Ticket to Ride Odds: Will the Cards You Need Come?

Welcome to Level 3. At Level 1 you learned that a blind card is your color or a locomotive about 1 time in 4. Now you put that number to work on the question behind every draw turn: how long until I can claim this?

All the numbers here come from the 110-card deck in the current box, 12 cards in each of 8 colors and 14 locomotives, worked out for a fresh deck. Mid-game, cards in hands and in the discard pile shift the odds a little. The shape of the answer does not change.

One card at a time

For a route in one color, a blind card helps if it is that color or a locomotive: 26 of 110 cards, about 24%. Two blind cards per turn bring about 0.47 useful cards per turn on average. Put the other way, blind draws alone bring about one useful card every two turns.

For a gray route, any color works as long as all the cards match. Gray routes are much easier to fill, because your biggest color pile grows as you draw for everything else.

How many useful cards will blind draws bring?

The chance of drawing at least this many useful cards (your color or a locomotive) in a run of blind draws:

Read it with your hand in mind. If you hold 2 blue cards and need a blue 4, you need 2 more. Blind draws alone get you there within 3 turns about 44% of the time and within 5 turns about 74% of the time.

If you hold nothing for a blue 6, you need 6 more, and blind draws alone are hopeless on any sensible timeline. That route has to be built from the face-up row, from cards you already hold, and from locomotives.

The face-up row changes everything

The face-up row is why long single-color routes are possible. At the start of the game, there is about a 45% chance that at least one of the 5 face-up cards is a specific color. Each time you take a matching face-up card, you get a sure hit instead of a 1 in 4 chance.

But the row is shared. Every player sees it, and the player before you takes from it first. A color that keeps appearing and never gets taken is a hint that nobody else is collecting it. A color that vanishes the moment it appears tells you a rival is.

Locomotives

There are 14 locomotives, about 13% of the deck. In a fresh deck, two blind cards bring at least one locomotive about 24% of the time. Over a game of many draw turns, you will see several, but rarely exactly when you need one.

Count them. Each locomotive played onto the board is one fewer in circulation until the discards are reshuffled. Late in a game, if most of the 14 have been spent on routes, do not plan a claim that depends on another one.

Odds become decisions

Put the table next to the board and three habits follow.

Plan routes in colors you already hold. A hand with 4 red cards makes every red route on your path cheap. Starting from zero in a new color is slow.

Prefer gray routes when you can choose. If two paths to the same city are equal, the gray one is easier to fill.

Claim when the odds turn against waiting. Say you need 1 more card for a contested 4-route. Two blind cards bring it about 42% of the time; three turns of blind draws, about 81%. If a rival is building toward that route, a face-up locomotive that finishes it now is worth more than a better draw later.

Tickets have odds too

Ticket draws follow the same logic. In a fresh deck of 33, there are only 5 tickets worth 20 or more. Three random tickets contain at least one of them about 40% of the time. Most draws are made of medium and short tickets, so draw for the ones that fit your network, not for the big numbers.

The habit

You will not run these numbers every turn. Run them for your one or two biggest routes, the ones that decide whether your tickets finish. After a few games, the table becomes a feel: two cards short is a few turns, four cards short is a long wait, and a long wait is when someone else takes the route.