What you need to understand about the IPv4 TTL or IPv6 Hop Limit value is that a router (supposed to be the end-host, too, for IPv4, but most OSes don't do this) will decrement the IPv4 TTL or IPv6 Hop Limit when it receives a packet, and it will discard the packet if it decrements to 0.
That means that a packet with a IPv4 TTL or IPv6 Hop Limit of 1 entering a router will result in the router discarding the packet because it will be decremented to 0.
For IPv4, see RFC 791, Internet Protocol:
The Time to Live is an indication of an upper bound on the lifetime of
an internet datagram. It is set by the sender of the datagram and
reduced at the points along the route where it is processed. If the
time to live reaches zero before the internet datagram reaches its
destination, the internet datagram is destroyed. The time to live can
be thought of as a self destruct time limit.
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Time to Live: 8 bits
This field indicates the maximum time the datagram is allowed to
remain in the internet system. If this field contains the value zero,
then the datagram must be destroyed. This field is modified in
internet header processing. The time is measured in units of seconds,
but since every module that processes a datagram must decrease the TTL
by at least one even if it process the datagram in less than a second,
the TTL must be thought of only as an upper bound on the time a
datagram may exist. The intention is to cause undeliverable datagrams
to be discarded, and to bound the maximum datagram lifetime.
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Time to Live
The time to live is set by the sender to the maximum time the datagram
is allowed to be in the internet system. If the datagram is in the
internet system longer than the time to live, then the datagram must
be destroyed.
This field must be decreased at each point that the internet header is
processed to reflect the time spent processing the datagram. Even if
no local information is available on the time actually spent, the
field must be decremented by 1. The time is measured in units of
seconds (i.e. the value 1 means one second). Thus, the maximum time
to live is 255 seconds or 4.25 minutes. Since every module that
processes a datagram must decrease the TTL by at least one even if it
process the datagram in less than a second, the TTL must be thought of
only as an upper bound on the time a datagram may exist. The
intention is to cause undeliverable datagrams to be discarded, and to
bound the maximum datagram lifetime.
Some higher level reliable connection protocols are based on
assumptions that old duplicate datagrams will not arrive after a
certain time elapses. The TTL is a way for such protocols to have an
assurance that their assumption is met.
For IPv6 see RFC 2460, Internet Protocol, Version 6 (IPv6) Specification:
Hop Limit
8-bit unsigned integer. Decremented by 1 by each node that forwards
the packet. The packet is discarded if Hop Limit is decremented to
zero.
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if the IPv6 Hop Limit is less than or equal to 1 {
send an ICMP Time Exceeded -- Hop Limit Exceeded in
Transit message to the Source Address and discard the
packet
}
else {
decrement the Hop Limit by 1
resubmit the packet to the IPv6 module for transmission
to the new destination
}
Notice that it says, "if the IPv6 Hop Limit is less than or equal to 1," the packet is discarded.
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8.2 Maximum Packet Lifetime
Unlike IPv4, IPv6 nodes are not required to enforce maximum packet
lifetime. That is the reason the IPv4 "Time to Live" field was
renamed "Hop Limit" in IPv6. In practice, very few, if any, IPv4
implementations conform to the requirement that they limit packet
lifetime, so this is not a change in practice. Any upper-layer
protocol that relies on the internet layer (whether IPv4 or IPv6) to
limit packet lifetime ought to be upgraded to provide its own
mechanisms for detecting and discarding obsolete packets.
Edit:
Here is an example where I pinged the next-hop router VLAN interface, and then I pinged the router Loopback0 interface, with a TTL of 1. I received ICMP replies for every ping attempt, but the pings to the loopback expired in transit:
D:\>ping 198.18.1.1
Pinging 198.18.1.1 with 32 bytes of data:
Reply from 198.18.1.1: bytes=32 time<1ms TTL=128
Reply from 198.18.1.1: bytes=32 time<1ms TTL=128
Reply from 198.18.1.1: bytes=32 time<1ms TTL=128
Reply from 198.18.1.1: bytes=32 time<1ms TTL=128
Ping statistics for 198.18.1.1:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 0ms, Maximum = 0ms, Average = 0ms
D:\>ping -i 1 198.0.0.8
Pinging 198.0.0.8 with 32 bytes of data:
Reply from 198.18.1.1: TTL expired in transit.
Reply from 198.18.1.1: TTL expired in transit.
Reply from 198.18.1.1: TTL expired in transit.
Reply from 198.18.1.1: TTL expired in transit.
Ping statistics for 198.0.0.8:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
