Today I played two 2 player games of the Strontium Dog Miniatures Game which got me thinking about the probability of returning Star Chips to the bag. I want to set out the chain of events that occurred in both games that left me scratching my head a little, but feel free to jump to the end of the article if you're simply here to find out what the statistical chances are of returning Star Chips to the bag!
Background and forces:
We decided both battles would be fought with 60 Notoriety and selected the following forces:
Band 1: Band 2:
Johnny Alpha (hero mode) Max Bubba
Wulf Sternhammer Kansyr
Middenface McNulty Steelkreeg
Durham Red Low Down O'Phee
Brute Mosely
Skull
We played a Search and Destroy Job with the Face-Off Encounter and replayed the same scenario with the same forces but switched sides. In both games, the protagonists - Johnny's team - were to destroy 3 crates. This seemed a little easy, particularly because the protagonist gets to place two of the crates in his own half of the board, while a third is in the centre of the board. While neither of us actually declared it, we both ended up ignoring the crates and decided to have Johnny's band take on Bubba and his crew. For deployment, forces were not allowed to deploy within 9" of the centre of the board or within 9" of an enemy unit.
Game 1:
Wulf and Middenface make use of the special mission-based Chicanery Card to Move D6" closer to enemies. Middenface is first to activate and uses a Time Bomb on Steelkreeg, disposing of the robot immediately! Middenface's Star Chip is returned to the bag, then comes out again. He then charges Brute Mosely, also incapacitating him! Middenface is Pinned and then Wulf is next to activate. Wulf charges into enemy territory and returns the Star Chip to the bag. Kansyr activates and attempts but fails to take control of Wulf. He also failed to send his Star Chip to the bag. Wulf activates and passes a Cool test to shake off the Pinned marker from Kansyr then then attacks Low-Down O'Phee. Low-Down falls under the might of Der Happy Stick as well and the Star Chip goes back into the bag again! Johnny Alpha activates and moves into range of Max Bubba, throwing a Melta-Bomb which reduces the outlaw to a mound of cooked flesh. With only Kansyr and Skull left, the outlaw player concedes defeat and the game ends on Turn 1 - without the outlaws even being able to fire at the S/D Agents!
Game 2:
Just as happened in the first game, the S/D team use the Chicanery Card to push up but this time I use the other Chicanery Card which buys me a free shot on Middenface with Steelkreeg and the awesome Firepak! Except the Firepak's roll isn't awesome and Middenface soaks up all of the damage! Max Bubba is first to activate and unleashes the Blazooka on Wulf but again, the S/D agent is unscathed! Middenface is next and takes out Steelkreeg with a Time Bomb, just as happened in Game 1. He is Pinned but Wulf is next and he takes out Brute and Low Down over two activations. The bad guys fail to inflict any wounds on their activations and the Johnny Alpha goes on a spree of about 5 consecutive actions, taking down Skull, Kansyr and a Stix (added from Collateral) and once again, with Max facing 4 unwounded S/D agents, the Outlaws concede defeat in turn 1!
Reflections:
From a narrative point of view I loved these games as Johnny and his team cut through opponents like a hot knife through butter, just as they do in the Strontium Dog comics! On the other hand, this definitely wasn't the most satisfying gaming session we've had; it's just a fact that the most rewarding games are those which are closely contested.
We were both agog at the sheer one-turn one-sidedness of both games due to their Star Chips being constantly returned to the bag. We've played a good number of games now and never seen the Star Chips dominate proceedings to such an extent (although my other regular opponent would tell you I always return Star Chips to the bag)! We were almost wondering if we played the game incorrectly! It got us talking about just how probable it was that Star Chips would be sent back to the bag and if these two games were as unlikely as they seemed.
Star Chip Return Probability:
Star Chips being returned to the bag with a Special result on the Combat Dice (a 1 in 6 chance), I guessed that with Cool of 5, Johnny must have been perhaps 80% likely to returning a Star Chip to the bag while characters of 4 Cool would have approximately a 60% chance. This was way out.
I would love to say that we sat down and worked this out ourselves but google-fu seemed and turned out to be the faster option. So, to be fair to the webpage where I found the information, here's their link:-
https://www.edcollins.com/backgammon/diceprob.htm?fbclid=IwAR1g4Uq7ba5F0B-GD7FZ2Ytd1P_wqV3eT7ez9rf4kqbetMCTpFhbTEQsS2g
Thanks Edward D. Collins!
To summarise his calculations for our game:-
Number of Combat Dice Rolled Chance of Returning Star Chip To Bag
1 16.67%
2 30.56%
3 42.13%
4 51.77%
5 59.81%
As you can see, the chances of returning a Star Chip are only marginally in your favour with characters who have a current Cool of 4+. Repeating the feat several times in a single turn definitely sees the odds stack up against you!
To find out the probability of Johnny Alpha consecutively returning Star Chips multiple times in a single turn, you multiply the percentages by each other.
Desired Number of Consecutive Successful Cool Tests for Cool 5 Chance of Success
2 59.81% x 59.81% 35.77%
3 59.81% x 59.81% x 59.81% 21.39%
4 59.81% x 59.81% x 59.81% x 59.81% 12.79%
5 59.81% x 59.81% x 59.81% x 59.81% x 59.81% 7.64%
6 59.81% x 59.81% x 59.81% x 59.81% x 59.81% x 59.81% 4.56%
Of course, most characters with Star Chips have a Cool of 4.
Desired Number of Consecutive Successful Cool Tests for Cool 4 Chance of Success
2 51.77% x 51.77% 26.80%
3 51.77% x 51.77% x 51.77% 13.87%
4 51.77% x 51.77% x 51.77% x 51.77% 7.18%
5 51.77% x 51.77% x 51.77% x 59.81% x 59.81% 3.71%
6 51.77% x 51.77% x 51.77% x 51.77% x 51.77% x 51.77% 1.92%
As you can see, the chances are ever-diminishing but I always think it's worth a go! The only time I would say when it may not be desirable is if you have a character with Gunfighter skill in a strong position; but that also comes down to probabilities so it's a judgement call!
Basically, as I like the odds in my favour, I don't think it is worth trying to send your Star Chip back to the bag unless you have a Cool of 4 or 5. That said, you can't make it a rigid rule not to attempt to put them back into the bag; the situation in the game will dictate that sometimes you have to go for it or you may lose the entire scenario (for whatever reason). In those situations you just have to go for it and whatever happens, have no regrets!
Bringing things full circle then, those two games we played were far from typical! The S/D Agents - while aided by some good Armoury Cards - really did some exceptional rolling and performed way beyond anything that could be expected. The fact that they did this two games in a row was unbelievable!
So when you play a scenario where things go gloriously insane like this, try to enjoy the fact that one side are fighting like legends! Next time I'm rooting for the bad guys though!
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