Χρόνια πολλά σε όλους!
Οφείλω να ομολογήσω ότι ο τίτλος είναι παραπλανητικός! Μιας και όλοι ασχολούνται αυτές τις μέρες (εκτός από κουραμπιέδες και μελομακάρονα!) με απολογισμούς, προϋπολογισμούς, και κάθε λογής υπολογισμούς, είπα να προσθέσω και ‘γώ λίγα ακόμη νούμερα στη ζωή σας!
Έχω συλλέξει και θα παρουσιάσω πίνακες που αφορούν πιθανότητες για διάφορες περιπτώσεις!
Θα ξεκινήσω για ορεκτικό με τα πιο ‘εύπεπτα’ στατιστικά:
Ο πίνακας 1 απεικονίζει την πιθανότητα να μοιραστεί μια συγκεκριμένη κατηγορία αρχικών φύλλων, ενώ στον πίνακα 2 εμφανίζονται τα ποσοστά νίκης ανά κατηγορία ‘μάχης’!
Όσοι, διαβάζοντας μέχρι εδώ, θεωρήσετε ότι το άρθρο αφορά αρχαρίους και ότι αυτά τα παίζετε στα δάκτυλα, θα συμβούλευα να μην βιαστείτε να σταματήσετε την ανάγνωση, καθώς οι επόμενοι πίνακες θα φανούν χρήσιμοι ακόμη και στους εμπειρότερους των παικτών!
Έστω ότι όλοι κάνουν fold έως εσάς, βρίσκεστε στο cutoff και έχετε Α9. Τι πιθανότητα έχετε να βρεθείτε dominated στους εναπομείναντες παίκτες; Ελάχιστα παραπάνω από 12%! Οι πίνακες 3 και 4 θα σας δώσουν όλα τα χρήσιμα στοιχεία για τα dominated hands!
Ο πίνακας 5 κάνει τα πράγματα πιο σύνθετα: δίνει την πιθανότητα να είστε dominated όταν έχετε ζεύγος από περισσότερους του ενός παίκτες, ενώ ο πίνακας 6 δίνει τις πιθανότητες να ΜΗΝ εμφανιστεί overcard στο board για κάθε street ξεχωριστά, όταν κρατάμε κάποιο ζεύγος. Είναι εντυπωσιακό το γεγονός ότι αν δεν έχουμε Α στο χέρι μας, αυτός θα εμφανιστεί ως το river στο 35% των περιπτώσεων, ενώ ακόμη εντυπωσιακότερο είναι όταν κρατάμε QQ να εμφανιστεί overcard ως το river στο 60% των περιπτώσεων. Γιατί τότε οι QQ δεν είναι 40-60 vs ΑΚ; Γιατί πολύ απλά υπάρχουν όλες εκείνες οι περιπτώσεις που θα εμφανιστεί Q, ή οι QQ θα κερδίσουν με κέντα ή χρώμα!
Ο πίνακας 7 απεικονίζει την πιθανότητα εμφάνισης συγκεκριμένου συνδυασμού καρτών στο flop. Με τον πίνακα 8 θα αγγίξουμε το ευαίσθητο θέμα των runner runner outs! Το ξέρατε ότι η πιθανότητα για runner runner flush είναι λίγο πάνω από 4%; Ή ότι η πιθανότητα για καρέ χωρίς set (ή trips) στο flop είναι 1 στις 1000 περίπου;
Και επειδή σας βλέπω ότι ‘μπουκώσατε’ από νούμερα, νομίζω πως ήρθε η ώρα για λίγη βασιλόπιτα!
Καλή χρονιά σε όλους και καλά κέρδη!
| Πίνακας 1: Πιθανότητα μοιράσματος | |
|---|---|
| Αρχικό φύλλο | Πιθανότητα |
| AKs (or any specific suited cards) |
0,30% |
| AA (or any specific pair) |
0,45% |
| AKs, KQs, QJs, or JTs (suited cards) |
1,21% |
| AK (or any specific non-pair incl. suited) |
1,21% |
| AA, KK, or QQ |
1,36% |
| AA, KK, QQ or JJ |
1,81% |
| Suited cards, jack or better |
1,81% |
| AA, KK, QQ, JJ, or TT |
2,26% |
| Suited cards, 10 or better |
3,02% |
| Suited connectors |
3,92% |
| Connected cards, 10 or better |
4,83% |
| Any 2 cards with rank at least queen |
4,98% |
| Any 2 cards with rank at least jack |
9,05% |
| Any 2 cards with rank at least 10 |
14,30% |
| Connected cards (cards of consecutive rank) |
15,70% |
| Any 2 cards with rank at least 9 |
20,80% |
| Not connected nor suited, at least one 2-9 |
53,40% |
| Πίνακας 2: Πιθανότητες αναμετρήσεων |
|
|---|---|
| Φαβορί vs Χειρότερο φύλλο |
Πιθανότητα |
| Pair vs 2 undercards |
83,00% |
| Pair vs lower pair |
82,00% |
| Pair vs 1 overcard, 1 undercard |
71,00% |
| 2 overcards vs 2 undercards |
63,00% |
| Pair vs 2 overcards |
55,00% |
| Πίνακας 3: Πιθανότητα Domination – Pairs |
|||||||||
|---|---|---|---|---|---|---|---|---|---|
| Hand | 2 Players | 3 Players | 4 Players | 5 Players | 6 Players | 7 Players | 8 Players | 9 Players | 10 Players |
| 22 | 5,88% | 11,41% | 16,62% | 21,50% | 26,09% | 30,43% | 34,49% | 38,34% | 41,94% |
| 33 | 5,39% | 10,48% | 15,29% | 19,88% | 24,16% | 28,26% | 32,12% | 35,76% | 39,22% |
| 44 | 4,90% | 9,55% | 14,00% | 18,21% | 22,22% | 26,02% | 29,66% | 33,09% | 36,37% |
| 55 | 4,41% | 8,63% | 12,66% | 16,55% | 20,20% | 23,74% | 27,10% | 30,33% | 33,42% |
| 66 | 3,93% | 7,69% | 11,31% | 14,81% | 18,15% | 21,38% | 24,49% | 27,45% | 30,33% |
| 77 | 3,43% | 6,74% | 9,95% | 13,05% | 16,04% | 18,97% | 21,75% | 24,47% | 27,11% |
| 88 | 2,93% | 5,80% | 8,58% | 11,29% | 13,90% | 16,47% | 18,95% | 21,37% | 23,72% |
| 99 | 2,46% | 4,84% | 7,19% | 9,47% | 11,71% | 13,91% | 16,05% | 18,13% | 20,17% |
| ΤΤ | 1,96% | 3,88% | 5,79% | 7,64% | 9,48% | 11,27% | 13,04% | 14,76% | 16,48% |
| JJ | 1,47% | 2,92% | 4,36% | 5,78% | 7,19% | 8,57% | 9,93% | 11,30% | 12,63% |
| 0,98% | 1,96% | 2,92% | 3,88% | 4,84% | 5,79% | 6,73% | 7,68% | 8,60% | |
| KK | 0,49% | 0,98% | 1,47% | 1,96% | 2,44% | 2,93% | 3,42% | 3,90% | 4,40% |
| AA | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Πίνακας 4: Πιθανότητα Domination – Non-Pairs |
|||||||||
|---|---|---|---|---|---|---|---|---|---|
| Hand | 2 Players | 3 Players | 4 Players | 5 Players | 6 Players | 7 Players | 8 Players | 9 Players | 10 Players |
| 32 | 27,18% | 47,46% | 62,45% | 73,43% | 81,41% | 87,15% | 91,23% | 94,08% | 96,06% |
| 42 | 25,72% | 45,29% | 60,03% | 71,08% | 79,27% | 85,31% | 89,69% | 92,86% | 95,11% |
| 43 | 24,73% | 43,77% | 58,33% | 69,35% | 77,66% | 83,86% | 88,46% | 91,84% | 94,29% |
| 52 | 24,25% | 43,04% | 57,51% | 68,58% | 76,96% | 83,27% | 87,98% | 91,46% | 94,00% |
| 53 | 23,27% | 41,52% | 55,73% | 66,74% | 75,21% | 81,68% | 86,58% | 90,25% | 92,99% |
| 54 | 22,29% | 39,96% | 53,91% | 64,85% | 73,37% | 79,99% | 85,06% | 88,94% | 91,89% |
| 62 | 22,78% | 40,78% | 54,93% | 65,93% | 74,48% | 81,05% | 86,06% | 89,83% | 92,69% |
| 63 | 21,80% | 39,20% | 53,04% | 63,98% | 72,57% | 79,27% | 84,45% | 88,43% | 91,47% |
| 64 | 20,83% | 37,62% | 51,15% | 61,97% | 70,57% | 77,37% | 82,72% | 86,91% | 90,15% |
| 65 | 19,84% | 36,06% | 49,22% | 59,90% | 68,50% | 75,40% | 80,90% | 85,27% | 88,71% |
| 72 | 21,31% | 38,47% | 52,21% | 63,15% | 71,82% | 78,61% | 83,91% | 88,01% | 91,15% |
| 73 | 20,33% | 36,88% | 50,28% | 61,08% | 69,73% | 76,61% | 82,08% | 86,37% | 89,71% |
| 74 | 19,35% | 35,26% | 48,29% | 58,92% | 67,58% | 74,53% | 80,12% | 84,59% | 88,13% |
| 75 | 18,36% | 33,64% | 46,30% | 56,74% | 65,32% | 72,32% | 78,05% | 82,68% | 86,41% |
| 76 | 17,38% | 32,01% | 44,25% | 54,48% | 62,99% | 70,04% | 75,86% | 80,65% | 84,56% |
| 82 | 19,84% | 36,11% | 49,43% | 60,23% | 68,94% | 75,93% | 81,51% | 85,91% | 89,38% |
| 83 | 18,87% | 34,49% | 47,39% | 58,02% | 66,67% | 73,74% | 79,44% | 84,02% | 87,68% |
| 84 | 17,87% | 32,86% | 45,37% | 55,74% | 64,34% | 71,42% | 77,22% | 81,97% | 85,81% |
| 85 | 16,91% | 31,20% | 43,27% | 53,41% | 61,91% | 69,00% | 74,90% | 79,76% | 83,77% |
| 86 | 15,93% | 29,53% | 41,14% | 51,03% | 59,39% | 66,45% | 72,41% | 77,39% | 81,55% |
| 87 | 14,94% | 27,86% | 38,98% | 48,56% | 56,78% | 63,79% | 69,78% | 74,88% | 79,18% |
| 92 | 18,37% | 33,73% | 46,54% | 57,13% | 65,88% | 73,02% | 78,85% | 83,56% | 87,34% |
| 93 | 17,40% | 32,08% | 44,42% | 54,79% | 63,43% | 70,58% | 76,50% | 81,35% | 85,33% |
| 94 | 16,41% | 30,41% | 42,30% | 52,39% | 60,89% | 68,04% | 74,01% | 78,99% | 83,10% |
| 95 | 15,44% | 28,73% | 40,14% | 49,92% | 58,26% | 65,36% | 71,37% | 76,45% | 80,72% |
| 96 | 14,45% | 27,01% | 37,94% | 47,37% | 55,55% | 62,57% | 68,59% | 73,74% | 78,13% |
| 97 | 13,48% | 25,31% | 35,70% | 44,79% | 52,73% | 59,63% | 65,65% | 70,84% | 75,33% |
| 98 | 12,50% | 23,58% | 33,41% | 42,11% | 49,82% | 56,59% | 62,53% | 67,75% | 72,33% |
| T2 | 16,89% | 31,30% | 43,54% | 53,88% | 62,57% | 69,84% | 75,90% | 80,87% | 84,98% |
| T3 | 15,91% | 29,62% | 41,38% | 51,39% | 59,95% | 67,16% | 73,26% | 78,35% | 82,62% |
| T4 | 14,94% | 27,91% | 39,15% | 48,86% | 57,20% | 64,35% | 70,46% | 75,64% | 80,04% |
| T5 | 13,95% | 26,19% | 36,91% | 46,25% | 54,37% | 61,40% | 67,50% | 72,74% | 77,24% |
| T6 | 12,98% | 24,47% | 34,63% | 43,57% | 51,43% | 58,32% | 64,36% | 69,63% | 74,20% |
| T7 | 12,00% | 22,74% | 32,29% | 40,82% | 48,41% | 55,11% | 61,07% | 66,31% | 70,93% |
| T8 | 11,02% | 20,96% | 29,94% | 38,00% | 45,26% | 51,76% | 57,58% | 62,78% | 67,41% |
| T9 | 10,04% | 19,20% | 27,53% | 35,11% | 42,02% | 48,26% | 53,93% | 59,03% | 63,65% |
| J2 | 15,43% | 28,84% | 40,46% | 50,47% | 59,05% | 66,39% | 72,62% | 77,87% | 82,28% |
| J3 | 14,44% | 27,12% | 38,20% | 47,84% | 56,20% | 63,44% | 69,67% | 75,00% | 79,51% |
| J4 | 13,46% | 25,40% | 35,90% | 45,17% | 53,27% | 60,36% | 66,53% | 71,89% | 76,52% |
| J5 | 12,48% | 23,64% | 33,57% | 42,39% | 50,21% | 57,13% | 63,22% | 68,56% | 73,26% |
| J6 | 11,51% | 21,88% | 31,20% | 39,58% | 47,06% | 53,75% | 59,71% | 65,01% | 69,71% |
| J7 | 10,52% | 20,10% | 28,79% | 36,67% | 43,79% | 50,23% | 56,03% | 61,25% | 65,92% |
| J8 | 9,56% | 18,31% | 26,36% | 33,71% | 40,43% | 46,55% | 52,14% | 57,22% | 61,84% |
| J9 | 8,57% | 16,51% | 23,85% | 30,65% | 36,93% | 42,71% | 48,05% | 52,94% | 57,46% |
| JT | 7,59% | 14,69% | 21,34% | 27,54% | 33,33% | 38,73% | 43,75% | 48,43% | 52,79% |
| Q2 | 13,96% | 26,34% | 37,26% | 46,87% | 55,30% | 62,64% | 69,01% | 74,49% | 79,20% |
| Q3 | 12,98% | 24,58% | 34,92% | 44,10% | 52,24% | 59,40% | 65,70% | 71,20% | 75,99% |
| Q4 | 12,00% | 22,81% | 32,55% | 41,26% | 49,06% | 56,02% | 62,21% | 67,69% | 72,50% |
| Q5 | 11,02% | 21,04% | 30,14% | 38,35% | 45,79% | 52,49% | 58,52% | 63,89% | 68,72% |
| Q6 | 10,03% | 19,24% | 27,67% | 35,37% | 42,39% | 48,80% | 54,60% | 59,87% | 64,64% |
| Q7 | 9,06% | 17,43% | 25,18% | 32,32% | 38,90% | 44,94% | 50,48% | 55,58% | 60,23% |
| Q8 | 8,08% | 15,62% | 22,64% | 29,19% | 35,27% | 40,92% | 46,15% | 51,02% | 55,51% |
| Q9 | 7,11% | 13,78% | 20,08% | 25,98% | 31,54% | 36,74% | 41,61% | 46,18% | 50,45% |
| QT | 6,12% | 11,93% | 17,46% | 22,70% | 27,67% | 32,38% | 36,82% | 41,05% | 45,03% |
| QJ | 5,14% | 10,08% | 14,81% | 19,35% | 23,68% | 27,84% | 31,82% | 35,64% | 39,28% |
| K2 | 12,48% | 23,80% | 33,96% | 43,11% | 51,30% | 58,58% | 65,01% | 70,73% | 75,70% |
| K3 | 11,50% | 22,01% | 31,54% | 40,19% | 48,01% | 55,04% | 61,35% | 66,98% | 71,99% |
| K4 | 10,51% | 20,21% | 29,09% | 37,21% | 44,60% | 51,33% | 57,46% | 62,97% | 67,95% |
| K5 | 9,55% | 18,40% | 26,57% | 34,13% | 41,10% | 47,46% | 53,35% | 58,71% | 63,58% |
| K6 | 8,56% | 16,58% | 24,03% | 30,99% | 37,46% | 43,44% | 49,00% | 54,11% | 58,87% |
| K7 | 7,58% | 14,74% | 21,45% | 27,75% | 33,70% | 39,24% | 44,42% | 49,27% | 53,80% |
| K8 | 6,61% | 12,89% | 18,85% | 24,47% | 29,81% | 34,84% | 39,60% | 44,11% | 48,35% |
| K9 | 5,62% | 11,01% | 16,17% | 21,08% | 25,80% | 30,28% | 34,55% | 38,64% | 42,52% |
| KT | 4,65% | 9,14% | 13,47% | 17,64% | 21,66% | 25,53% | 29,26% | 32,84% | 36,29% |
| KJ | 3,67% | 7,24% | 10,73% | 14,11% | 17,40% | 20,59% | 23,71% | 26,72% | 29,66% |
| KQ | 2,70% | 5,34% | 7,95% | 10,50% | 13,01% | 15,48% | 17,90% | 20,27% | 22,61% |
| A2 | 11,02% | 21,21% | 30,57% | 39,17% | 47,02% | 54,17% | 60,65% | 66,50% | 71,71% |
| A3 | 10,05% | 19,38% | 28,07% | 36,10% | 43,50% | 50,32% | 56,57% | 62,27% | 67,45% |
| A4 | 9,06% | 17,56% | 25,51% | 32,95% | 39,86% | 46,28% | 52,24% | 57,73% | 62,80% |
| A5 | 8,08% | 15,72% | 22,92% | 29,72% | 36,09% | 42,07% | 47,67% | 52,91% | 57,79% |
| A6 | 7,11% | 13,87% | 20,29% | 26,38% | 32,19% | 37,68% | 42,87% | 47,73% | 52,35% |
| A7 | 6,13% | 11,99% | 17,62% | 23,01% | 28,15% | 33,08% | 37,78% | 42,26% | 46,53% |
| A8 | 5,14% | 10,11% | 14,91% | 19,54% | 24,01% | 28,31% | 32,45% | 36,43% | 40,28% |
| A9 | 4,16% | 8,21% | 12,16% | 15,99% | 19,73% | 23,34% | 26,85% | 30,28% | 33,58% |
| AT | 3,18% | 6,31% | 9,37% | 12,37% | 15,30% | 18,18% | 20,99% | 23,75% | 26,45% |
| AJ | 2,21% | 4,38% | 6,53% | 8,65% | 10,74% | 12,81% | 14,85% | 16,86% | 18,85% |
| AQ | 1,22% | 2,44% | 3,66% | 4,85% | 6,06% | 7,25% | 8,43% | 9,60% | 10,78% |
| AK | 0,25% | 0,49% | 0,73% | 0,98% | 1,22% | 1,47% | 1,71% | 1,96% | 2,21% |
| Πίνακας 5: Πιθανότητα Domination – Pairs (από περισσότερους του ενός) |
||||||||
|---|---|---|---|---|---|---|---|---|
| Hand | 3 Players | 4 Players | 5 Players | 6 Players | 7 Players | 8 Players | 9 Players | 10 Players |
| KK | <0,001% | 0,001% | 0,003% | 0,004% | 0,007% | 0,009% | 0,012% | 0,016% |
| 0,006% | 0,018% | 0,037% | 0,061% | 0,091% | 0,128% | 0,171% | 0,220% | |
| JJ | 0,017% | 0,051% | 0,102% | 0,171% | 0,257% | 0,360% | 0,482% | 0,621% |
| TT | 0,033% | 0,099% | 0,200% | 0,335% | 0,504% | 0,709% | 0,950% | 1,226% |
| 99 | 0,054% | 0,164% | 0,330% | 0,553% | 0,836% | 1,177% | 1,580% | 2,045% |
| 88 | 0,081% | 0,244% | 0,493% | 0,828% | 1,253% | 1,769% | 2,378% | 3,084% |
| 77 | 0,112% | 0,341% | 0,689% | 1,160% | 1,758% | 2,487% | 3,351% | 4,353% |
| 66 | 0,149% | 0,454% | 0,918% | 1,550% | 2,353% | 3,335% | 4,503% | 5,861% |
| 55 | 0,191% | 0,583% | 1,182% | 1,998% | 3,040% | 4,318% | 5,840% | 7,619% |
| 44 | 0,239% | 0,728% | 1,480% | 2,506% | 3,821% | 5,438% | 7,371% | 9,635% |
| 33 | 0,291% | 0,890% | 1,812% | 3,075% | 4,698% | 6,699% | 9,099% | 11,919% |
| 22 | 0,349% | 1,068% | 2,180% | 3,706% | 5,673% | 8,107% | 11,034% | 14,484% |
| Πίνακας 6: Πιθανότητα να μην εμφανιστεί overacrd |
|||
|---|---|---|---|
| Hand | Στο flop | Ως το turn | Ως το river |
| KK | 77,45% | 70,86% | 64,70% |
| 58,57% | 48,60% | 40,15% | |
| JJ | 43,04% | 32,05% | 23,69% |
| TT | 30,53% | 20,14% | 13,13% |
| 99 | 20,71% | 11,90% | 6,73% |
| 88 | 13,27% | 6,49% | 3,10% |
| 77 | 7,86% | 3,18% | 1,24% |
| 66 | 4,16% | 1,33% | 0,40% |
| 55 | 1,86% | 0,43% | 0,09% |
| 44 | 0,61% | 0,09% | 0,01% |
| 33 | 0,10% | 0,01% | 0,00% |
| Πίνακας 7: Πιθανότητα σύνθεσης του board |
|||
|---|---|---|---|
| Board | Flop | Turn | River |
| Τρία ομόχρωμα |
5,18% | 13,52% | 23,59% |
| Τέσσερα ή περισσότερα ομόχρωμα |
1,06% | 3,39% | |
| Rainbow (όλα διαφορετικά) |
39,77% | 10,55% | |
| Τρία συνεχόμενα φύλλα (αλλά όχι τέσσερα) |
3,48% | 11,82% | 25,07% |
| Τέσσερα συνεχόμενα φύλλα (αλλά όχι πέντε) |
3,88% | 18,99% | |
| Τρία ή περισσότερα συνεχόμενα ΚΑΙ ομόχρωμα |
0,22% | 0,87% | 2,17% |
| Trips (αλλά όχι full house ή καρέ) |
0,24% | 0,94% | 2,13% |
| Ζεύγος (αλλά όχι 2 ζεύγη, trips, ή καρέ) |
16,94% | 30,42% | 42,45% |
| Δύο ζεύγη (αλλά όχι full house) |
1,04% | 4,72% | |
| Πίνακας 8: Πιθανότητα σχηματισμού συνδυασμού runner-runner |
|||
|---|---|---|---|
| Συνδυασμός | Φύλλα | Πιθανότητα | Αντιστοίχιση σε outs |
| Καρέ | 2 | 0,09% | 0,02 |
| Trips (χωρίς επαφή στο flop) |
3 | 0,28% | 0,07 |
| 4 | 0,56% | 0,13 | |
| 5 | 0,93% | 0,22 | |
| Δύο ζεύγη ή trips (χωρίς επαφή στο flop) |
6 | 1,39% | 0,33 |
| 7 | 1,94% | 0,46 | |
| 8 | 2,59% | 0,61 | |
| 9 | 3,33% | 0,78 | |
| Χρώμα | 10 | 4,16% | 0,98 |