Hot Dice strategy: when to bank

Hot Dice looks like pure luck, but every turn is a string of decisions: which scoring dice to keep and whether to roll again. This tutorial walks through a sample turn, gives the exact odds of busting with one to six dice, and turns them into simple rules for when to bank, which dice to keep and how to play the race to 10,000. All the numbers use the scoring on this site, which is set out in the Hot Dice rules.

What you will learn

• How a turn plays out, roll by roll.
• The chance of a bust with one, two, three, four, five and six dice.
• When banking beats rolling on.
• Which dice to keep, and when keeping fewer dice is better.
• How the opening score and the final round change your choices.

A sample turn, step by step

Maya rolls all six dice: 1, 5, 5, 2, 3, 6. She could keep the 1 (100), the 1 and one 5 (150), or all three scorers (200). She keeps only the 1 and rolls five dice, because five dice rarely bust and give her the best chance of a big set.

Her five dice show 4, 4, 4, 5, 2. Three 4s are 400, and with the 5 that is 450. If she kept only the 4s she would have 500 and two dice to roll; two dice bust almost half the time, so she decides to stop. Since she is banking, she keeps the 5 as well and banks 550.

Leo starts his turn with 2, 3, 3, 4, 6, 6. There is no 1, no 5, no three of a kind, no straight and no three pairs: a bust on the first roll. It happens about once in every 43 first rolls, and there is nothing to do but pass the dice.

The odds of busting

A roll busts when none of the dice you rolled can score. These are the exact chances for the scoring on this site, where a straight and three pairs count when all six dice are rolled:

The pattern is the whole game in one table. With five or six dice a bust is rare, so rolling on is almost always right. With three dice it is a real risk, and with one or two dice you are betting your turn on a coin toss or worse.

When to bank

The question is not “how many points do I have?” but “how many points do I have for the number of dice I would roll next?” A big turn total is safe to risk with six dice and foolish to risk with one.

Working out the expected points of every choice for the scoring on this site gives these banking points, if all you want is the most points per turn on average:

• Six dice (hot dice): keep rolling. Even a large turn is worth more rolled than banked, because a bust is so unlikely.
• Five dice: keep rolling until the turn is around 3,000.
• Four dice: bank at about 1,000.
• Three dice: bank at about 450. At 400 it is a toss-up.
• Two dice: bank at 250 or more.
• One die: bank at about 350. At 300 rolling and banking are worth the same.

The one-die number surprises people: it is higher than the two-dice one. A single die that rolls a 1 or a 5 gives you hot dice and six fresh dice, which is a big prize. Two dice score more often, but usually leave you with one die and the same dilemma.

These are averages. Use them as a starting point and adjust for the score race, as below.

Which dice to keep

After a roll you must keep at least one scorer, but you don’t have to keep them all. If you are going to roll again, the dice you leave in matter as much as the points you take out.

1. One 1 often beats more points

A single 1 with five dice to roll is worth more, on average, than a 1 and a 5 with four dice to roll, and more than both 1s with four dice. The extra 50 or 100 points rarely make up for the lost die. The same goes for a single 5 rather than two 5s.

2. Small sets aren’t always worth keeping

With 2, 2, 2, 1, 4, 6, keeping three 2s (200) leaves three dice. Keeping just the 1 (100) leaves five. The 1 with five dice is clearly better on average, because three dice bust more than a quarter of the time. Big sets are different: three 1s (1,000) or three 6s (600) are worth taking.

3. Take everything when it gives hot dice

If keeping every scorer means all six dice have scored, take them all: you get six fresh dice and a bust becomes rare again.

4. Take everything when you bank

If you have decided to stop, keep every scoring die from the last roll. Leaving a 5 behind just throws away 50 points.

The opening score

With an opening score of 500, you can’t bank until a single turn reaches 500. Until then you must roll on, even with one die and 450 on the table. That makes early turns riskier, so keep fewer dice in the opening turns: more dice in hand means fewer busts on the way to 500. Once you are on the board, the normal banking points apply again.

Playing the race to 10,000

The banking points above maximise your average turn. Near the end of a game, winning matters more than averages.

• When you are ahead, bank a little earlier than usual. A safe 300 that keeps you in front is worth more than a risky 600.
• When someone is close to 10,000 and you are far behind, small banks won’t catch them. Aim higher before you stop.
• When your bank would reach 10,000, banking starts the final round. With a healthy lead, take it.
• In the final round, you get one turn. Banking anything less than the leader’s total is pointless, so roll on until you pass them (or tie, if a shared win is good enough) or bust.

The hard computer on this site plays exactly this way: expected value for most of the game, and a “pass the leader” plan in the final round.

Common beginner mistakes

1. Keeping every scorer every time. It looks greedy-safe, but it leaves you with few dice and lots of busts.
2. Rolling one or two dice with a big turn. A 600-point turn with two dice left has an almost even chance of ending at 0.
3. Banking 100 with five dice. With five dice you will score again more than nine times in ten.
4. Forgetting the final round. Reaching 10,000 gives everyone else one more turn, and a big final turn can still overtake you.
5. Ignoring the scoreboard. The right risk depends on the score race, especially in the last few turns.

A practice plan

1. Play a few games against the easy computer. It banks at 300, so you will see how often small banks fall behind.
2. Play against medium, which banks by the number of dice left, and try the banking points from this page.
3. Try the hard computer and watch which dice it keeps: often a single 1 when you would have taken more.
4. Turn on the 500 opening score for a tenser start, then play a family game and see who has the steadiest nerve.

Ready? Play Hot Dice now. For a dice game where you plan a whole scorecard instead of a single turn, try Yacht Dice, and our dice games for the family post has more ideas.

Written by the Pass and Play Games team.