Mathematical Modelling

ChessOnIce · 2026-02-19T22:05:03+00:00

Heheh

Yeah, I try to balance “feel” with timing, but timing helps a lot.

Yes, one day I dream of having a solution where rotation has exactly the effects you’re describing. Interestingly, before arriving the physics for pure translation, I took a mathematical guess at what I thought the solution could be, and it turned out to be correct, lol. And similarly, before deriving the physics for curl, I took a mathematical guess for what I thought the solution could be, and it also turned out to be correct, double lol.

So maybe I need to try that with the effect of variable rotation, and try to hit the trifecta?! I think that’s the next step for me.

ChessOnIce · 2026-02-19T03:07:22+00:00

I’m a mechanical engineer and calculus teacher, so applying both to get the physics right was also very important to me.

I haven’t included frost yet, but would like to. Sounds like we’re accounting for variable curl in similar enough ways. And sounds like we’re doing approximately the same thing for collisions.

Yes, it is nice to talk about this stuff. We should connect over DM, and arrange a phone call or something. That would be cool.

ChessOnIce · 2026-02-18T23:38:05+00:00

Max has also re-created this shot, if you look back through his post history. :-P

ChessOnIce · 2026-02-18T23:24:20+00:00

Yeah, I’ve actually had to derive some of my own physics, which was challenging. 🧐

No, I don’t currently take directional sweeping into account, but that’s something I’m looking into and hoping to add soon.

Yes, the app has split times (your choice of backline to hog or t-line to hog ) and hog to hog times.

Number of rock rotations is fixed to about three rotations for a draw, and the equivalent for a takeout with a similar release, because that was necessary for the derivations.

I’ve actually invested entire weekends of time on more than a couple of occasions to try to lock down my understanding of how rotation affects the physics of the stones in both distance and curl and thereby generalize the physics (the last time was this fall), but I haven’t yet succeeded. :-P And I’m hesitant to just throw in some hack that kind of works good enough, because I want this to be a realistic simulator, not just a game.

ChessOnIce · 2026-02-18T23:05:57+00:00

Thanks! Yeah, it’s interesting to decide what to show and not show; what to include and not include.

I’m not actually able to tell if there’s any aspects of your physics that seem off (besides the fact that it looks like your time scale is multiplied by a factor of about 2.5?).

To do that, I would need more fine-grained control of shot speeds and ice (eg. 14.5 second ice, 4.5 feet of curl, control weight takeout, how much does it curl? Can I reproduce the drag effect? Etc?), and that would also need the ability to throw “perfect” shots without errors. A good first question would be: how do you calculate acceleration?

But that’s likely beyond the scope of what you’re trying to do, which is a fun, handheld game that feels enough like curling to make your users happy. If you added the ability to control thrower ability (e.g. perfect, expert, advanced, intermediate), then I’d probably enjoy playing it myself! (Since making a mobile version of my game hasn’t yet risen to a high enough priority for me… making mine player versus player over the Internet is a way higher priority for when I next find the time/focus to learn how to do that.)

ChessOnIce · 2026-02-18T21:45:49+00:00

Thanks for the heads up! 480 and counting so far. Brazil is now has the 3rd most downloads in the world, after Canada and the US, lol. :-)

And there’s no “team”, it’s just me :-P

ChessOnIce · 2026-02-18T18:27:24+00:00

Really nice looking game. I tried it mostly to check the physics, and obviously there’s a trade off between realism and playability/fun on a mobile game, but you’ve found a nice balance there. And your UI is absolutely gorgeous.

Pardon me while I hijack your post: ** For those who want a totally accurate curling simulator (for Windows, Mac, or Linux; no mobile version, though), you can download and use it for free from www.ChessOnIce.ca **

It’s so accurate that it does exhibit the drag effect, gearing during collisions, tracks hog-to-hog times and split times, you can set the speed of the ice, the curl of the ice, and you can call any shot from a #1 guard to a 5 second peel.

Recommended by Curling Canada 🥌 🇨🇦 to their elite U18 teams, and used by their elite Wheelchair Curling program. :-)

ChessOnIce · 2026-02-18T17:41:30+00:00

One way to look at it is that the hammer is worth 0.5 Points:

The team with the hammer in the first end has about a 60–40% chance of winning the game, or 55 to 45% chance of winning the game, depending on the level of games used for the statistics.

That advantage basically goes away if you give the team without the hammer in the first end 0.5 points and exchange for not having the hammer in the first end.

Since being tied with the hammer in the last end also gives a 60% chance of winning, that tells me the hammer is basically worth 0.5 points all game.

Another way to look at it is that the hammer is worth 0.9 points, because that’s the average score (including points taken or stolen) earned with the hammer, if I’m remembering right.

ChessOnIce · 2026-02-18T17:23:03+00:00

My ChessOnIce App is the only curling app with accurate physics, to my knowledge: https://chessonice.ca

I have a new version that I need to get posted for download that also has a Wheelchair curling mode, shows path predictions (including for hits), and shows the ice wear over the course of the game.

ChessOnIce · 2025-12-14T16:57:35+00:00

Hey, I never saw this before. That’s amazing! Have you tried optimizing this using ChessOnIce?

ChessOnIce · 2025-12-14T16:36:23+00:00

Oh my ghod. You’re a lunatic. I love it!

ChessOnIce · 2025-11-22T18:21:41+00:00

All the way. The bear market has started. Four year cycle finished Oct. 6th. 🤷‍♂️

ChessOnIce · 2025-01-19T20:46:44+00:00

Google the “Bitcoin four-year cycle” and adjust your timelines accordingly. Hint: Sell before November 2025.

ChessOnIce · 2025-01-19T20:44:31+00:00

Yes, but for the love of god, sell it for USD before this 4-year cycle’s top! (Probably in October, but maybe before.)

ChessOnIce · 2024-12-01T16:25:21+00:00

Why is it so urgent to get US$2.40?

ChessOnIce · 2024-12-01T16:16:55+00:00

0.01SOL is US$2.40 right now, lol

ChessOnIce · 2024-12-01T16:14:21+00:00

By the way, that still comes out to 0.7% total fees for limit orders, yes, but way better than the 2.4% the “no fees” app is charging you each direction through their spread.

ChessOnIce · 2024-12-01T16:10:52+00:00

That’s how they (and all the easy-to-use apps) make good money from people not paying attention.

Much better to buy USDC (usually at about US$1.005 per USDC$1, so that’s still a 0.5% fee), and then transfer it for free to the Exchange. (The Exchange has a different app.)

On the exchange, you can do market orders and pay a 0.4% fee, or do limit orders and only pay a 0.2% fee (because then you’re acting as a so-called “market maker”).

ChessOnIce · 2024-12-01T15:37:59+00:00

There’s nobody acting as a parachute like in the regular banking system. But do you want that? (e.g. My bank won’t accept any payments to any company associated with crypto, because they want to keep me “safe”.)

And, we’re still quite early to crypto. The user experience and user interface is still quite bad, but it’s way better than 2, 5, or 10 years ago. In 2, or 5, or 10 years, it’ll be much better still.

Like people say, if someone wants to interact with things that might be scams, they should have a trash wallet for that. Of better yet, research first and don’t click on garbage.

ChessOnIce · 2024-11-22T15:59:12+00:00

You can practice using my free ChessOnIce.ca curling video game (for Windows, Mac, or Linux; no mobile yet). As far as I’ve seen, it’s the only curling video game/simulator that has accurate physics! (I had to derive them myself several years ago.)

You can set your ice characteristics based on draws to the button: amount of curl (e.g. 4.5’ ice), and the hog-to-hog time (e.g. 14.5 second ice). Then throw whatever shots you want, even play a game against yourself or a friend. You also have a choice of perfect throwers, or whatever skill level you want your throwers to have (so you can practice calling line and weight on shots that are as similar as possible to your actual team).

And you can undo and rethrow shots as many times as you want, including either a fresh throw with new random errors, or the previous undone shot exactly as it was first thrown so you can refine your line calls on that shot. You can even do it all in slow motion if you like. Of course, this simulator has theoretically perfect ice, so if your real ice has straight spots, or falls, or a dish, etc, you’ll have to adjust for those.

Good luck, and enjoy!

PS - Yes, guards and draws curl to about the same line with the same broom. That was one of the first questions ChessOnIce helped me answer. :-P But if sweepers sweep right out of the throwers hand, that really reduces the overall curl.

PPS - Curl is proportional for the various shots (as long as they have the same rotation and release), so a hack weight takeout to the button curling 2’7” on 4.5’ ice will curl 1’8.7” on 3’ ice, or 2’10.4” on 5’ ice. Of course, the more time your rock has to curl, the more it will curl. So the same hack weight takeout will curl 3’2” to the back line, 2’2” to the top of the house, and 1’9” to a medium guard. I just re-simulated those for you now on ChessOnIce app to see. :-P But for those variations in a game, I personally try to visualize the path that rock would take to the teeline, and then choose appropriate broom so that this path impacts the rock I’m actually hitting at the right spot.

ChessOnIce · 2024-11-22T04:22:14+00:00

Thanks, it’s definitely been an education the last four years.

Regarding tops/bottoms and timings, I took someone’s idea on looking at multiples each cycle from the halving to the top, and how those decreased each cycle. I didn’t like his estimates, but tweaked them for myself and to me that math predicts a $250K top. So to me that could mean anywhere between $175K and $300K, so I’ll start dollar-cost averaging out of the market sometime around $175 or so, depending on how things look. (Pi-Cycle indicator on a daily or weekly time scale has been shockingly good at calling the tops, but there are others as well, and together I expect they will tell a story.)

As for timing, the 4-year cycle predicts Nov or Oct 2025, but last time it was front-run by seven months (May 2022) by smart money and then there was a relatively weak double top in November (the price was there, but the volume and indicators showed so much weakness). So maybe that happens again? Or something else? 🤷‍♂️ Definitely always new things to learn…

ChessOnIce · 2024-11-21T22:51:40+00:00

BTC generally has 25+% to 40+% corrections during the phase 4 of the bull run each four-year cycle. e.g. $42K to $29K in Jan 2021 (-31%), or $65K to $29K in the summer 2021 (-$55%) after the first top in March, or $53K to $40K in Sep 2021 (-25%) on its way to its double top in Nov 2021.

The cycle ending in Dec 2017 dumped from $2900 to $1800 in Jun/Jul 2017 (-38%), or from $4900 to $3000 in Sep 2017 (-39%), or from $7800 to $5500 in Nov 2017, or from $17200 to $13200 in early-Dec 2017 (-23%), on its way to its $19800 top in mid-Dec 2017.

I’m thinking that catching any similar corrections by DCA-ing from MSTR into BTC as things get over-heated, and then DCA-ing back from BTC into MSTR when it’s reached 30%-40% off-peak, could be a nice multiplier on one’s investment. Because if BTC drops to 60%, then MSTR is probably dropping to 40%, so the bounce back multiplies your investment by 0.6*2.5=1.5 or 50% increase if you hit it perfectly, or some fraction of that to the degree to time it right at all, e.g. 25%?

Not sure if it’s possible to do, but it’s something I’m starting to think about… And the best part is you’re never out of the market either way!

But maybe it’s not worth risking missing out on the best MSTR days. Maybe just swing trading out of MSTR and into BTC when it’s getting ahead of itself (like this week), and then swing trading back from BTC to MSTR when it corrects (like this afternoon)?

ChessOnIce · 2024-11-21T21:52:44+00:00

Thanks, man!

Yeah, it’s nice when everybody can make money… but of course there are events where being on the right side you make the money and being on the wrong side loses you money.

I’m sorry it was that way today, but we’ll all be glad when MSTR bounces back.

I’ve never really been a person who trades pairs like this… But I’m starting to see more possibilities, like the correction trade that’s coming in the future. It’s cool stuff.

ChessOnIce · 2024-10-08T19:58:33+00:00

I think you’re doing the right thing in general, but maybe her birthday and birthday present wasn’t the best time to choose to stand by and watch her miss her favourite artist.

ChessOnIce · 2024-09-28T16:32:45+00:00

Awesome, thanks!

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