Questions about Variance and the Mental Game

I dont know about live, im sure there are many human factors too and you listed some of them.

Regarding online, i have discussed this topic with several people and it comes down to rake.
If there was no rake, running it as many times as possible is the way afaik.

Rake favors running it once, especially in games with a rec.
Basically you want to win as much money possible with as little hands as possible.

In the long term when you RIO with superior equity, you win villains stack with less hands, meaning paying less rake.
Also if they get a double up, you can now play deep with them, in high rake games the deeper the better.

Personally i normally RIT, with some exceptions (vs shortstack or just decide to go for it with 80%+ equity).
I know its -EV, im just willing to pay little bit more to lessen the variance in order to keep my mindset more healthy.

I don't think what you're saying is correct mathematically.

Imagine hero has a 10bb win rate. If there was 0 variance, and villain is 100bb deep, it would take exactly 1000 hands to stack villain. It would be a slow, linear transfer of chips.

Now, if we introduce variance, hero is still expected to win after 1000 hands. It's just more likely it could take more or less.

Intuitively, it seems to me that there's a 50% chance it would take less than 1000 hands and 50% chance it would take more. Correct me if I'm wrong about that.

This practice is almost certainly not based on math. If hero has 99% equity, in practice, most of the time, it will make no difference whether we run it once or twice. (Either way, we're very likely to win the entire pot). But the principal is the same, regardless of whether we have 99% equity or 50% equity. Running it more times reduces variance. The question is whether or not variance is +EV.

You are right, there is no mathematical difference long term. Equties are the same, its just like playing the same spot multiple times for less money.

The EV difference comes in because of rake. You simply play more pots because of RIT, you split more often and end up playing more hands/pots.

About my own preference - its not based on math, its simply a mental thing.

If its purely about numbers then yes, but there are other factors.

Example online, if a fish wants to RIT and you deny it, he might quit the game. So you need to do it just to keep him happy.

I question why this is true. If there is 0 variance, we know it would take exactly 1000 hands to stack Villain for 100bb.

If we introduce variance, why do you believe it will take fewer hands? It could take fewer hands, or it could take more. It's possible you could go on a downswing and require much more than 1000 hands to stack villain.

Anything can happen when there is variance, but its about probability of it happening.

RIT was actually first used in live games, it was simply used so that the games would run longer and not break.

Imagine you get it in with 75% eq for $100 10 times or same hand for $50 20 times, the game simply runs longer and you play more hands in 2nd option.

Here's what you're saying: If we play heads up, and agree that we quit after someone wins 100bb, then we will pay less rake by RIO. Someone will win 100bb faster if we RIO.

However, if we agree: We're going to play 1000 hands heads up, no matter what. We're going to pay the same rake no matter what.

Your concept makes sense in practice. In real life, people play poker until they bust, then they quit. So, the casino wants people to RIT so they play longer and pay more rake.

But your EV doesn't change. You still pay the same amount of rake per hand. It's just a psychological choice to quit after you win or lose a lot of money.

If you RIO, humans more likely to psychologically play shorter sessions (I've won or lost $XXX, let's quit). But your EV is the same per hand, and you pay the same rake per hand.

Here's an extreme example. Let's say we both have 50% equity. There are 20 cards in the deck. I have 10 outs, you have 10 outs.

If we run it once, somebody wins the full pot and we pay 5% of pot in rake.

If we run it 20 times, we are both guaranteed to win 50% of the pot, and but we still both pay 5% of pot in rake.

We can repeat this exercise a million times. Running it Once, we're flipping coins but still paying Pot * 0.05 in rake.

Running it 20 times, we're guaranteed 50% of the pot every time, but we still pay the same amount in rake per hand.

Running it once is better if we both agree - we'll stop after someone loses all their money.

Yeah, my examples were in a vacuum and if its all just a 1 big long run.

In simple - run multiple times = splitting pot more often = playing more hands in general = paying more rake.

In real life if its +EV or not depends on several other factors that is nothing to do with raw numbers.

I not mean paying rake in 1 specific hand, i mean what affect RIT has on future hands.

Example rec has only $100 to play with.

Guy get its in on the turn with 50% eq, well its a flip if he goes broke or can continue in the game.
If we RIT we basically run $50 2 times, instead of $100 once. Yes, equity is same, but there is a higher chance he wont go broke because he is risking less.
Higher chance of staying in the game means he will play more hands and pay more rake.

Splitting more pots = playing more hands *only* if we accept that humans are more likely to quit playing after winning or losing big.

However, winrate, by definition, is profit divided by # hands. If Villain is required to play 1000 hands in a long session, it doesn't matter whether we run it once or 40 times. Our EV per hand is the same. Our winrate per hand is the same. It's just a psychological phenomenon that people will quit early after losing.

Yes, I agree. But that's because he's made the arbitrary decision to quit after losing $100. Running it once or twice doesn't change the EV per hand. It just means the player is more likely to quit early.

If the player is a winning player, then he will lose money, because winning players want to play as many hands as possible.

If he's a losing player, then he will save money, because losing players want to play as few hands as possible.

If you arbitrarily decide "I will quit after losing $100" - then if you're a winning player, you want to stay in the game as long as possible.

If you're a losing player, you hope to increase variance because it means you play less.

Bottom line: poker players care about profit per hand, and rake per hand. Running it multiple times doesn't change profit or rake per hand.

In a hand itself it doesnt yes, but there is a difference between playing 1k or 2k hands in order to win the same amount.
Theoretically the less hands you play for same profit the better.

Here's the best way I can explain it. Imagine we both have $50 on the table, and we agree to play until someone goes bust.

We each put $50 in the pot, I have 60% equity, you have 40% equity. If we run it once, I'm expected to win $57, you're expected to win $38, and casino is guaranteed $5. Game ends.

However, if instead, we cash out our all-in equity, I get $57, and you get $38. We play another hand. This time, the pot is 38*2 = $76. Casino takes $3.8 in rake, I cash out $43.32, you cash out $28.88. Now, I have $62.32, you have $28.88, and casino has $8.8 rake.

We play a third hand. $57.76 pot. I cash out $32.92, you cash out $21.95, and casino takes $2.74.

Now, I have $66.36, you have $21.95, and casino has $11.54 in rake.

Notice that a winning player is just like the casino: They take a rake on every pot. If I'm a better poker player than you, eventually I'm going to win all your money. My preference is to play as many hands as possible so that I can realize my 60% vs 40% skill edge over you. Eventually, the game ends after the winning player and casino have busted the losing player.

Another insight: Assuming 5% rake, you need at least 52.6% equity to break even. (52.6 * 95 = 50). Therefore, if you have at least 53% equity, over a trillion hands, you're guaranteed to profit. However, over a small sample, you could easily lose.

A winning player wants to minimize variance and play as many hands as possible. A losing player wants to maximize variance and play as few hands as possible.

I think we are talking about 2 different concepts and thats fine.

Im simply suggesting the more times we run the longer the game runs and the longer you stay at a poker, which means you play more hands and pay more.

I'm surprised that my last post didn't adequately explain the concept. If you're a winning player, you're expected to win $ on every hand. You want to play as many hands as possible.

The more hands we play, the more the winning player and casino wins, and the more the losing player loses.

I broke down how this concept works in my last post. Running it twice means we play more hands, which is GOOD for the winning player. They end up with more $ by slowly grinding the fish over 1000 hands.

I think i look at this too much from my POV.

Example in a 6max game with 5 regs and 1 rec, for the sake of argument lets say all regs are equal skill.
I will be happy to take a big equity advantage spot once vs rec, i want him to lose fast so he doesnt lose to other regs.
Also in this game when you are involved with other players, nobody is beating the game pre rb.
So its in my interest that there is a high chance that the rec loses to me asap.

Yes sure, i want to play much hands with him. But im talking more in the context of how he is using his 100bb, i want to have high BB/100 vs him.
When i RIT i give him more chances to win and essentially more chances to other regs to win from him.

Guess when its HU its different.

This is fundamentally wrong from a math perspective. The fact that there are 4 other pros doesn't really matter (you all have the same incentive to keep the fish in the game as long as possible).

I can explain the concept pretty simply.

Forget about rake. Let's say you have a 1bb advantage versus fish in every pot. If there is 0% variance, you win 1bb every hand. After 100 hands, you win 100bb.

With max variance, you can go all in with 50.5% vs 49.5% equity. Same expected value of 1bb per hand.

Of course, you prefer the 0% variance option because it allows you to realize your 1bb edge 100 times. You play a winning game 100 times, and win 100bb.

If you flip 50.5% vs 49.5%, now you only play a winning game 1 time. You win your 1bb in EV, then the game ends.

Bringing in other professionals doesn't change this basic math concept. It's tempting to want to selfishly stack the fish for yourself so the other pros can't get his chips.

But that's a fallacious way of thinking because your EV against the fish is still only 1bb.

By flipping with the fish, you are actually HELPING him.

Here's a simple hypo that clearly proves the point:

Imagine you're at a table with 5 pros and 1 fish. If there's 0% variance, the fish is GUARANTEED to lose all his money. On average, the pros will split his 100bb equally among themselves. Your EV is 20bb.

Now imagine you employ your donk strategy. You go all in with 50.5% equity. On average, you win 1bb. By minimizing your total hands, you minimize your profit.

If I was a pro at your table, I would actually encourage you to employ your donk strategy because it will actually help me.

If you flip with fish, there's a 51% chance you win. In that scenario, the game ends and I earn 0bb.

However, there's a 49% chance fish doubles up to 200bb. You donk out.

Now, me and the 3 other pros can split fish's 200bb equally. My EV in this runout is 50bb.

Averaging it together, when you employ your donk strategy: Your EV is 1bb, me and the 3 other pros each average roughly 25bb, and fish averages -100bb.

By donking with the fish, you kill your own action and let the other pros devour the fish 49% of the time when you're unlucky and bust.

Bottom line: You win money in poker by making + EV decisions. If you're a winning player, your goal is to play as many hands as possible. There is no shortcut that involves stacking fish with variance. You want to keep extracting EV for as long as possible.

Rake is the most important part in the "rit vs no rit" argument.

Other stuff is mostly just a personal preference how to handle short term variance.

Anyway, i said my piece. Welcome to hear more opinions.

I'm surprised that this simple illustration wasn't enough to convince you:

If we each have $50, I have a 60% vs 40% skill advantage, and casino takes a 5% rake:

After 1 hand, my EV is $57, yours is $38, and casino's is $5. With your donk strategy, this is where the game ends.

However, with my 0% variance strategy, I can cash out my $57. We play another all-in pot for $76. I cash out $43.32, you cash out $28.88, and casino takes $3.8.

After 2 hands, I have $62.32, you have $28.88, and casino has $8.8.

After 3 hands, I have $66.36, you have $21.95, and casino has $11.69.

After 4 hands, I have $69.43, you have $16.68, and casino has $13.89.

Cashing out our all-in equity allows us to play infinite hands until fish is completely busted. It's a fairly straight-forward concept.

I was not aware we were talking about "Cashout equity", i was talking about RIT, which is a completely different thing.

If cashout equity option was rake free, then yes its great.

But its not for free anywhere. I believe in GG its 1% flat for all pots, even higher in some other sites. No reg uses it, as its massively -EV.

It's the EXACT same concept. RIT allows us to approach our cashout equity. The more times we run it, the closer we are to our cash equity. If we run 40 rivers, we will EXACTLY realize our cashout equity. I'm surprised I have to explain this very basic concept...

Do you agree that taking cashout equity (assuming no additional fees/ rake) is good because it allows us to play more hands vs fish?

I get it yes, i have no argument against it.
Im just saying when you RIT game will run longer, which means playing more hands and paying more.

Yes, though, no point to discuss this, sites will never make this feature for free.

Your logic is contradictory. You say (1) you don't like RIT because it means playing more hands, but (2) you like taking cashout equity - which means playing even MORE hands.

Taking cashout equity is exactly the same as running it 40 times.

Its 2 different things.

1st is - what happens after you choose how you play the hand

2nd is - something that happens within a hand

Imagine a PLO tourney FT, now lets say people need to pay $1 everytime they enter a hand.

One is just a normal tournament, maybe lasts 3 hours.
The other one is RIT allowed tournament, it will probably run for 5-6 hours because there will be many split pots.

End price result will be the same, but the 2nd option paid a lot more in fees.

Same concept applies to cash games, that is all im saying.

Are you able to articulate why you believe RIT is bad, but cashing your all-in equity is good? I'm curious to understand your though process.