Bene Factum

2013/02/08

Taking your shot

Filed under: Gaming Blog — Tags: , , — AlexWeldon @ 8:10 pm

I’ve been playing Sid Sackson’s seminal classic Can’t Stop the last few days, in its new iPad form. Although I’d (shamefully) never played it until now, simply hearing it described was enough for it to serve as partial inspiration for my own Picnic Blitz, as some reviewers have noticed.

Although I found the AI a challenge for my first few attempts, I learned quickly and, as is often the case with board game AIs, was soon able to defeat it a large majority of the time in one-on-one games. Its biggest weakness, I’ve observed, is that it does not to give enough (or perhaps any, it is hard to tell) consideration to the likelihood that you will be able to win on your next move. It will make an otherwise-sensible preparatory move to improve its odds of completing a column on its next move, without realizing that it isn’t likely to get a next move, and should instead shoot for a win immediately, even if the odds of success are small.

The choice between attempting to win on one’s current move or instead building up power to try to win on a subsequent move is a common dilemma in games; it’s embodied in a very pure form in Can’t Stop (and other press-your-luck dice games such as Nada), but it occurs frequently in other games in a more complex, harder-to-quantify way; deciding when to stop building units and launch a final assault in a military game, or whether to call an opponent’s all-in in poker vs. folding and trying to find a better spot, or when to change gears from building power to going all-out for victory points in many Euro games.
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2012/10/18

Mentalist Poker – a very simple bluffing game

Filed under: Gaming Blog — Tags: — AlexWeldon @ 3:05 pm

I’m a big fan of poker, and of bluffing games in general. If you’re keeping up to date with me, you know that my next release, which will be on shelves soon, is Cash or Crash, a card-based bluffing game that is an elaboration on the basic concept of the classic Liar’s Dice.

This morning, I had an idea for another bluffing game, but one so simple that I could never market it in its basic form, and indeed would be surprised if I turned out to be the first to have come up with it. I haven’t tested it yet, but it’s one of these games that’s so simple as to be self-evident; it’s probably susceptible to mathematical analysis, but if humans have a hard time playing Rock-Paper-Scissors randomly, I doubt that a computer generated table of optimal move-selection probabilities would help anyone become unexploitable in this game.

I am going to start by explaining the game as originally envisioned, as a two-player game. Additional multi-player rules will be given afterwards – both a simple version, and a more elaborate one. The simple version is much the same as the two-player game, but suffers from the problem of being highly dependent on seating order, and would be too easily abused by colluding players sitting next to one another. The more elaborate version would be much more appropriate for cash play, though of course I cannot recommend gambling if you live in a place where gambling is illegal, or are under the legal age.

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2012/08/13

Cash or Crash announcement

Filed under: Site News — Tags: , , , — AlexWeldon @ 7:19 pm

I’m pleased to make the official announcement of the first of the two games of mine that MJ Games is going to be publishing this fall. It’s called Cash or Crash and it is, as it says on the back of the box, the “ultimate bluffing game.” The boxes and cards have already been produced, and now that the final French translation of the rules has been approved and sent off to our printer, production should soon be complete and the games on their way to store shelves for the fall.

Although Cash or Crash is themed as a game of commodity speculation, the fundamental mechanic will be familiar to fans of the traditional dice game known variously as Liar’s Dice, Perudo, Cachito or Santaba; players are invested in a bubble market for one or more of Oil, Wheat or Gold, trying to get rich by correctly timing the collapse and getting out at the right time. Each player is privy to his or her own “insider information” (face down cards) and must attempt to determine what cards the others have played based on their bids, all while bluffing them with his or her own bids.

Like Liar’s Dice, the players’ predictions for the total value of the commodities must constantly escalate, up until someone decides that the market is poised to collapse, whereupon he or she announces “SELL!” and the cards are revealed. If the market had indeed grown too big, the last bidder loses the round and his or her cards, while if it still had room to grow a bit bigger, the seller suffers the consequences instead.

Where Cash or Crash differs, however, is in offering a wider variety of tactical options and a poker-like escalation of stakes over the course of a round. Unlike Liar’s Dice, players cannot change from one commodity to another at will… but they are allowed to bid on multiple commodities at once. So, if the current bid is 4 Gold, the player cannot simply switch to 5 Oil, but can choose between increasing to 5 Gold, or branching out and saying “4 Gold and Oil,” which puts even more pressure on subsequent players, as these combination bids must turn out to be correct for both commodities. Alternately, players may switch to any single commodity of their choice, but only by investing an additional card, thus expanding the market (and their own knowledge of it), but simultaneously increasing the amount they stand to lose if they are the eventual loser of the round.

The game is playable by up to eight players (each with an identical stack of ten cards to start with) and the endgame becomes a tense war of attrition, culminating in an intense battle of wits between the final two players. The rules also include Blitz and Endurance rules, so you can play it as short filler or a longer, more serious competition, plus an optional Doubling rule for the nerviest sharks. Regardless of the version you play, Cash or Crash offers all the tension of the final table of a poker tournament, without the need for money on the line.

2012/05/15

AlexWeldon.com portfolio site launched!

Filed under: Site News — Tags: , , , — AlexWeldon @ 9:19 pm

Portfolio website screenshotAs promised previously, I’ve created a second website, AlexWeldon.com, to host my art & design portfolios. Both Bene Factum and AlexWeldon.com link to each other; you can access the latter through the new “Portfolio Website” navigation link.

Aside from my game design career, I’m a multi-talented creative freelancer. I’ll take on almost any kind of writing, editing, design, illustration or fine art contract, and my rates are reasonable. If you’re in the market for a writer or artist, please check out my portfolio and don’t hesitate to get in touch.

2012/05/01

Fun with Probability – conclusions

Filed under: Gaming Blog — Tags: , , , — AlexWeldon @ 4:07 pm

I’ve been busy the past couple of weeks, and failed to summarize the general conclusions I think can be drawn from my analysis of the simple dice game I proposed. But I’d like to do so before I forget about it entirely.

As a refresher, the basic premise of the game is that players, in turn, get to pick what number they’re going to try to roll on a die. If only one player gets their number, they win, but if two or more do, the one who picked the harder number to roll is the winner.

The conclusions that I reached from my analysis, and which I think have general application to most games in which players get to choose their level of risk, are as follows:

  1. It’s never correct in this game for anyone but the last player to choose a very safe (better than 50% shot) number. The reason is that someone choosing afterwards can always take just a slightly bigger gamble (but still better than 50%) and win most of the time. What this means in general for games of this sort is that you don’t want to play it too safe until you know what your opponents are doing – and even then, only play it safe if you feel they’re all likely to fail. Games are not for the risk-averse!
  2. In a two-player game, you always want to either push just a little harder than your opponent, or else play it as safe as possible if you think he’ll fail. This kind of brinksmanship is intuitive, but the key strategy in most games of this sort would be in determining exactly where that brink lies. In the simple case of a game where the bigger gambler wins if both succeed and you keep going if both fail, you’re shooting for around a 40% chance of success.
  3. When playing with more than two players, you don’t want to match anyone else’s strategy too closely if others still have a chance to adjust theirs. This is the least intuitive results, as gamers often fall into “groupthink” patterns, wherein everyone plays a similar strategy. But it makes sense when you think about it; if two people are doing the same thing, the third player is effectively playing against a single opponent (albeit one who gets two shots at succeeding), and it’s thus easier for him to pick a winning counter-strategy. If the opponents vary their strategies, it’s hard for the remaining player to find a single counter-strategy that works against both.
  4. When your opponent gets a chance to react to your strategy, your best move is generally the one which puts him in a position where all choices are equally attractive. When there’s little advantage to choosing one strategy over another, you minimize the advantage of having that choice.

These are interesting conclusions, and intuitively correct once they’re pointed out. The third – about adopting different strategies than your opponents rather than imitating – is the most interesting of them, and will probably merit additional investigation another day.

Related: Fun with Probability – Part I

Related: Fun with Probability – Part II

Related: Fun with Probability – Part III

2012/04/19

Fun with probability – Part III

Filed under: Gaming Blog — Tags: , , , , — AlexWeldon @ 9:28 pm

Over last couple of days, I’ve been working on analyzing a simplistic game that I came up with to talk about risk-reward decisions in multiplayer games. What I thought would lend itself to easy analysis in order to prove a point, however, turned out to be a pretty complex and interesting math problem. Yesterday, I presented my findings for the two-player case. As you’d expect, it gets a lot more complicated when you add a third player; so much so that I didn’t even bother trying to work anything out for a four-player situation.

The first interesting thing to notice is an elaboration on what I said previously, about larger die sizes (and thus a larger range of choices) favoring the player who gets to pick last. When we think about multiplayer games, we can see that the actual concern has to do with the number of choices relative to the number of players; the extreme case would be that in which we have as many players as there are sides on the die. In that case, we know that all numbers will be chosen in the end. Thus, the first player has just as much information as the last, and can therefore choose the best number for himself, meaning that the last player is at the greatest disadvantage.

In the three-player case, it (perhaps surprisingly) turns out that the break-even point is once again that of the standard six-sided die. The first player should choose 4, the second should choose 5 (just as in the two-player game) and the third is now left with no better choice than to pick 1 and hope the other two fail. Thus, the second player has a 1/3 chance of winning outright, the first player will win 1/2 of the 2/3 of the remaining times, thus 1/3 as well… leaving 1/3 for the third player.

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Fun with probability – Part II

Filed under: Gaming Blog — Tags: , , , — AlexWeldon @ 2:45 am

Yesterday, I posted about a little thought experiment game I’d come up with to look into risk-reward decisions in multiplayer games.

In the game, each player in turn picks a number, from 1 up to the highest number on whatever die is being used. Then everyone rolls, trying to get their number or higher. Out of those who succeeded, the one who picked the highest number (i.e. who took the biggest risk) wins. If everyone fails, they all reroll until at least one person succeeds.

It’s easy enough to work out some basic results for the two-player version on paper. Yesterday, I posed six questions of increasing difficulty to be answered, whether mathematically or simple guesswork. Here they are again, now with the answers.
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2012/04/17

Fun with probability – part I

Filed under: Gaming Blog — Tags: , , , — AlexWeldon @ 7:40 pm

A friend of mine just posted on my Facebook wall, linking to this YouTube video about “Grime Dice,” a set of five dice with numbered faces chosen to have some interesting non-transitive properties; the first is that each of the dice will statistically beat two of the other dice, forming two “A beats B beats C beats D beats E beats A” loops, like Rock-Paper-Scissors-Lizard-Spock. The second, more remarkable property, is that if you roll two dice at a time instead of one, and add the totals, one of these loops remains unchanged, while the other reverses in order (so that E beats D beats C beats B beats A beats E).

After writing my last post, about how risk-reward decisions are affected by a game in which the goal is achieving an all-time high score, I got to thinking about more general cases of risk-reward decision-making in games, and how that is, like these Grime dice, a non-transitive thing. If you have the opportunity to see what kinds of risks your opponents are taking, you’re usually going to want to gamble either just a little bit bigger, so as to come out slightly ahead if you both succeed, or – if you feel your opponent’s strategy is too high-risk, play as safely as possible and count on them failing.

Having been reminded of this by the Grime dice, I decided to invent an extremely minimalist dice game to take a closer look at this idea in the abstract.
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2012/04/13

8×10 Barred Grid Cryptic #1

Filed under: Pencil Puzzles — Tags: , , — AlexWeldon @ 8:47 pm

This is another old cryptic of mine. A couple of the clues weren’t quite to my liking anymore, so I redid them, but there were some pretty good ones that didn’t need changing! Some of the clues are harder than others, but the grid is so open that any word you have trouble with should solve itself by checked letters eventually.

Download: (PDF) (JPG)
Solutions: (PDF) (RTF)

2012/04/10

Pursuing high scores – a limit case

Filed under: Gaming Blog — Tags: , , , , — AlexWeldon @ 1:23 pm

I’ve been obsessively playing Reiner Knizia’s Deck Buster on my iPad lately, despite thinking that it’s objectively not a great game, certainly not as good as his earlier offering Yoku-Gami. I think a lot of the addiction stems from the fact that I was an early adopter and managed to get the #1 global high score in one of the game modes early on… now I’ve been bumped down to #3 and, being a highly competitive person, can’t help but feel a need to try to win my crown back.

The trouble is that, when shooting for a score as high as I need to be #1 again, I find myself being forced to adopt strategies that aren’t nearly as much fun as the ones I was employing when I first started out. Whereas consistency is usually and intuitively a desirable trait in a game player, the nature of competing for high scores encourages exactly the reverse.

What I realize now is that there’s an additional problem with big group games that I failed to mention in my last post and that it’s really what’s going on here, because when the goal is a high score, a seemingly single-player game is actually more like an infinity-player game! Let me explain.

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