Breakthrough draughts

[Casper van der Tak]

If there are more people who'd be interested in launching such experimental GMI tournaments using crowdfunding, let's set up an association (does not need to be officially registered for the time being), so that we have a bit of 'weight' when we start the fund-raising. For the moment, just a message "I am in" will do.

[TAILLE]

Small tweak to your proposal: win =
opponent is out of moves (=current rules) ELSE
(first to get 1 king AND opponent gets at most 1 king) ELSE
(first to get 2 kings AND opponent gets at most 2 kings) ELSE
...

This similar to the rules in eg high jump in athletics: highest distance wins, then least attempts. Here: most kings wins, then quickest to get the equal number of kings.

So eg 1K+2M vs 1K should usually win for majority, unless minority gets first king and can block majority from getting 2nd king, but this should be rare.

The advantage here is that equal games where one side is ahead in tempi and gets first king wins the game as long as he manages to prevent his opponent from getting 2nd king first. This keeps the race character of the regular game of trying to get a king as quickly as possible. It is easy to keep track of as well, since piece identity is irrelevant.

Hi Rain, just a small example to fully understand your proposal:


White to play

Suppose that black is the potential winner (that means that means that black got its second king before white. Note that black got also a material advantage!).
Having in mind the variant 50-45 2-7 39-34! 7x40 45x34 (here there are two white kings against one black king and white becomes the postenetial winner) 50x45 48-37W+
I have two questions:
1) Is it a good understanding of your proposal?
2) Is it really a possibility we want to build? (Black has increased its material advantage but it has lost the game!)

[Rein Halbersma]

Small tweak to your proposal: win =
opponent is out of moves (=current rules) ELSE
(first to get 1 king AND opponent gets at most 1 king) ELSE
(first to get 2 kings AND opponent gets at most 2 kings) ELSE
...

This similar to the rules in eg high jump in athletics: highest distance wins, then least attempts. Here: most kings wins, then quickest to get the equal number of kings.

So eg 1K+2M vs 1K should usually win for majority, unless minority gets first king and can block majority from getting 2nd king, but this should be rare.

The advantage here is that equal games where one side is ahead in tempi and gets first king wins the game as long as he manages to prevent his opponent from getting 2nd king first. This keeps the race character of the regular game of trying to get a king as quickly as possible. It is easy to keep track of as well, since piece identity is irrelevant.

Hi Rain, just a small example to fully understand your proposal:


White to play

Suppose that black is the potential winner (that means that means that black got its second king before white. Note that black got also a material advantage!).
Having in mind the variant 50-45 2-7 39-34! 7x40 45x34 (here there are two white kings against one black king and white becomes the postenetial winner) 50x45 48-37W+
I have two questions:
1) Is it a good understanding of your proposal?
2) Is it really a possibility we want to build? (Black has increased its material advantage but it has lost the game!)

In the final position, both have one king, so it would depend on who got the first king.
Endgame databases with such tiebreak rules are annoying to build, agreed.

[Jaap van Galen]

Ik probeer even een samenvatting te maken van wat hier gezegd is. Volgens mij een belangrijk onderwerp, al zullen lang niet alle dammers het daar mee eens zijn. Maar waarom steekt de KNDB hier zijn nek niet een keer voor uit? Of moeten we zoals Casper het zegt hebben van privé-of crowdfunding?
For Taille, i'm trying to make a summary of an I think very important topic. Unfortunately many draughts-players don't agree on that. I would hope that for at least one time the Dutch council will invest in this idea, and that we are not as Casper says dependent on private investors.

Hi,
Do you know"breakthrough" draughts variant (I do not know if this is the correct wording)? You take the standard rules of the international draughts game but you decide that the first side with a
king wins the game. With this rule the game becomes extremely difficult because you can see that the draw does not exist.
.......
I have programmed only the 10x10 international draugths game and the 8x8 and 10x10 breakthrough draugths games.
As an addition information, for solving the 8x8 breakthrough draughts game I had to generate the 16 pieces endgame database which
needed a lot of time, firstly to find an efficient compression mechanism and secondly to generate the database itself.

Congratulations Gérard with this impressive result!

In 2003 we already played an experimental tournament with this rule, but with one difference: after a breakthrough
the game continues, and the player with the king only wins when he survives. To put it in other words: a regular game is played and only
when there is no winner, the victory goes to the player who first got a king. In this way draws are also impossible but the game stands
much closer to draughts as we know it....

Last month, I spoke with Jaap Bus who as you know is one of the two motors behind the organisation of the computer draughts competitions. According to Jaap, the strongest 4 programmes nowadays literally never beat each other anymore. And indeed, the strongest grandmasters with the games between them are not far behind those 4 programmes.

Of course this is a terrible observation but because the great majority of players are not super GMI the international draughts game looks still very interesting. Even the possibility of a draw is not a problem because, as a consequence, the best payer will try to take risks and even be in a losing position before turning the table and win anyway after a mistake of their opponent.
This context is difficult : at the very top level (the 4 strongest programs or the 4 strongest GMI) the international draughts game is quit dead because almost all games will be a draw but in all other situations the game keeps attractive.
As far as I am concerned, as programmer of the quite strong Damy program, I prefer to switch to a different version.

...I think the question of reducing draws is important. The simple rules, board and pieces of draughts can be a strength. We can explain our rules within 5 minutes, and after that,
nobody should forget. If we can create a complex game from such simple rules, this is elegant and attractive. The problem is that if at the highest level games almost always end in draws, t
he simple rules work against us - it will just appear we are playing a simple game. Worse, a simple game for simple souls.
With such a bad image it will be difficult to promote the game, because eventually, the negative feedback will cause most people to lose interest.

In this brainstorming I would like to propose another solution.
The side with a material advantage wins the game (we have to define the value of king) and, in case of equality, the side which obtains the first king wins.
May be I have some doubt when a side obtains a king but this king is captured some move later before reappearing in the endgame.

If there are more people who'd be interested in launching such experimental GMI tournaments using crowdfunding, let's set up an association (does not need to be
officially registered for the time being), so that we have a bit of 'weight' when we start the fund-raising. For the moment, just a message "I am in" will do.

We all see the advantages of the breakthrough draughts : no draw are possible and the game becomes very complicated because the feeling is that a tiny mistake could very easily change a win in a loss. This last point is interesting in order to change the image of children game comparing to chess game for example...
I am of course very interesting by experimentations!

[TAILLE]

Small tweak to your proposal: win =
opponent is out of moves (=current rules) ELSE
(first to get 1 king AND opponent gets at most 1 king) ELSE
(first to get 2 kings AND opponent gets at most 2 kings) ELSE
...

This similar to the rules in eg high jump in athletics: highest distance wins, then least attempts. Here: most kings wins, then quickest to get the equal number of kings.

So eg 1K+2M vs 1K should usually win for majority, unless minority gets first king and can block majority from getting 2nd king, but this should be rare.

The advantage here is that equal games where one side is ahead in tempi and gets first king wins the game as long as he manages to prevent his opponent from getting 2nd king first. This keeps the race character of the regular game of trying to get a king as quickly as possible. It is easy to keep track of as well, since piece identity is irrelevant.

Hi Rain, just a small example to fully understand your proposal:


White to play

Suppose that black is the potential winner (that means that means that black got its second king before white. Note that black got also a material advantage!).
Having in mind the variant 50-45 2-7 39-34! 7x40 45x34 (here there are two white kings against one black king and white becomes the postenetial winner) 50x45 48-37W+
I have two questions:
1) Is it a good understanding of your proposal?
2) Is it really a possibility we want to build? (Black has increased its material advantage but it has lost the game!)

In the final position, both have one king, so it would depend on who got the first king.

That means that we have to remenber who got the first king, who got the second king etc. In addition what happen when all or a part of the kings are captured during the game? It is of course feasable but IMO we have to build a simpler solution typicaly based on a unique token which can change several time from a side to the other.
Example of rule:
At the beginning of the game noboby has the token
Each time a side gets more kings than the opponent it wins the token
If all kings disappear the token returns to nobody.

Endgame databases with such tiebreak rules are annoying to build, agreed.

It is never a problem. The programmers are all skillful and they can take into account any rule!
Clearly the rules have to be made only for human and programmers will follow.

[TAILLE]

In this brainstorming I would like to propose another solution.
The side with a material advantage wins the game (we have to define the value of king) and, in case of equality, the side which obtains the first king wins.
May be I have some doubt when a side obtains a king but this king is captured some move later before reappearing in the endgame.

Let me try to clarify my proposal above with the handling of a unique token.
First of all I have to define what a material advantage is:
The side with the higher number of kings has the advantage ELSE
The side with the higher number of men has the advantage ELSE
equality

Now how I handle the token.
If there are no kings on the board the token is on a neutral position ELSE
if a side gets a material advantage then it wins the token

Note 1 : in the first phase of the game, when no kings are on the board the token remains neutral.
Note 2 : during the phase with kings on the board the token may change several time from one side to the other

[Rein Halbersma]

In the final position, both have one king, so it would depend on who got the first king.

That means that we have to remenber who got the first king, who got the second king etc. In addition what happen when all or a part of the kings are captured during the game? It is of course feasable but IMO we have to build a simpler solution typicaly based on a unique token which can change several time from a side to the other.
Example of rule:
At the beginning of the game noboby has the token
Each time a side gets more kings than the opponent it wins the token
If all kings disappear the token returns to nobody.

My proposal only requires N tokens, which you can easily put on your scoresheet. Just write BWB... etc if black got first 1st king, white got first 2nd king, black got first 3rd king etc. In the final position, just count the highest number of kings, if that is the same for both players, you look in the N tokens. Eg if final position has 2 kings each, it is white who wins.

[Casper van der Tak]

Ik probeer even een samenvatting te maken van wat hier gezegd is. Volgens mij een belangrijk onderwerp, al zullen lang niet alle dammers het daar mee eens zijn. Maar waarom steekt de KNDB hier zijn nek niet een keer voor uit? Of moeten we zoals Casper het zegt hebben van privé-of crowdfunding?
For Taille, i'm trying to make a summary of an I think very important topic. Unfortunately many draughts-players don't agree on that. I would hope that for at least one time the Dutch council will invest in this idea, and that we are not as Casper says dependent on private investors.

(...)

I agree, this in an ideal world, this would be picked up by KNDB or FMJD. However, I am not expecting any action from either organization, so we need to do it ourselves, if we want such cycle of experimental tournaments. Maybe I'll make a new topic, because here it might be 'snowed under'.

[Michel Stempher]

No, it has nothing to deal with international draughts. Please keep this in a niche world.

[Henk de Witt]

First of all, Gerard, congratulations on the result, which is quite a feat! We can take it as an indicative result that 32-28 in our classical game is the best opening move, something I have suspected for a long time.

I think the question of reducing draws is important. The simple rules, board and pieces of draughts can be a strength. We can explain our rules within 5 minutes, and after that, nobody should forget. If we can create a complex game from such simple rules, this is elegant and attractive. The problem is that if at the highest level games almost always end in draws, the simple rules work against us - it will just appear we are playing a simple game. Worse, a simple game for simple souls. With such a bad image it will be difficult to promote the game, because eventually, the negative feedback will cause most people to lose interest.

This is a reason I have been for quite some time in favor of alternative rules that would lower the percentage of draws (and I believe it is quite similar to the reasons why Henk promoted the Delft rules). There are different ways to go about it, including breakthrough, killer, alternative counting rules (resulting is small and big victories depending on material at the end), and different board sizes & forms (e.g. 9x11, 10x11, etc). One can even consider reducing time available, although to me this does not look like the right approach to make the game structurally more attractive: reducing the time to think seems a poor way to create a game of thought (there are other reasons for limiting time which may be more valid, for example that it could be more attractive for the spectator and more "modern", but I digress).

Within the "breakthrough" family, I like to keep the possibility of combinations that involve giving the opponent a king and then using the king during the combination. With some of the others, I also like keeping some of our old strategic principles, so that if you get a king at a high expense, which is then captured at low cost, you will in the end lose. One way of doing this is use the rule that the player who obtained the first king still on the board in the final position wins. Compact, simple rule.

I see draughts as a family of games with common principles and rule sets, with details differing between the family members. Tournaments and championships can then be organized in different members of the family. Similar say to billiards or bridge.

What I think needs to be done now is experimenting in actual GMI-only tournaments with these alternative rules, and find out what attracts the most media attention, is preferred by spectators, and can draw in the most funding. How to finance these tournaments? If there is interest here and people to work on it, I believe it should be easy to crowdfund an experimental tournament cycle, and I would be happy to work on that together with others.

I see this as complementing actions such as those by Marcel on the distribution of low cost game materials. Materials is important to popularize at the bottom, and image is important, to make the game more attractive and keep those we get interested.

Ha Casper! Met veel genoegen bovenstaand verhaal gelezen. Ik kan vast verklappen dat op zaterdag 25 augustus a.s. in Delft een toernooi met vier grootmeesters wordt gehouden, waarin remise niet mogelijk is. Drie Nederlandse kampioenen hebben inmiddels (onder voorbehoud) toegezegd. Jaap van Galen heeft met behulp van anderen een regel bedacht om een beslissing te forceren als in de slotstand beide spelers precies evenveel materiaal hebben. Het forceren van een beslissing door te kijken wie het eerst op dam kwam speelt ook een rol. Ik neem aan dat Jaap tzt een en ander nader zal toelichten. Jouw idee van crowdfunding om dit soort toernooien (mede) te financieren is zeer waardevol! Het is al langer mijn idee dat meer particuliere toptoernooien wenselijk zijn. Discussies in KNDB-verband zijn eindeloos en lopen steeds weer stuk. Tot frustratie van de meer ideeënrijke en dynamische dammers. Het zelf organiseren van leuke, spannende toptoernooien is zeer bevredigend en stimulerend! En heeft naar alle waarschijnlijkheid meer effect. Crowdfunding kan hier een belangrijke rol spelen. Ik zal hier later op terug komen.

Hello Gérard, 25 August 2018 we will have a grandmaster tournament in Delft. Four players, draws are not possible. Your idea of a break-through plays a role in our discussion.

[Casper van der Tak]

First of all, Gerard, congratulations on the result, which is quite a feat! We can take it as an indicative result that 32-28 in our classical game is the best opening move, something I have suspected for a long time.

I think the question of reducing draws is important. The simple rules, board and pieces of draughts can be a strength. We can explain our rules within 5 minutes, and after that, nobody should forget. If we can create a complex game from such simple rules, this is elegant and attractive. The problem is that if at the highest level games almost always end in draws, the simple rules work against us - it will just appear we are playing a simple game. Worse, a simple game for simple souls. With such a bad image it will be difficult to promote the game, because eventually, the negative feedback will cause most people to lose interest.

This is a reason I have been for quite some time in favor of alternative rules that would lower the percentage of draws (and I believe it is quite similar to the reasons why Henk promoted the Delft rules). There are different ways to go about it, including breakthrough, killer, alternative counting rules (resulting is small and big victories depending on material at the end), and different board sizes & forms (e.g. 9x11, 10x11, etc). One can even consider reducing time available, although to me this does not look like the right approach to make the game structurally more attractive: reducing the time to think seems a poor way to create a game of thought (there are other reasons for limiting time which may be more valid, for example that it could be more attractive for the spectator and more "modern", but I digress).

Within the "breakthrough" family, I like to keep the possibility of combinations that involve giving the opponent a king and then using the king during the combination. With some of the others, I also like keeping some of our old strategic principles, so that if you get a king at a high expense, which is then captured at low cost, you will in the end lose. One way of doing this is use the rule that the player who obtained the first king still on the board in the final position wins. Compact, simple rule.

I see draughts as a family of games with common principles and rule sets, with details differing between the family members. Tournaments and championships can then be organized in different members of the family. Similar say to billiards or bridge.

What I think needs to be done now is experimenting in actual GMI-only tournaments with these alternative rules, and find out what attracts the most media attention, is preferred by spectators, and can draw in the most funding. How to finance these tournaments? If there is interest here and people to work on it, I believe it should be easy to crowdfund an experimental tournament cycle, and I would be happy to work on that together with others.

I see this as complementing actions such as those by Marcel on the distribution of low cost game materials. Materials is important to popularize at the bottom, and image is important, to make the game more attractive and keep those we get interested.

Ha Casper! Met veel genoegen bovenstaand verhaal gelezen. Ik kan vast verklappen dat op zaterdag 25 augustus a.s. in Delft een toernooi met vier grootmeesters wordt gehouden, waarin remise niet mogelijk is. Drie Nederlandse kampioenen hebben inmiddels (onder voorbehoud) toegezegd. Jaap van Galen heeft met behulp van anderen een regel bedacht om een beslissing te forceren als in de slotstand beide spelers precies evenveel materiaal hebben. Het forceren van een beslissing door te kijken wie het eerst op dam kwam speelt ook een rol. Ik neem aan dat Jaap tzt een en ander nader zal toelichten. Jouw idee van crowdfunding om dit soort toernooien (mede) te financieren is zeer waardevol! Het is al langer mijn idee dat meer particuliere toptoernooien wenselijk zijn. Discussies in KNDB-verband zijn eindeloos en lopen steeds weer stuk. Tot frustratie van de meer ideeënrijke en dynamische dammers. Het zelf organiseren van leuke, spannende toptoernooien is zeer bevredigend en stimulerend! En heeft naar alle waarschijnlijkheid meer effect. Crowdfunding kan hier een belangrijke rol spelen. Ik zal hier later op terug komen.

Hello Gérard, 25 August 2018 we will have a grandmaster tournament in Delft. Four players, draws are not possible. Your idea of a break-through plays a role in our discussion.

Henk, dat is mooi, ik zie er naar uit! En hoop dat dit de eerste van een serie toernooien zal worden.

[TAILLE]

First of all, Gerard, congratulations on the result, which is quite a feat! We can take it as an indicative result that 32-28 in our classical game is the best opening move, something I have suspected for a long time.

I think the question of reducing draws is important. The simple rules, board and pieces of draughts can be a strength. We can explain our rules within 5 minutes, and after that, nobody should forget. If we can create a complex game from such simple rules, this is elegant and attractive. The problem is that if at the highest level games almost always end in draws, the simple rules work against us - it will just appear we are playing a simple game. Worse, a simple game for simple souls. With such a bad image it will be difficult to promote the game, because eventually, the negative feedback will cause most people to lose interest.

This is a reason I have been for quite some time in favor of alternative rules that would lower the percentage of draws (and I believe it is quite similar to the reasons why Henk promoted the Delft rules). There are different ways to go about it, including breakthrough, killer, alternative counting rules (resulting is small and big victories depending on material at the end), and different board sizes & forms (e.g. 9x11, 10x11, etc). One can even consider reducing time available, although to me this does not look like the right approach to make the game structurally more attractive: reducing the time to think seems a poor way to create a game of thought (there are other reasons for limiting time which may be more valid, for example that it could be more attractive for the spectator and more "modern", but I digress).

Within the "breakthrough" family, I like to keep the possibility of combinations that involve giving the opponent a king and then using the king during the combination. With some of the others, I also like keeping some of our old strategic principles, so that if you get a king at a high expense, which is then captured at low cost, you will in the end lose. One way of doing this is use the rule that the player who obtained the first king still on the board in the final position wins. Compact, simple rule.

I see draughts as a family of games with common principles and rule sets, with details differing between the family members. Tournaments and championships can then be organized in different members of the family. Similar say to billiards or bridge.

What I think needs to be done now is experimenting in actual GMI-only tournaments with these alternative rules, and find out what attracts the most media attention, is preferred by spectators, and can draw in the most funding. How to finance these tournaments? If there is interest here and people to work on it, I believe it should be easy to crowdfund an experimental tournament cycle, and I would be happy to work on that together with others.

I see this as complementing actions such as those by Marcel on the distribution of low cost game materials. Materials is important to popularize at the bottom, and image is important, to make the game more attractive and keep those we get interested.

Ha Casper! Met veel genoegen bovenstaand verhaal gelezen. Ik kan vast verklappen dat op zaterdag 25 augustus a.s. in Delft een toernooi met vier grootmeesters wordt gehouden, waarin remise niet mogelijk is. Drie Nederlandse kampioenen hebben inmiddels (onder voorbehoud) toegezegd. Jaap van Galen heeft met behulp van anderen een regel bedacht om een beslissing te forceren als in de slotstand beide spelers precies evenveel materiaal hebben. Het forceren van een beslissing door te kijken wie het eerst op dam kwam speelt ook een rol. Ik neem aan dat Jaap tzt een en ander nader zal toelichten. Jouw idee van crowdfunding om dit soort toernooien (mede) te financieren is zeer waardevol! Het is al langer mijn idee dat meer particuliere toptoernooien wenselijk zijn. Discussies in KNDB-verband zijn eindeloos en lopen steeds weer stuk. Tot frustratie van de meer ideeënrijke en dynamische dammers. Het zelf organiseren van leuke, spannende toptoernooien is zeer bevredigend en stimulerend! En heeft naar alle waarschijnlijkheid meer effect. Crowdfunding kan hier een belangrijke rol spelen. Ik zal hier later op terug komen.

Hello Gérard, 25 August 2018 we will have a grandmaster tournament in Delft. Four players, draws are not possible. Your idea of a break-through plays a role in our discussion.

At least to know that discussions exist is good news because we know that a grandmaster tournament leads to (too) many draws.

[TAILLE]

I said several times that breakthrough draughts is more complicated than international draughts.
FYI after having studying various endgames (i.e. at most 20 pieces on the board) from GMI during worldchampionship I made small statistics concerning draw games with the following results:
1) On average each side has a little more than 4 moves allowing to draw
2) When analysing these games in a breakthrough context the winning side has on average 2 moves allowing to win
3) Taking now only the winning positions in breakthrough draughts context and taking aside the positions leading to a quite obvious tactical win then, in the great majority of cases, the move chosen by the GMI (in the international draughts context) is also a winning move in the breakthrough context
4) In addition my own feeling is that the side which seems to have a small advantage (in the international draughts context) is really the side with a winning position in the breakthrough context.

Of course if somebody is interested by the analysis of a particuliar drawing game I will be happy to bring my help fo the breakthrough context.

[TAILLE]

Just for your curiosity here after a breakthrough draughts analysis:

[Event "Polish Open Karpacz 2017"]
[White "Virny, Vadim"]
[Black "Shvartsman, Alexander"]
1. 32-28 17-22 2. 28x17 12x21 3. 37-32 7-12 4. 41-37 1-7 5. 31-26 19-23 6. 26x17 12x21 7. 37-31 7-12 8. 32-27 21x32 9. 38x27 14-19 10. 43-38 10-14 11. 49-43 11-17 12. 46-41 2-7 13. 31-26 5-10 14. 42-37 7-11 15. 47-42 19-24 16. 34-29 23x34 17. 39x19 14x23 18. 37-32 10-14 19. 35-30 14-19 20. 30-25 20-24 21. 41-37 4-10 22. 44-39 10-14 23. 50-44 17-22 24. 37-31 23-28 25. 32x23 19x28 26. 42-37 11-17 27. 37-32 28x37 28. 31x42 22x31 29. 26x37 16-21 30. 33-29 24x33 31. 39x28 6-11 32. 38-32 14-19 33. 44-39 18-22 34. 39-33 12-18 35. 43-38 22-27 36. 37-31 18-23 37. 31x22 15-20 38. 25x14 19x10 39. 28x19 17x39 40. 32-28 13x24 41. 38-33 9-13 42. 33x44 13-18 43. 44-39 8-13 44. 40-34 11-17 45. 42-38 13-19 46. 39-33 10-14 47. 45-40 18-22 48. 48-42 14-20 49. 34-29 20-25 50. 29x20 25x14 51. 42-37 14-20 52. 37-31 21-27 53. 33-29

Position after 35…22-27

White to move

Breakthrough analysis :
This position is a winning one and 36.40-35 is the only winning move.
36. 37-31
for a breakthrough analysis this move is a losing move . The reason is that it gives black a tempi advantage without any compensation. Against a weaker opponent surely Virny would not have made this move. Against Shvartsman I suspect Virny has correctly calculated that in exchange of a rather small disadvantage he has managed to simplify the position in order to reach the draw
18-23 37. 31x22 15-20 38. 25x14 19x10 39. 28x19 17x39 40. 32-28 13x24 41. 38-33 9-13
Here black had 12 winning moves. It’s exceptional and prove undoubtedly a black advantage. In a international draughts game this advantage looks however too small for a win. Black can of course take the control of square 27 but White can easily get a good compensation by taking the control of the square 29.
42. 33x44 13-18 (black here had 10 winning moves) 43. 44-39 8-13 (black here had 8 winning moves) 44. 40-34 11-17 (black here had 8 winning moves) 45. 42-38 13-19 (black here had 7 winning moves) 46. 39-33 10-14 (black here had 7 winning moves) 47. 45-40 18-22 (black here had 4 winning moves) 48. 48-42 14-20 (black here had 3 winning moves) 49. 34-29 20-25 (black here had 3 winning moves) 50. 29x20 25x14 51. 42-37 14-20 (black here had 5 winning moves) 52. 37-31 21-27 (black here had 4 winning moves) 53. 33-29 B+
You can see that all black moves were certainly the best moves in a breakthrough draughts context : after the initial small combination black manages to create a lot of winning moves limiting a potential mistake.
I would have been very happy to see Virny play the 36.40-35 move and the game would have been far more complicated and interesting. But we were … in the international draughts context and in this context 36.37-31! was the best way to reach the draw without great difficulties.

[Jan Pieter]

I would have been very happy to see Virny play the 36.40-35 move and the game would have been far more complicated and interesting. But we were … in the international draughts context and in this context 36.37-31! was the best way to reach the draw without great difficulties.

There is one thing you forget. The position only is interesting because black chose for complications in order to create chances. In breakthrough draughts Schwarzman probably would have played 33. ... 11-16 instead of the daring 33. ... 22-27 followed by 35. ... 27-31.