Chip Value (1): The Principle of Diminishing Chip Value
One of the most important skills for a SNG player is the ability to understand and calculate the real value of chips. By doing so properly, you will be able to better understand the tradeoff between risk and reward in all of the situations you face. Naturally, as you gain a fuller understanding, you will make more profitable decisions at the table.
Why is this ability so crucial and what does "chip value" actually mean?
Surely you have an intuitive sense of how important chips are in SNGs. For example, in most SNGs you can’t rebuy after you lose all of your chips. Therefore, it is often argued that one should handle their chips more carefully and wisely in SNGs.
Of course this is true, but simply knowing this fact is not enough when it comes to evaluating chip value. Imagine that you are playing in a cash game where you only have one buyin available. Should your decisions be exactly as “cautious” as those that you make in a SNG?
The answer is a clear no, and this lesson is going to show you why. You will make the first step to understanding the real value of chips by learning the principle of diminishing chip value.
Important: Chips in SNGs have different value than in cash games! 
The chip value in SNGs is different than in cash games
In order to be able to understand the real value of your stack, you need to see the relationship between the quantity of one's chips and their real value.
The number of chips in cash games equals their value
Consider first the following example from a cash game: $0.05/$0.10 NoLimit Hold’em.
Seven players fold and a maniac, who sits in the SB, raises allin. Hero makes an easy call with his aces and wins the hand. Assuming that there is no rake, Hero has a stack of $20.
You can clearly see that by doubling his stack Hero has also doubled his money.
The number of chips in SNGs and their value are not directly correlated
Imagine, however, that Hero is in a 9man $10 SNG with a 50/30/20 payout structure (for simplicity purposes suppose there is no rake).
At the beginning of the game, each player’s 1,500 chips are worth $10 (the buyin). If Hero busts before getting into the money, he loses $10. However, if Hero wins and at the end has all 13,500 chips, he doesn’t get $90, but only $45.
Hero has 100% of the chips, but gets only 50% of the buyins. He has multiplied his stack by nine, but hasn’t equally multiplied its value. What follows from this observation is that chips that he won were worth less than ones that he risked.
From this observation we can derive the general principle:
The principle of diminishing chip value: A chip you are about to win in a SNG is not necessarily worth as much as the one you're risking to win it! 
That is exactly how we understand the value of chips in SNGs.
Different kinds of expected value
Take a look at the following example from a 10seater Double Or Nothing SNG (once again suppose there is no rake). It's a type of a SNG which awards 5 of 10 players double their $10 buyin as a prize. This example is a bit extreme, as it's based on an unusual situation, but it clearly shows the specific nature of chip value in SNGs.
First hand of the game has just been dealt. Posted blinds are very small, so it can be assumed that all players have equal stacks worth $10 each. Five players have gone allin and two others folded. You sit in the button and assume that with pocket aces your equity in this spot is 40%. You also assume that if you call, both SB and BB fold.
You have now a 40% probability of winning 9,030 chips (supposing there are no ties); by calling you win 2,112 chips on average. Therefore this call is very profitable in terms of chips.
At the same time, you have 40% probability of winning a prize, which is $20 (20% of the prizepool), but you also have a 60% chance of busting from the game with nothing. Therefore, in terms of money, you lose $2 on average  calling is unprofitable here.
As you can see, in this situation calling makes you earn chips, but lose money.
An interesting thing is that also folding can be evaluated here. This aspect is more complicated and interesting though, so you will learn about it in the next lessons.
Below you can find details regarding calculations:
Call expected value in terms of chips (cEV):
cEV = your stack if won * your equity + your stack if lost * probability of losing  chips you risk
your stack if won = 9030
your equity = 40%
your stack if lost = 0
probability of losing = 60%
chips you risk = 1500
cEV = (9030 * 40% + 0 * 60%)  1500 = 2112
Call expected value in terms of money ($EV):
$EV = value of your stack if won (prize) * your equity + value of your stack if lost * probability of losing  value you risk (your buyin)
value of your stack if won (prize) = $20
your equity = 40%
value of your stack if lost = $0
probability of losing = 60%
value you risk (your buyin) = $10
$EV = ($20 * 40% + $0 * 60%)  $10 =  $2
Since chips won in SNGs are not necessarily worth as much as ones you already have, it can be said that you risk more “value” in order to win less “value”. That is why in SNGs you need more equity than in cash games in order to call a bet profitably.
In respect of the above, expressing the difference between a given number of chips and their value uses two types of the expected value: chip expected value (cEV) and monetary expected value ($EV).
 Chip expected value (cEV):
The average number of chips you can expect as the result of an action.  Monetary (dollar) expected value ($EV):
The average amount of money you can expect as the result of an action, based on your current prize pool equity. $EV is the monetary equivalent of cEV. $EV is also used to describe the monetary value of a given stack.
Recognising the real profitability of decisions
This leads to the very important conclusion  always think about your decisions in terms of their real profitability (monetary expected value: $EV), instead of profitability measured in chips (chips expected value: cEV).
This approach is crucial, as it helps you to recognise decisions earn you chips but lose you money. The above example showed you that such a scenario is possible.
Important: A given decision can be +EV (profitable in terms of chips) but $EV (not profitable in terms of money). 
In the next lessons, you will see how the above statements correspond to specific ingame situations by learning about the fundamentals of the Independent Chip Model.
Summary
In this lesson, you have learned how you should think about and recognise the value of your chips.

Related article: Poker and the value of money
Next steps
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Discussion
#1 Ramble, 04 Oct 13 17:00
Truly a great article  only suggestion is that you explain what/where the 40% equity comes from in the DoN SNG example (i.e. AA vs 5 random hands will win roughly 40+% of time). Many new players will have no idea what is meant by "40% equity". (I hope I'm not one of them... lol).#2 fruitcake1, 07 Nov 13 16:09
At the end of the day winning the most chips is name of the game. The theory just doesn't make any sense to me.#3 matabear, 13 Dec 13 04:45
This article is great thankyou. I agree with Ramble though  it would be good to make a brief explanation of what the 40% equity means. I took a guess it meant that AA will win 40% of the time in a similar situation as Ive seen it on t.v poker graphics.#4 damien28173, 02 Jan 14 21:13
fruitcake1 that's why u will be cursed to stay in the micros forever.#5 hyppolito, 21 Jan 14 15:41
@fruitcake1I see your point. But this is one of the great examples of when folding AA préflop is profitable.
Let's try to give you another good spot. Imagine this situation: you are on a satellite tournament with 20 guaranteed packages to play WSOP main event at Las Vegas, value at USD15k. You have been played for 8 hours. There are 21 players left, in 3 tables. You are the 10th in chip stack.
3 players with more chips than you and almost same stack go allin preflop before you. You have AA and it's your turn. What do you do?
The answer is: you fold and pack your stuff. You are going to Vegas!
#6 SymonPeter, 28 Jan 14 06:14
Sorry, maybe it's a stupid question, put i'm not sure to understand in your example of calculation of the Monetary expected value ($EV) the value of your stack if won (prize) `= 20$. What this amount represent ? (the first in money position ?) Thanks,#7 alex777uk, 21 Feb 14 14:28
I agree with rumble, maybe an explanation of where that 40% come from will make the article better#8 Jaquare, 05 Jun 14 01:46
Agree with rumble and the others as well about the 40% because noob like me need an explanation for this stat!!! Would be great to receive an answer!#9 Pontooner, 17 Jun 14 17:30
Totally agree re the 40%. I've tried calculating this every which way and cant work it out!!#10 FlipFlop123, 15 Jul 14 15:25
#7 #8 get one of those simulator programs select Double up SNG format and make the situation you will get that 40% going against unknown cards#11 nozfardu, 30 Jul 14 22:45
In the example above it is a double or nothing game, meaning 5 players walk away with double entry fee.with 5 all ins, 4 players are going out that round leaving 6.
so risking all in on AA if you win you get a prize, lose you get nothing.
Odds are a couple are holding 2 suited and good chance of flush busting you.
Maybe another pocket pair also that could flop the set.
Why risk your prize on that big a gamble?
Better to fold, let 4 go out and continue playing with only 1 more needed to be knocked out.
#12 legendrigion, 12 Aug 14 21:09
good#13 lietuvis21x, 15 Aug 14 18:01
tnx!#14 Acrobat75, 19 Aug 14 09:26
Thanks for the article!#15 4s4s4s, 19 Oct 14 18:27
ty.#16 azhardelisya, 11 Dec 14 18:18
Ty#17 omega21, 09 Feb 15 10:04
Interesting things happen in sng's with ev's,though.#18 mirth, 06 Apr 15 13:13
this article helps me combine the amount of chips in relation to the payout structure, and when folding even a good hand can be profitable#19 jethrotu11, 27 Jun 15 04:17
ty#20 Davidius, 29 Sep 15 20:21
If you have 40% chance of winning 9,030 chips, how come you win 2,112 on average?0,4 x 9,030 = 3,612
or am I doing my math wrong?
#21 stameninho, 20 Oct 15 08:34
At the same time, you have 40% probability of winning a prize, which is $20 (20% of the prizepool),How did this 20% come up???
Please some help here.
#22 stameninho, 20 Oct 15 09:45
Now I get it. 5 players reach the prizepool, which is double their buyin. So $100/5=$20 per player reached the prizepool. (in a Fifty50 SNG) Nice.#23 hassux, 25 Jan 16 21:37
badi nik kiss emou#24 sedinbsng, 01 Apr 16 20:42
ok#25 sedinbsng, 02 Apr 16 00:09
ok#26 azwan77, 02 Dec 16 21:26
Nice#27 faronel, 16 Jan 17 12:10
For a player who is not really familiar with poker math concepts, this article was quite hard to read. The definitions of cEV and $EV were confusing since I understood it as a simple formula of average. Instead, the author could have shown a formula of how the mentioned results are calculated.So, I had to do an extra searching in order to fully understand the content of this article.
If EV formula is: (the amount of chips already in the pot before your move multiplied bythe probability of winning the hand, i.e. win equity)  (the amount of chips you are putting in multiplied by the probability of you losing this hand, i.e. loss equity), then
cEV:
Chips already in play: 4 allins with 1500 chips + 1SB of 10 chips and + 1BB of 20 chips = 7530
7530 * 0,4 = 3012
1500 (your allin) * 0,6 = 900
3012  900 = 2112
BUT...
$EV:
Winning $20 at 40% is +$8.
Losing $10 at 60% is $6,
so it makes +$2 or a +EV move? Or am I getting something wrong?
#28 ptortoise, 24 Jan 17 12:40
Its very difficult to understand this for me. I'm confused. Should I persist trying, or move on with other skills?#29 mindensejto, 17 Apr 17 21:00
Reply to Davidius's comment. cEV is the expected value of the call, not the expected value of Hero's ending stack. The formula of 0,4 x 9,030 + 0,6 x 0 = 3,612 shows the expected value of Hero's ending stack after him playing. But Hero started with 1500. So calling means Hero gets 3612  1500 = +2112 chips on average on top of his starting stack. Here is another way of calculating the +2112. You take the chips you can get on top of your starting chips.0,4 * 7530  0,6 * 1500 = 2112. Where you take the 7530 as the plus chips Hero gets 40% of time and 1500 where he looses his chips 60% of the time.