I've just started looking at your videos and really like your clear explanations, thanks! I would like to watch them in the appropriate order, but are having some problems finding the suggested (chronological?) order. Can I suggest that you add an episode number at the beginning of each episode title 😊
Thanks for sharing your computations and nicely explaining your methodology. Here's a couple other factors that you might want to think about for future computations. First, in a game we choose 4 cards from 6, which means that not all 4-card hands are equally likely. For example, 5TJQ is far more common than A38K. (An easy heuristic is: the more points a hand is worth, the more common it is.) In your loop, you could factor this in by weighting each hand by is score. Second, it seems a little strange to average over the dealer and pone. What if some hands really like going first and some hands like going second? Maybe it would be useful to know if there are any patterns for hands that are particularly good for the dealer or non-dealer. Third, (you mentioned it already but) a strategy for hands might be good to simulate and give more accurate values. On average, the dealer + non-dealer score from the play is closer to 5 than 4 (I think it's actually way more). If you don't want a hard-code strategy, you could use strategies that have variable parts like a 'prefered playing order' for each hand, or even some NNs or trees. But as you said, the optimal pegging strategy factors in what your opponent is most likely to have and that requires distilling a lot of information. Finally, maybe this was bait, but you said something about the non-dealer never leading a 5... I can't help myself! There are lots of times the non-dealer should definitely lead a 5 for safety. E.g. 5TJQ, if you lead the 5 and the dealer makes 15 with one of 9 remaining Ts, Js or Qs then you get your points back and avoid a lot of traps. Anyway, thanks for the very nice video.
Thanks for the comment Yes I mention "the non-dealer should never lead a five", but only as an example of a personal rule that someone might have. I didn't mean to suggest this is my own personal rule, or that it's a rule that everyone should follow. So yes, this is perhaps something I could've articulated a bit better in the video. But the point - and this ties into your comment about adding strategy into the simulations - is that this becomes extremely nuanced. As I mentioned in another comment, I didn't introduce any strategy into the simulations because I didn't want to influence the results with my own personal playing tendencies. I also don't believe there are any strategies in cribbage that are 100% applicable in every possible situation (even though I think expected average is a good strategy to employ most of the time), so this video represents just a purely numeric analysis, and a very brief one at that! Introducing situation-dependant strategy would take considerable effort to program, and the computations I've done here are only scratching the surface of what is possible. Also, www.cribbage-play.com/cribbage_hands.shtml claims the average total playing/pegging points in a given round is 5.6 . My figure is lower because my calculations don't factor in strategy.
A way this can be simulated is to use the average number of points for dealer and pone and use eg a standard distribution connected to these points. You then just run a simulation of the scores when starting on a different point. Of course the points per hand is not a normal distribution, but it might be enough to get a first estimate. Best regards Micke
Hi, I have been wondering how the probability of winning depends on each extra point a player starts with. This can be very informative. Eg if pone or dealer starts with one or two points how does this translate to winning percent increase. Is there any possibility you can simulate this? Best regards Micke
All possibilities. As I mentioned in the video, I didn't introduce any strategy into the simulations, because I didn't want to influence the results with my own personal playing tendencies or biases. Moreover, I don't believe there are any strategies in cribbage that are 100% applicable in every possible situation, for every position on the cribbage board. For example, you mention playing the lowest card. Assuming you mean leading with the lowest card? I'm not sure this is the optimal strategy to use in real game-play for every situation, because at 120 points I might be inclined to lead a 10 to bait my opponent into playing a 5 and then I pair with my own 5 and win the game. So this video represents just a purely numeric analysis, still based on the cribbage rules of scoring, but with no strategy written into the code.
I've just started looking at your videos and really like your clear explanations, thanks! I would like to watch them in the appropriate order, but are having some problems finding the suggested (chronological?) order. Can I suggest that you add an episode number at the beginning of each episode title 😊
Thanks for sharing your computations and nicely explaining your methodology. Here's a couple other factors that you might want to think about for future computations.
First, in a game we choose 4 cards from 6, which means that not all 4-card hands are equally likely. For example, 5TJQ is far more common than A38K. (An easy heuristic is: the more points a hand is worth, the more common it is.) In your loop, you could factor this in by weighting each hand by is score.
Second, it seems a little strange to average over the dealer and pone. What if some hands really like going first and some hands like going second? Maybe it would be useful to know if there are any patterns for hands that are particularly good for the dealer or non-dealer.
Third, (you mentioned it already but) a strategy for hands might be good to simulate and give more accurate values. On average, the dealer + non-dealer score from the play is closer to 5 than 4 (I think it's actually way more). If you don't want a hard-code strategy, you could use strategies that have variable parts like a 'prefered playing order' for each hand, or even some NNs or trees. But as you said, the optimal pegging strategy factors in what your opponent is most likely to have and that requires distilling a lot of information.
Finally, maybe this was bait, but you said something about the non-dealer never leading a 5... I can't help myself! There are lots of times the non-dealer should definitely lead a 5 for safety. E.g. 5TJQ, if you lead the 5 and the dealer makes 15 with one of 9 remaining Ts, Js or Qs then you get your points back and avoid a lot of traps.
Anyway, thanks for the very nice video.
Thanks for the comment
Yes I mention "the non-dealer should never lead a five", but only as an example of a personal rule that someone might have. I didn't mean to suggest this is my own personal rule, or that it's a rule that everyone should follow. So yes, this is perhaps something I could've articulated a bit better in the video. But the point - and this ties into your comment about adding strategy into the simulations - is that this becomes extremely nuanced. As I mentioned in another comment, I didn't introduce any strategy into the simulations because I didn't want to influence the results with my own personal playing tendencies. I also don't believe there are any strategies in cribbage that are 100% applicable in every possible situation (even though I think expected average is a good strategy to employ most of the time), so this video represents just a purely numeric analysis, and a very brief one at that! Introducing situation-dependant strategy would take considerable effort to program, and the computations I've done here are only scratching the surface of what is possible.
Also, www.cribbage-play.com/cribbage_hands.shtml claims the average total playing/pegging points in a given round is 5.6 . My figure is lower because my calculations don't factor in strategy.
Thanks, cribbage and probability / statistics: like it
A way this can be simulated is to use the average number of points for dealer and pone and use eg a standard distribution connected to these points. You then just run a simulation of the scores when starting on a different point. Of course the points per hand is not a normal distribution, but it might be enough to get a first estimate.
Best regards
Micke
Hi, I have been wondering how the probability of winning depends on each extra point a player starts with. This can be very informative. Eg if pone or dealer starts with one or two points how does this translate to winning percent increase. Is there any possibility you can simulate this?
Best regards
Micke
Do you simulate each hand to all possibilities or do each player always play their lowest card?
All possibilities. As I mentioned in the video, I didn't introduce any strategy into the simulations, because I didn't want to influence the results with my own personal playing tendencies or biases. Moreover, I don't believe there are any strategies in cribbage that are 100% applicable in every possible situation, for every position on the cribbage board. For example, you mention playing the lowest card. Assuming you mean leading with the lowest card? I'm not sure this is the optimal strategy to use in real game-play for every situation, because at 120 points I might be inclined to lead a 10 to bait my opponent into playing a 5 and then I pair with my own 5 and win the game. So this video represents just a purely numeric analysis, still based on the cribbage rules of scoring, but with no strategy written into the code.