# Is there an optimal swing die value for Changeling VS Iago?

Button Men is played until one player wins 3 rounds. For the first round, Swing Dice selection is done in secret. On following rounds, only the player that lost the round is allowed to change it's value.

Changeling: dX, dX, dX, dX, dX

Iago: d20, d20, d20,dX

Swing Dice (dX): Values for X may be any number between 4 to 20 inclusive, including nonregular dice like 13 or 7 sided dice. If a character has multiple dX dice, the value of X must be the same for all dX dice.

Is there an optimal swing die value for Changeling, and if so what is it?

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## 1 Answer

If you believe in basic Swing Die strategy, then '6' is the appropriate value for X for Changeling.

The formula for Swing Die selection is:

(A-B)*2/3 = (Sides the Bigger Character must keep)

Where 'A'/'B' are character's dice side totals.

The general theory is

1) If you can force your bigger opponent to have to keep two or more dice, then you will have a distinct advantage. You are more likely to go first as a smaller character (smaller characters usually have dice more dice with fewer sides, and are therefore more likely to have the lowest die).

2) Select the biggest die possible, that condition 1) will hold true.

Until Changeling has won has won 2 matches, a swing die value dX='6' requires that Iagomust keep 2 dice to not lose by points. If you read down column '6', Iago must keep between 22.7 and 33.3 sides to not lose, even if they take all Changelings dice. Iago cannot select a Swing Die value that allows them to only keep a single die and still win.

Once Changeling has won 2 rounds, then their best Swing Die value of dX should probably be '20' unless Iago has selected dX=4 or 5. With 2 wins for Changeling, the only way Iago could switch swing die values is by losing and giving you your 3rd round win for the match. If Changeling doesn't have 2 wins yet, dX='18' is your next best swing die value. It gives you the biggest die possible, without requiring that you keep more than a single die. The best that Iago can do is select dX='4' for their next swing die, which only requires you to keep 17.3 sides. Even if they do happen to win an Iago'4' vs Changeling'18' round, you can switch back to Changeling dX='6' with your swing Die and require Iago keeps 2 dice again.

``````Changeling|'4' |'5' |'6' |'7' |'8' |'9' |'10'|'11'|'12'|'13'|'14'|'15'| '16'| '17'| '18'| '19'| '20'|
+--+  +----+----+----+----+----+----+----+----+----+----+----+----+-----+-----+-----+-----+-----+
|60|  | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 |  80 |  85 |  90 |  95 | 100 |
+--+--+----+----+----+----+----+----+----+----+----+----+----+----+-----+-----+-----+-----+-----+
Iago| 4|64|29.3|26.0|22.7|19.3|16.0|12.7| 9.3| 6.0| 2.7|-0.7|-4.0|-7.3|-10.7|-14.0|-17.3|-20.7|-24.0|
Iago| 5|65|30.0|26.7|23.3|20.0|16.7|13.3|10.0| 6.7| 3.3| 0.0|-3.3|-6.7|-10.0|-13.3|-16.7|-20.0|-23.3|
Iago| 6|66|30.7|27.3|24.0|20.7|17.3|14.0|10.7| 7.3| 4.0| 0.7|-2.7|-6.0| -9.3|-12.7|-16.0|-19.3|-22.7|
Iago| 7|67|31.3|28.0|24.7|21.3|18.0|14.7|11.3| 8.0| 4.7| 1.3|-2.0|-5.3| -8.7|-12.0|-15.3|-18.7|-22.0|
Iago| 8|68|32.0|28.7|25.3|22.0|18.7|15.3|12.0| 8.7| 5.3| 2.0|-1.3|-4.7| -8.0|-11.3|-14.7|-18.0|-21.3|
Iago| 9|69|32.7|29.3|26.0|22.7|19.3|16.0|12.7| 9.3| 6.0| 2.7|-0.7|-4.0| -7.3|-10.7|-14.0|-17.3|-20.7|
Iago|10|70|33.3|30.0|26.7|23.3|20.0|16.7|13.3|10.0| 6.7| 3.3| 0.0|-3.3| -6.7|-10.0|-13.3|-16.7|-20.0|
Iago|11|71|34.0|30.7|27.3|24.0|20.7|17.3|14.0|10.7| 7.3| 4.0| 0.7|-2.7| -6.0| -9.3|-12.7|-16.0|-19.3|
Iago|12|72|34.7|31.3|28.0|24.7|21.3|18.0|14.7|11.3| 8.0| 4.7| 1.3|-2.0| -5.3| -8.7|-12.0|-15.3|-18.7|
Iago|13|73|35.3|32.0|28.7|25.3|22.0|18.7|15.3|12.0| 8.7| 5.3| 2.0|-1.3| -4.7| -8.0|-11.3|-14.7|-18.0|
Iago|14|74|36.0|32.7|29.3|26.0|22.7|19.3|16.0|12.7| 9.3| 6.0| 2.7|-0.7| -4.0| -7.3|-10.7|-14.0|-17.3|
Iago|15|75|36.7|33.3|30.0|26.7|23.3|20.0|16.7|13.3|10.0| 6.7| 3.3| 0.0| -3.3| -6.7|-10.0|-13.3|-16.7|
Iago|16|76|37.3|34.0|30.7|27.3|24.0|20.7|17.3|14.0|10.7| 7.3| 4.0| 0.7| -2.7| -6.0| -9.3|-12.7|-16.0|
Iago|17|77|38.0|34.7|31.3|28.0|24.7|21.3|18.0|14.7|11.3| 8.0| 4.7| 1.3| -2.0| -5.3| -8.7|-12.0|-15.3|
Iago|18|78|38.7|35.3|32.0|28.7|25.3|22.0|18.7|15.3|12.0| 8.7| 5.3| 2.0| -1.3| -4.7| -8.0|-11.3|-14.7|
Iago|19|79|39.3|36.0|32.7|29.3|26.0|22.7|19.3|16.0|12.7| 9.3| 6.0| 2.7| -0.7| -4.0| -7.3|-10.7|-14.0|
Iago|20|80|40.0|36.7|33.3|30.0|26.7|23.3|20.0|16.7|13.3|10.0| 6.7| 3.3|  0.0| -3.3| -6.7|-10.0|-13.3|
``````
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