If you are player A in a 3-player hand, what are the odds that EITHER player B or player C win the hand. I.e., you have the low but need them BOTH to lose. What are your odds? And, if you are Player A in a 3-player hand and need to swing BOTH of them, what are the odds of that? You need a half-swing, i.e., either push/win and they both lose or win and they both push/lose. Thanks in advance.
Take the low is preferable [1] You are player A and have the low and need both B and C to lose in order to advance. One player advance ..........BkRll.......Bet A.........900..........5 B........1000......400 C........1000......400 Using the 3 player outcome tables that I posted previously you have a 31.1% chance of advancing. [2] You are player A and need a half swing against both B and C in order to advance. ...........BkRll.......Bet A..........900.......400 B.........1000.......400 C.........1000.......400 In this situation where A bets 400. A needs swings against both B and C; his chance of advancing is only 13.8% ..................................BlueLight
Too bad I think what masonuc is asking in the first question (still using Bluelight's tables): Neither of 2 players win -- 44.4%, so the leader acting first and betting small will be “unhappy” 55.6%. Answer to the second question will vary based on differences between the bankrolls and how big BR3 bet is (in relation to his brl), and the skills of playing. It will be between 11.6% (all-in, bj covered by single win) to about 20% (bets 5 times the gap but lesser than 1/3 of the bankroll). Now, let me guess the situation, where more important may be not what are the chances of somebody winning but what are the chances of somebody not winning. Let’s say your 2 opponents have two rounds to overcome you and you are forced to bet small in front of them. In the next to last hand both of them win their bets 30.9% of the times, and at the same time one (either) of them wins 24.7%. Carrying this situation to the last hand, and you betting all-in if one of your opponents moved ahead of you, your total final chances of winning the round are about 28%. I know it sucks big time when there are big numbers in your favor, in big game. Big Sorry. S. Yama
Using Wong's 2 player tables (for players B and C for situation [1] where A bets minimun and his result means nothing) Wong gives the probability of both players (B and C) losing as 31%. This is close to the 31.1% I gave. If player A is BR1 say with 1100 bankroll and still takes the minimum then A has extra chances to win when B and/or C push insted of lose. My tables give 42.48% for A to win. Using Wong's tables give: ....................B...C ....................L...L...........31 ....................L...P...........05 ....................P...L...........05 ....................P...P...........01 ...........................Total...42 Assuming BR1 "A" has to bet first then he should take the high. The best B and C can do if they both gang up on him would be for B to take the 2nd high and C to take the low. A will have a 47.68% chance to advance in this case. ............................BlueLight
Correction to A taking high With BJ paying 3-2 and A taking high by going all in then both B and C can both take the second high and both take the first low by holding 1 chip. Now A's chance of winning is 44.47%. This reflects what happens when A pushes, now both B and C can pass A if one of them wins. .....................................BlueLight
