All-In Insurance

I tried to make some calculations to see how much in EV it actually costs to make an insurance.

I had a hand where I had 100bb stack vs. one opponent and there was 0,5bb dead money in the pot (total pot of 200,5bb).
I had 85% equity and insurance cost was 17,7bb (1,77$).

In my calculations the insurance costs 2,6bb (0,26$).

All-in insurance is -EV for sure, but sometimes it's worth to pay couple of bb's to reduce the variance and avoid big downswings. Especially in PLO.

Well you pay $1.77 only 85% of the time. The other 15% you get your $10 without "paying" anything. I did some calculation and in your spot it seems like insurance costs you 0.45 of a cent in equity... If I did the calculation right ofcourse. I would like to see your input.

Your pot equity without insurance:
$20.05 x 85% + $0 x 15% = $17.0425
Round it down to $17.04

Your pot equity with insurance:
($20.05 - $1.77) x 85% + $10.00 x 15% =
$18.28 x 85% + $1.50 =
$15.538 + $1.50 = $17.038
Round it up to $17.04

It really costs you $0.0045 in equity which is less than half a cent.

The only thing you forgot is that when you get bad-beated, you still pay the insurance, so you don't get 10 dollars but 10-1.77 = 8.23 dollars, which indeed makes the insecurance -2.6bbEV

No, you dont. I mean normally in poker, insurance is paid only if you win. IDK what is exactly the case with N8, and there isnt an exact information about it anywhere.

Have anyone actually lost an insured pot and paid out the insurance then?

I think it makes sense that you only pay insurance when you win the pot, but I think you have another error in your calculations.

Your pot equity with insurance:
($20.05 - $1.77) x 85% + $10.00 x 15%

I think you don't win (20.05 - 1.77) 85% of the time... You win 20.05 85% of the time and from that you always lose -1.77..

So in my mind it goes like this:
[($20.05 x 85%) - 1.77] + ($10.00 x 15%) =
17.0425 - 1.77 + 1.5 =
16.7725$

That's exactly the same calculation as I made only explained differently

I am not sure if you pay the insurance in a case of bad beat. If not, then it has pretty much the same EV as without insurance. Have to check it when I play there next time.

Originally posted by la55i
I think it makes sense that you only pay insurance when you win the pot, but I think you have another error in your calculations.

Your pot equity with insurance:
($20.05 - $1.77) x 85% + $10.00 x 15%

I think you don't win (20.05 - 1.77) 85% of the time... You win 20.05 85% of the time and from that you always lose -1.77..

So in my mind it goes like this:
[($20.05 x 85%) - 1.77] + ($10.00 x 15%) =
17.0425 - 1.77 + 1.5 =
16.7725$

If you calculate it this way, it means you always take away 1.77. Even when we lose... It doesnt matter if its in brackets with the winning odds or not

Heres a picture of a guy that lost an insured hand. The pot was HU with 10 cents overlay from the BB. So they stacked off (5.48-0.10)/2 = 2.69 each And he ended up with his starting stack. IDK what his insurance price was though...

But I also played a short-stacked 4-way pot. I was all in for 0.85 stack, the pot was 3.50 heads-up after 2 of the villains folded to the flop bet of the third one.
I had 71.34%.

They offered me to pay 0.35 to save my 0.85. Meaning that if I lose the pot I will remain with 0.85 and not 0.50
Anyway I won the pot and got 3.05. 0.35 was the insurance and 0.10 was rake (the rake in PLO on N8 is 3%)

Here are some calculations:

Not insuring
71.34% x 3.50 = 2.49690

Paying the insurance only when we win:
71.34% x (3.50 - 0.35) + 28.66% x (0.85) =
2.24721 + 0.24361 = 2.49082

Paying it always:
71.34% x (3.50) + 28.66% x (0.85) - 0.35 =
2.4969 + 0.24361 - 0.35 = 2.39051

It means we pay 1 bb in equity here. Kyyberi said its 2.6bb. Thats kind of a big difference. While by only paying when we win, the result is consistent with my previous calculation.

So in conclusion there is no juice when you insure your hand and you dont pay insurance when you lose the hand (the "juice" is actually like half a cent because they round the numbers in their favour which is reasonable).

Now this starts to make sense.

That's what I get too. I don't know how I calculated it a bit wrong in the OP as I didn't include the calculations.

But as it seems it doesn't really lower your EV, I will start to use it a lot more.

Hi, guys. I just attended Kyyberi's PLO coaching and was discussing insurance. Firstly:

1. are you guys including rake in your calculations?

2. In my opinion these are the reasons to take insurance (quoted from: https://poker.stackexchange.com/questions/401/insurance-in-cash-games-in-which-situations-is-it-a-good-idea-and-for-how-much)

Protecting your bankroll: It is true, you should never play above your bankroll requirements but NOBODY can say they never played a game above their bankroll. If a certain level is more profitable for you than a lower level and if you know you can find insurance deals on that higher stake, then I think you should take the insurance and play at that higher level. This can also apply to transition periods from lower to higher stakes.

Emotional control or tilt control: Unless you have nerves of steel, a bad beat can cause even more losses due to bad play after a bad beat. Maybe you can avoid this if you take an insurance deal for a big pot.

Variance: Variance can be a bitch, the mentality is bad, even worse is that it may force you to lower the stakes you are playing in. -EV for less variance is something that can be considered IMHO.

This is all hypothetical of course as you cannot find someone that will constantly offer you a deal for all-in pots. Even if you did, the price would matter a lot. How much -EV I would be giving away can be a determining factor but I have no idea what the optimum price wold be for insurance.

As we know, and as Kyyberi said himself, all insurance is -ev and I just cannot see how paying out money in an already high-rake game when we are favourite is not a complete no-no in poker just to mitigate the bad beats we are all going to take 20-25% of the time anyway....It is just another way to pay the house extra money imo unless I misunderstand things? I don't believe EV is the correct concept in question when discussing insurance more about your bottom line/winrate.

PS Another good thread here:

https://www.deucescracked.com/forums/111-Off-Topic/topics/547931-Is-Insurance-Negative-EV-

Conventional insurances are -EV as company needs to make profit. Here site doesn’t make profit.

With or without insurance you pay the rake if you win the hand. So it doesn’t matter.

In your first link was an example of offered insurance with 2% juice. That is -EV. Nirmally no one offers insurances with 0% juice, therefore in general it’s almost always -EV. But at Natural8 there is no juice. So it’s EV 0.

If you think it’s -EV despite the math, then think this: If site doesn’t make profit from insurance, where does the lost money go then?

^ What Kyyberi said, plus you dont pay rake if you lose the pot but win the insurance. You end up with the exact stack you started the hand with.
And more:
If you think the site wants to make more money by "rigging" the insurance in their favour (AND BY NO MEANS I AM SAYING THIS IS THE CASE WITH N8!!!, I am just speculating), the person who insured would be the one to profit because he will win more pots, so the site is basically rigging the insurance in his favour

Just insure!

Thanks for the reply guys! I definitely didn't mention anything about rigging so we won't go there! I am no expert but Kyyberi says there is no juice, but isn't the 17.7BB's he pays if he wins the juice or is juice supposed to be paid only when you lose? I am just trying to understand this concept because I have always refused insurance and am wondering if I am making a mistake and I want to fully understand. I am just suggesting that the poker site offers insurance based on the premise that it will get paid 67%+ of the time. Obviously it will profit over time, no? I am by no means a maths guy so won't be able to do any further calculations but, based on Kyyberi's example, with 2 100BB stacks going all in, you will lose a massive 17.7BB's on average 67%+ (or thereabouts over time) and win back 100BB's 33% or less of the time. Do these 2 scenarios even out BB's-wise?

Thanks in advance guys

The calculations are there.

Juice is the amount that insurance pays over the EV0 amount. If EV0 insurance would pay $5, then if you pay $5,50 for it there is $0,50 juice. The one who gives the insurance makes profits from the juice.

In the example there is an all-in on the turn, 100bb stacks and hero has 85% equity.

Let's repeat the situation 100 times and hero wins 85 of those.

Without the insurance

85 times hero wins pot of 200,5bb = 17042,5bb
15 times hero loses 100bb stack = -1500bb

After 100 repetitions hero has 15542,5bb

With insurance

85 times hero wins pot of 200,5bb, but pays insurance of 17,7bb = 15538bb
15 times hero loses but keeps his stack = 0bb

After 100 repetitions hero has 15538bb.

Difference is about 0,05bb per hand. If the insurance cost is 1c lower, it would be the same difference but benefits the player. So it's uite understandable that it's rounded up.

I can't explain it any clearer. Insurance is EV0 so it doesn't affect your winnings directly in the long run.

What was strange yesterday, I had 60% equity and it allowed me to use insurance. So maybe it has changed or there was some bug in the software (as it should allow it only when you are at least 67% favorite).

Many thanks Kyyberi. Maybe not the rip-off I thought it was and perhaps I will start taking it in specific circumstances like very deep pots and especially when there is a deepstacked recreational player at the tables. Thanks for the info.

Pretty sure it's -EV now. Not a 100% because they changed it so that you have to re-insure when you are on the turn if you are still ahead, but if you are behind your flop insurance stays. Calculating only the flop insurance, it's definitely -EV, but I am not sure if the turn re-insurance is in player's favor much or not.

Just run it 3 times.

You pay exactly what you agree on only when you win the pot.
If you lose the pot, your opponent wins the whole pot, and you win whatever % of the pot you insured and you don't pay anything extra. You also don't pay rake.

It used to be that you insure only for exactly whatever you started the hand with and it used to be that you insure only on the equity you have on the street on which you went all in. That's why it was easy to calculate before.

Now, you can choose how much of the pot you want to insure AND you MUST insure on the turn if you are still ahead with a new price. That's why it's difficult to calculate if it will cost you EV.

The 2% I wrote in the quote was after calculating only the flop "juice" in a hand I watched, but it does not take into account the re-insurance on the turn, which maaaay be just good enough to make it 0EV.

They told you they don't take any fee on top of what you agree on when you choose how much of the pot you want to insure. But I don't think they really grasp what you are asking them - does it cost you any EV.

I hope I made sense.

Maybe if you insure a couple of pots and write down exactly what % of the pot you insured and what were the prices on the flop and on the turn, we will be able to calculate if it's really 0EV. But I still highly doubt it.

This was taken from the insurance page:

3. If it is possible that the pot can be split on the next street, the maximum premium is 20% of the pot on the Flop, and 45% of the pot on the Turn. If it is not possible that the pot can be split on the next street, the maximum premium is 25% on the Flop and 50% on the Turn.

I have no clue wtf anything of this means.