My New Idea, Gambling Chess

[Dice Man]

Okay, this might already exist in the world, but I haven't seen anything to actually confirm it.

This is the general idea:

Chess is one of those games that has very little luck factor in it. Of all the people I have played at it, I have quite a good idea who is better and who is worse than me. Furthermore, those who I am slightly slightly better than I feel that I could beat them 80% of the time, and those who are slightly slightly better than me I think could beat me 80% of the time. (I'd say these people respectively are only about 1% worse and better than me). Those 20% values only really allow for the possibility of somebody making a stupid error which they would probably regret as soon as they had seen it (as opposed to being outplayed by a long term strategy) Against somebody who plays chess relatively competetively (say on the national level) I think I would probably win about 1 in a 1000 games.

For these reasons I would be unwilling to bet very much money playing chess. If somebody challenged me who I had previously thought was a worse player than me, I'd find it likely that they had improved sufficiently, and the bet would not be worth it. If the game was heads up poker, and again somebody challenged me confidently who I had previously thought I was better than, I would probably accept because I know that no matter how great they have become at it, I still have a half-decent chance of winning, because luck is so important to heads up play.

So I have thought of a version of chess that involves dice and therefore chance. There are obviously lots of variants of Gambling Chess, so these rules are just suggestions and subject to later agreement with whoever I'm playing with.

As with standard chess, a player must decide what move they want to make first, and then the dice take over.

With sliders (queens, castles and bishops), the piece can only move maximum D6 places (i.e. the number given by a fair 6-sided die). If you say you want to move 5 places, then if the die rolls 5 or 6, you are successful, if it is 4 or less than the piece must stop short and move only the number of spaces in that direction prescribed by the die.

With non-sliders, the piece may only move if you roll 3+ on a D6. If you roll 1-2 your turn is effectively forfeited. (A variant could be that it is only forfeited if you roll a 1, and that if you roll a 2, you have to make a different move with a different piece)

Kings can move on a 2+.

If a player is in check, they can opt to move a piece to intercept the check, and if that fails to move, they get another opportunity to move the king.

So what are the main effects of these sorts of rules?

It means there is a lot of risks with using sliders, because if you miss your target you may end up in front of a pawn. You ought really to consider the expected utility of your piece ending up on any of the pieces it could end up on if you are making a long move.

It means there are surprise victories. In standard chess, in my experience at least, the player that wins is usually the one that grinds down his opponent bit by bit. In Gambling Chess, you ought to put your opponent in check as much as possible, because you could get a surprise early victory if their king fails to move by rolling a 1. This also means you should attempt to get out of check by moving other pieces before you have to move your king.

Gambling Chess is a lot like poker, because you have to weigh up the expected value of many possible outcomes that your choices could lead to. Consider the following sort of trivial example. Say that you are black and it is your turn to move.



What is the expected value of you attempting to take the white queen? Let's say that this is a mini-game, where you get 1 point for taking the opponent's queen and -1 for being taken.

If you attempt to take it, you succeed directly 1/3 of the time. The other 2/3 of the time you put yourself in a tough position. 1/6 of that time you end up right in front of their queen so they instantly take you next turn.

1/6 of the time you end up 4 places from them, 1/6 of the time 3 places and 1/6 2 places. Furthermore we know that if any of those possibilities occur, they try to attack us next turn. I think we can calculate the EV of attacking here as so:

(1/3 x 1) + (1/6 x -1) + (1/6 x [5/6 x -1 + 1/6 x 1]) + (1/6 x [4/6 x -1 +1/6 x 1 + (1/6 x [5/6 x -1 + 1/6 x 1])])
+ (1/6 x [1/2 x -1 + 1/6 x 1 + {1/6 x (5/6 x 1 + 1/6 x -1)} + (1/6 x (4/6 x 1 + 1/6 x -1 + 1/6 x {5/6 x -1 + 1/6 x 1}))])

= 1/3 - 1/6 - 4/36 - 22/216 - 44/1296

= (432 - 216 - 144 - 132 - 44)/ 1296

= -104/1296

= - 13/162

= -0.08

So in this particular version of Gambling Chess, it is always irrational to attack enemy pieces that are 5 or more squares away (at least with no other pieces around doing stuff). Of course some players might still do it because they are in a gambling mood, and if they take that one piece, the whole game could swing in their favour (maybe it leads directly to a check-mate as well for added EV, but how can you calculate that?)

What if they are 4 squares away from you? I suspect it is really borderline to attack them, but probably slightly +EV. The calculation is:

(1/2 x 1) + (1/6 x -1) + (1/6 x[5/6 x -1 + 1/6 x 1]) + (1/6 x [4/6 x -1 +1/6 x 1 + 1/6 x (5/6 x 1 + 1/6 x -1)])

= 1/2 - 1/6 - 4/36 - 7/108

= 1/26

= 0.04

Yes, slightly +EV to attack a piece 4 spaces away. These calculations have taken me about an hour, (I got the first one wrong about 3 times first) and this is in a 2-piece game! It gets more complicated if you include something like this:



So yeah, this looks like a pretty tough game. It's possibly one of those games like No Limit Holdem where a computer cannot yet play better than a person can play it. I really don't know. I think this game (in the long run) would be a better test of human intelligence than standard chess is.

In conclusion, Gambling Chess is probably the shit. Plus it's such a flexible game in that you can add and change the ground rules so much. You can give players better odds by having the better player play with one or two less pawns (or more). And there are over 1000 kinds of chess pieces that you can add into the game to mix it up a bit (weird shit like grasshoppers and nightriders- See Fairy chess piece - Wikipedia, the free encyclopedia for more)

Another way that it's like poker is that the whole game will usually be decided on a few important moves. When you start the game, moving pawns and getting your knights out is a bit equivalent to winning or losing pots in the first blind level of a deep stack: they can put you ahead or behind but not by much. Later on in the tournament you'll be more likely to stick it all in on a probable coinflip. Your responsibility as a good player is to try to get the better % on the coinflip, with better EV. In Gambling Chess there are bound to be some crucial moves that are decided by chance, like getting lucky with a long-range check, or taking of your opponent's queen etc. As with the poker player, the Gambling Chess player has to just go for a strategy that'll give them a better edge in the long term.

Also, like poker, it'd be very difficult to tell who is the better between two players over a finite amount of games, whereas in regular chess it's quite obvious. This means that there will be more action, and possibly, addiction, as lots of people think they are really good at it.

[lucky_scrote]

tldr


cliff notes plz

[Dice Man]

Cliff notes: Chess + Dice = The Shit (probably)

[PokerWoody]

This is just the wrong place to post all that stuff i didn't read.

[Dice Man]

I'm not expecting anybody to go through the ridiculously long calculations or anything. The whole point of doing that was basically to show that using game theory to work out how to play Gambling Chess is basically impossible. Remember that game theory paper that Chris Ferguson wrote on limit holdem? (And Ferguson doesn't really ever apply game theory when he plays poker: his game theory background is partially to make idiots think that he is really capable of doing those calculations in his head. In reality he's just a good player like other good players.) Even then it was quite a basic limit holdem and the paper was impossible to actually understand for non-mathematicians. And yet we all know how to play chess and no limit poker without doing any of these hideous equations. That's what makes it a good game. We can only ever tend towards the optimal strategy, the actual optimal strategy is simply impossible to work out. There isn't a computer in the world that could work out that stuff.

[Gus Mango Fish]

I've just ploughed through that. An interesting idea for a game I think. I'd have a go. Bring a chess set with you to the next game we're both at and I'll give you a game of Gambling Chess if we both bust out.

[PokerWoody]

Originally Posted by PokerWoody

This is just the wrong place to post all that stuff i didn't read.

Yeah, sorry Dice. I didn't mean to sound rude, just that your idea scared me before I read it.

[Top Pair Ace Kicker]

I got as far as the part saying non-sliders.

Do I win a prize?

[lev1athan]

Originally Posted by Dice Man

In conclusion, Gambling Chess is probably the shit.

PMSL at that... I'll take on the winner of Diceman vs Donk Dale.

I reckon it's an awesome idea... we should give this a few dry runs to see if it is indeed awesome - or, entirely plausibly - gash.

[RoloCookie]

Sounds pretty cool, scary number of possibilities there though. I think I might challenge a friend to a few games. Not sure it'll catch on as a gambling game though sheer complexity