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MHill
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Toy Soldiers

December 3rd, 2014, 10:35 pm

The kids are playing a game with their toy soldiers. They're using these rules:FUBARThe kids are playing that a small group of talented heroes are wading their way through hordes of evil henchmen. To make it fair, how many evil henchmen should there be for every talented hero?Simplified, the rules are a bit like:For each soldier, roll a dice to see if he's activated. If activated, shoot at an enemy - roll dice to see if they hit.If a soldier is hit, roll a dice to see if their armour saves them. Else remove them from the game.My starting point was that each toy soldier should be worth the expected number of times it hits an enemy. So this would be a bit like doing discounted cash flows. My projected 'cashflows' could be approximated as p(soldier is activated)×p(soldier hits target).I'd then discount these by the probability that the soldier hadn't been killed immediately before that 'cashflow'. That seemed OK, assuming everyone had an equal likelihood of being hit every turn (I thought I'd get away with that assumption, as both armies are supposed to be equal at the beginning of the game). That way, when working out relative values between soldiers, the unknown discount rate cancels out. That then seemed to get messy when armour came into it. With armour, a soldier has a different discount factor. It seemed to me that I then needed to know the probability of getting hit. Hopefully I'm missing something obvious.Then there's the 'range' of the weapon. My thinking is that this should effect the discount rate of just the first few 'cashflows'. If you have a rifle with a long range, then you're going to stand well back at the beginning of the game. That way you get to make some hits before the enemy moves to get you within their shorter range. Beyond that, I reckoned a lot of the advantage had probably gone.I haven't really thought through the 'suppression' or vehicle rules yet. One thing that's bugging me though is how to quantify the fact that a vehicle can move faster. It means you can get troops in and out of combat faster, but how would you quantify the benefit?Any ideas welcome!
 
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Traden4Alpha
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Toy Soldiers

December 3rd, 2014, 11:07 pm

QuoteOriginally posted by: MHillMy starting point was that each toy soldier should be worth the expected number of times it hits an enemy. So this would be a bit like doing discounted cash flows. My projected 'cashflows' could be approximated as p(soldier is activated)×p(soldier hits target).This does not seem right because it ignores the chance of death. How about a probabilistic finite state machine in which soldiers are in possible states such as: solider_deactivated, solider_activated, target_hit, solider_hit, and solider_dead. Various probabilistic state transitions control the progress of the soldier states. You could also matrix these states with geographic states, but it will get messy
 
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MHill
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Toy Soldiers

December 4th, 2014, 5:54 pm

T4A - thanks. I'll look into that. Outrun - no, experience of playing Monopoly with them says otherwise.
 
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Traden4Alpha
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Toy Soldiers

December 4th, 2014, 7:35 pm

There's also the variant on the fair cake cutting algorithm1. Have the kids decide the ratio of heroes to henchmen2. Flip a coin3. Heads: the kids play the heroes, Tails: the kids must be the henchmen4. GOTO 1 (for Cuch)
 
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MHill
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Toy Soldiers

December 5th, 2014, 2:49 pm

T4A - the simplicity has a lot of appealOutrun - the kids are at a coding session this weekend. I'll suggest this as a topic.I'm going to try & keep it a simple as possible (I'll never be able to explain it to the kids otherwise, but mainly cos my little brain will melt!).I plan to start considering games on a featureless tabletop. There is one hero, and x 'green', unarmed & unarmoured evil henchmen. If the hero has a gun, he starts a distance from the henchmen equal to the gun's range, and starts shooting at them from the start. The henchmen move directly toward the hero to attack. I'll write down the probabilities at each turn, and solve for x. Repeat for various 'Expertise' heroes. Then repeat for 'veteran' vs 'seasoned' etc, to check that this scales linearly.Got to try and keep it simple! - I'm already wondering if the hero has an optimal strategy by alternately shooting then running away.
 
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Traden4Alpha
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Toy Soldiers

December 5th, 2014, 3:25 pm

QuoteOriginally posted by: MHillT4A - the simplicity has a lot of appealOutrun - the kids are at a coding session this weekend. I'll suggest this as a topic.I'm going to try & keep it a simple as possible (I'll never be able to explain it to the kids otherwise, but mainly cos my little brain will melt!).I plan to start considering games on a featureless tabletop. There is one hero, and x 'green', unarmed & unarmoured evil henchmen. If the hero has a gun, he starts a distance from the henchmen equal to the gun's range, and starts shooting at them from the start. The henchmen move directly toward the hero to attack. I'll write down the probabilities at each turn, and solve for x. Repeat for various 'Expertise' heroes. Then repeat for 'veteran' vs 'seasoned' etc, to check that this scales linearly.Got to try and keep it simple! - I'm already wondering if the hero has an optimal strategy by alternately shooting then running away.If you are doing empirical studies, then simply record the mean-time-to-death for henchmen and heroes adjusted by the hero-henchmen ratio. After you've test-played the game for a while, the fact that M heroes survive about as long as N henchmen gives an approximate "fair" ratio.You could even build this empirical process into the design of the game, somewhat like handicapping in golf. Rather than judge a player's skill by whether they win or lose in a fair battle, one judges based on the henchman-per-hero kill ratio over some duration of play. Maybe each hero gets 5 lives and gets to choose the number of henchmen they'll face. If heroes know they are judged on this ratio, then they have incentives to choose the greatest number of henchmen they think they can handle.
 
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Traden4Alpha
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Toy Soldiers

December 5th, 2014, 4:07 pm

One question: is the game play structured for duration (the hero side moves/plays one hero per turn & the henchman side moves/plays one henchman per turn ) or intensity (all M heroes move each turn and all N henchmen move each turn)?
 
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MHill
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Toy Soldiers

December 5th, 2014, 5:39 pm

Oddly, neither. A player rolls a dice to activate a unit (a single model, or group of models). If the activation succeeds, they get to roll to activate another unit. Else the other player gets a go. Repeat until rolls have been made for all units. Start next turn.
 
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Traden4Alpha
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Toy Soldiers

December 5th, 2014, 6:17 pm

QuoteOriginally posted by: MHillOddly, neither. A player rolls a dice to activate a unit (a single model, or group of models). If the activation succeeds, they get to roll to activate another unit. Else the other player gets a go. Repeat until rolls have been made for all units. Start next turn.Interesting! So if one activation entitles the player to roll for another activation, it's possible that player #1 could slaughter their opponent during their first turn (not unlike a pool player that sinks all their balls in one turn). That would seem to add a higher-rorder of volatility to the age play with some turns resulting in no deaths and some turns resulting in a very large number of deaths. P(activation) is going to have a very large impact on fair value of the hero-to-henchman ratio.
 
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MHill
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Toy Soldiers

December 5th, 2014, 9:01 pm

It does indeed! Even in my simple example it has a big impact. If the hero with a gun has a high p(activation), he can get a lot of shots in before the unarmed henchmen (with low p(activation)) do anything at all. I feel the need to change the rules already! Who'd be a henchman?
Last edited by MHill on December 4th, 2014, 11:00 pm, edited 1 time in total.
 
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Traden4Alpha
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Toy Soldiers

December 5th, 2014, 9:32 pm

QuoteOriginally posted by: MHillIt does indeed! Even in my simple example it has a big impact. If the hero with a gun has a high p(activation), he can get a lot of shots in before the unarmed henchmen (with low p(activation)) do anything at all. I feel the need to change the rules already! Who'd be a henchman?If you have two or more players, they could take turns being henchmen who try to kill the player's competitors.