When to turn in flat-rate spoils

[StevenJoyce]

I've been thinking about when its worthwhile to delay turning in spoils in a flat-rate game, and I'd appreciate comments by more experienced players. I'm thinking that, aside from a few exceptions, you should cash a set of spoils whenever you have that option.

Scenario #1: You have 3 red spoils cards and 1 green spoils card at the beginning of your turn. You could turn the red cards in for 4 troops, or you could wait a turn. If you get a blue spoils card (1/3 probability, assuming you can get a card), you will turn in a mixed set of spoils for 10 troops. If you get a red or green spoils card (2/3 probability), you get 4 troops. Thus, at the cost of a one turn delay, you increase your expected number of troops by (1/3)*(10-4)+(2/3)*(4-4) = 2.0. Now sometimes you don't have very many productive options for using extra troops on the current turn, and the gamble would be worth it. Other times, the strategic situation may be ambiguous, and a one turn delay would help clarify where the extra troops should be placed. But usually there's some pressing need (surviving another turn, eliminating an opponent, busting an opponent's bonus, securing your own bonus, or even simply being able to safely get another spoils card) that makes a one-turn delay significantly more costly than giving up the opportunity for an average of 2.0 troops.

In all other scenarios, the benefit from delay is even less.

Scenario #2: 3 green cards, 1 red card (or blue card). 6 troops immediately, versus a 1/3 chance at a one-turn delayed 10 troops, for an expected gain from delay of (1/3)*(10-6)+(2/3)*(6-6) = 1.33.

Scenario #3: 3 blue cards, 1 red card (or green card). 8 troops immediately, versus a 1/3 chance at a one-turn delayed 10 troops, for an expected gain from delay of (1/3)*(10-8)+(2/3)*(8-8) = 0.67.

Scenario #4: 3 red cards. 4 troops immediately, versus a 2/9 chance at a two-turn delayed 10 troops, for an expected gain from delay of (2/9)*(10-4)+(7/9)*(4-4) = 1.33.

Scenario #5: 3 green cards. 6 troops immediately, versus a 2/9 chance at a two-turn delayed 10 troops, for an expected gain from delay of (2/9)*(10-6)+(7/9)*(6-6) = 0.89.

Scenario #6: 3 blue cards. 8 troops immediately, versus a 2/9 chance at a two-turn delayed 10 troops, for an expected gain from delay of (2/9)*(10-8)+(7/9)*(8-8) = 0.44.

Does this analysis seem reasonable, or am I overlooking something?

[kingpin01]

Good mathematical analysis, but game situation is more important, I think. If you can reduce your opponent's bonus by breaking a continent, or getting them below 12 territories, or if you can take (and hold) a continent, or knock out one of your opponents, then it's worth it to take the cards right away. If you think that you are more likely to knock someone out with a 10 point bonus, then the risk of waiting another turn is more worth it (plus you would have the bonus of at least 3 more armies from your current turn).

[nippersean]

I always take 3 blues or mixed set straight away. Obviously if you get 4 reds / 4 greens you won't improve so I'd put them on straight away too and unless exceptional circumstances, like you need them right now, wait if you have 3 greens and 1 blue. etc

[karelpietertje]

if you have a set (no matter 3 red or mixed) in 1v1, cash it immediately.
if you have a set (no matter 3 red or mixed) in a 3+ player game, cash it when you have 5 cards.

[stahrgazer]

I agree with kingpin, it's situational dependent. If I can break a bonus now by taking 4 armies from a red set, I'll do so; likewise if I can get a worthwhile bonus with strong hopes of keeping it for the next turn.

Another scenario is when owning terrs on the cashes; if you own all three, that 4 is worth 10; own 2, worth 8 and so forth.

[SuicidalSnowman]

if you have a set (no matter 3 red or mixed) in 1v1, cash it immediately.
if you have a set (no matter 3 red or mixed) in a 3+ player game, cash it when you have 5 cards.

I think this is most effective...

[hahaha3hahaha]

-deleted-

[StevenJoyce]

if you have a set (no matter 3 red or mixed) in 1v1, cash it immediately.
if you have a set (no matter 3 red or mixed) in a 3+ player game, cash it when you have 5 cards.

Many of you have endorsed this rule of thumb. Could someone explain the logic behind it? Suppose I'm in a four player game, and I have three spoils -- one of each color. The above rule suggests that I wait two turns to claim my 10 armies, rather than taking them now. (Generally speaking. Some of you have suggested exceptions to the rule.) What advantage do I gain by delaying?

[Koganosi]

10 sets turn them in immediatly. And normally I do 8 sets 2.

If I get 6 or 4. I try to get a better. If I dont I just cash it immediatly. Or I keep it for a later moment, the board can always change.

Urs

Koganosi

[BaldAdonis]

The analysis would benefit from including territory bonuses that cards give. If you have 3R1G with a bonus for the green and either 1 or 0 bonuses for the reds, then waiting becomes even more valuable. Conversely, if you have a 3 card set with bonuses for all, then waiting for a mixed set has a very low expectation, which depends on how many territories you control. For example, holding 3 blues with bonuses on each has a negative expected gain unless you control more than half of the map (ducy?).

Also, the way it's written, scenario's 2 and 4 look like they have the same value, but in the latter you need to wait 2 turns. Maybe expected gain/turn would be a better measure.

[Mr Changsha]

One scenario when it is certainly worth waiting is if you think your opponents my throw at each other if you wait. For example, if you have a 3 card rainbow and your opponents have 5 cards, it can be good to hold...if you judge that the first laid set won't go your way. If you think it will then you must lay, of course, but if you as player a holds, player b hits c, c hits b...then your (hidden) set is worth so much more...it might even get you an elimination.

I'm always looking to do this in flat rate speed games that have been reduced to 3 players, though one has to 'massage' the board prior to attempting it and, of course, it is dependent on your ability to read the board correctly.

[natty dread]

I don't usually cash sets at less than 5 cards unless I really need them. It's a good insurance to have a set in your sleeve in case someone breaks your bonus...

Besides, there's another advantage in cashing at 5: when you do that you'll be left with 2 cards, and another card from spoils = 3 cards for the next turn so if you're lucky you might be able to cash two turns in a row. If needed.

[rockfist]

If your first three cards are Blue waiting to get a rainbow is not worth it.

[flexmaster33]

Wait for a rainbow only in situations where you have no pressing need for the extra troops. The game situation really dictates when you should turn in. Wait if you can obviously afford to, but if you're questioning it, I would opt for the turn in.

Also, keep in mind, if you're sitting there with three reds and one of another color, you are probably stuck with a small 4 set at some point regardless, so get it out of the way early and try to reload on your next set.

[Joepjoep]

One scenario when it is certainly worth waiting is if you think your opponents my throw at each other if you wait.

I concurr. If cashing in puts a big crosshair on your ass in a multiplayer, and the troops are only going to be used to stack, better to keep the set in hand. Keeps the troops out of view and they can be easily positioned where you need them when you need them.
Edit: Old thread, my bad.