# Is there an optimum formula for deciding chip denominations?

I play in a \$1-2 NL game where they use chips in values of 1, 2, 5, 10, 20, and 50. I feel like it's tedious to try to keep track of the values of 6 different colors of chips. If you have a 5 and a 20 chip, the 10 really seems quite pointless.

I'd like to find some kind of guideline or rule of thumb for deciding the chip values. That way I can go back to the host and show him that there's data and it's not just me whining about it.

Here are some considerations for denomination choice:

1. If your supply of chips is limited, large denominations can be used similar to "cash plays".
2. We like to minimize the average number of chips per denomination per bet.
3. We like to maximize the number of possible bet sizes for denominations in use.
4. We like to minimize the effort required to count bets.
5. We like to make change easily.

(1) justifies keeping a small number of large-denomination chips; (2) and (3) justify using many denominations; (4) justifies using few denominations; and (5) justifies small gaps between denominations. "Optimal" is going to depend on (a) your priorities with respect to the above and (b) the distribution of bet and pot sizes.

Without enumerating the chip combinations for the entire bet distribution, let's try it for 10 big blinds, which is a medium-large average pot size in No Limit Holdem:

``````[1] [2] [5] [Avg]    [1] [2] [10] [Avg]    [1] [5] [Avg]
20   0   0   6.7     20   0    0   6.7     20   0    10
18   1   0   6.3     18   1    0   6.3     15   1     8
16   2   0   6.0     16   2    0   6.0     10   2     6
15   0   1   5.3     14   3    0   5.7      5   3     4
14   3   0   5.7     12   4    0   5.3      0   4     2
13   1   1   5.0     10   5    0   5.0              [6]
12   4   0   5.3     10   0    1   3.7
11   2   1   4.7      8   6    0   4.7
10   5   0   5.0      8   1    1   3.3
10   0   2   4.0      6   7    0   4.3
8   6   0   4.7      6   2    1   3.0
8   1   1   3.3      4   8    0   4.0
6   7   0   4.3      4   3    1   2.7
6   2   1   3.0      2   9    0   3.7
5   5   1   3.7      2   4    1   2.3
5   0   3   2.7      0  10    0   3.3
4   8   0   4.0      0   0    2   0.7
4   3   2   3.0                 [4.2]
3   1   3   2.3
2   9   0   3.7
2   4   2   2.7
1   7   1   3.0
1   2   3   2.0
0  10   0   3.3
0   5   2   2.3
0   0   4   1.3
[4.0]
``````

The left column is clearly superior to the middle, using fewer chips per denomination on average and forming more bets. The last column is easiest to count and has the same total chip average as the first column (6x2 = 4x3). Since we don't have data on bet and pot size frequency, we can't be much more thorough, and as shown multiple combinations are valid depending on your needs.

Two or three small denominations and, if necessary, one "supply" denomination give us:

``````{1, 2}
{1, 5}          // +1 easy count, -1 large supply
{1, 5, 10}
{1, 5, 20}      // +1 easy count
{1, 5, 50}      // +1 easy count, -1 lots of change
{1, 2, 5}       // +1 lots of bets, -1 harder count
{1, 2, 10}
{1, 2, 20}
{1, 2, 5, 10}
{1, 2, 5, 20}
{1, 2, 5, 50}
``````

None of the other combinations seem attractive unless you have an unusual chip supply. I would go with `{1, 5, 20}`, and if you happen to be short on smaller denominations, `{1, 2, 5}`, `{1, 2, 10}`, `{1, 2, 5, 10}`, and `{1, 2, 5, 20}` are decent alternatives.

Unless you're actually short of physical chips - 3 distinct values (1 / 5 / 25) should be plenty. It just gets too confusing otherwise.

• Casinos have 1,5,25,100 - more than enough for 1/2 game and if you want you can add in 500 chips. Keep it simple.
– Subs
Commented Jul 25, 2012 at 0:18
• The asker's game might be using chips with "\$20" printed on them. Otherwise I agree the standard casino denominations work nicely. Commented Jul 31, 2012 at 5:27

From my experience, the biggest chip should be 10 times the big blind.
Especially if the maximal buy in is limited to somewhere around 100 times the big blind.

In this case I believe you should use 1\$, 2\$, 5\$, 10\$, 20\$ chips.
although 20\$ chips are relatively big, they can be used as psychological "tool" to put more pressure on the other players.

• This is how I have been setting up my home games it scales well to the crowd. (1n + 2n + 5n + 10n + 20n) n = .10c for micro stakes, 1\$ for regular stakes, and \$10 for med-high stakes. Commented Jul 20, 2012 at 12:35

In this case, I think the chips with value 1 and 2 should be more than 60 - 70 % of all chips. You use them the most, the ones with 20 and 50 are rarely used.

• I think you make an interesting point about the distribution of chips in play with respect to what is used most frequently. Commented May 4, 2012 at 15:07

I don't speak for cash games. At home with my kids, it is pointless to play for money so I decided to choose the denominations {1,2,5,10,25} and for every game each player has 100 total. The total of 100 would correlate to 100% of one's total assets. Although, I am not yet so sure that 100 can manage well the surge of variance when one is using optimum decision using EV. I am still trying to observe further what the correct total stack is for optimal play to reap its reward.

In general, you want a 4x-5x gap between chip denominations. There is really no reason to have a \$2 chip if you already have a \$1 chip. You could just play two \$1 chips. For what its worth, this matches the typical casino denominations of 1/5/25/100/500. Keep in mind as well that fewer colors to remember is easier for everyone, and fewer mistakes will be made.

A good way to sort things out is to make the smallest chip equal to the small blind and then apply the 4x-5x rule to define the next chip denomination, rounding to even numbers. As mentioned above the highest chip you will need is 10x the big blind.