Let’s make this clearer with an example:
- You and another player are all-in.
- You do not know how much equity in the pot you have.
- Pot is 100a. You have 50a invested in the pot. No rake.
- You use the all-in cash out feature when prompted.
- What will be all-in cash out fee be?
From the example above:
- If you have 25% equity the all-in cash out fee will be 0.25a.
- If you have 50% equity the all-in cash out fee will be 0.50a.
- If you have 75% equity the all-in cash out fee will be 0.75a.
Let’s do this same example but with a different pot size:
- You and another player are all-in.
- You do not know how much equity in the pot you have.
- Pot is 200a. You have 100a invested in the pot. No rake.
- You use the all-in cash out feature when prompted.
- What will be all-in cash out fee be?
Once again, from the example above:
- If you have 25% equity the all-in cash out fee will be 0.50a.
- If you have 50% equity the all-in cash out fee will be 1.00a.
- If you have 75% equity the all-in cash out fee will be 1.50a.
Noticing any interesting patterns?
The first very obvious one is as follows: the more likely you are to win the hand once all-in, the higher the fee.
The implications of this are interesting but most of them will be explored later in the article.
The second interesting pattern is that the deeper the effective stacks, the higher the fee.
Does your winrate double from 50a effective to 100a effective? What about from 100a effective to 200a effective? We have to be careful and understand the implications of this if we are going to use all-in cash out at deeper effective stacks. Funnily enough, I am confident this is the the reason why PokerStars doesn’t allow us to take chips off of the table for their version of Short Deck/ 6+.
There’s a few other interesting applications for cash out at deeper effective stacks that we’ll go over as well.
Lastly, but not really shown in the examples, the more players in the pot, the smaller the equities get, but the bigger the fees get.
So this one is tough and a bit counter intuitive. It acts as a bit of a consequence to the two prior patterns. We know that the less equity we have, the smaller the fee. The deeper the effective stacks, the higher the fee. Don’t be deceived by us having less equity. Since the pot is bigger, our fee is bigger.
Let’s take a look:
- You and three other players are all-in.
- You do not know how much equity in the pot you have.
- Pot is 400a. You have 100a invested in the pot. No rake.
- You use the all-in cash out feature when prompted.
- What will be all-in cash out fee be?
One more time:
- If you have 25% equity the all-in cash out fee will be 1.00a.
- If you have 33% equity the all-in cash out fee will be 1.32a.
- If you have 50% equity the all-in cash out fee will be 2.00a.
So now you know that both the effective stacks and overall pot size affect how much we pay. Granted, the general increased fee on bigger pot size is offset by how much more money in the pot there is.
„Okay but why do we need to know this?“
To illustrate that calculating a blank, one size fits all, ante per 100 cost for allin cash out is hard. How many 50/50 flips will you have per 100 hands? How many at 75/25? 25/75? At what effective stacks? How big is the pot compared to your initial investment (how many players)?
If we flip 50/50 six times in 100 hands at 100a effective stacks, then the cost will be 6a/100 for using cash out. If we only do it 3 times then it will be 3a/100.
I think you get the idea.
I can’t do the math to tell you exactly how much it would cost you because I don’t know how often you’ll use it and where. Your play style itself might change how often you have to use it as well.
At least now you know how to find out how much it would cost you to use it.
