Dealer H17 S18. Min Bet = 5. Max Bet = 500. The situation is given below. Player..... .BkRll........Bet.........Cards............Action Aaron.......1550........500..........10 + K..........Stands Baker.......1000........500............9 + 9..............? Dealer.........................................6 The situation is very dim for Baker. What is Baker's : (1) Best line of action? (2) What must happen for Baker to win? (3) What is his probability to win? ......................................BlueLight
Baker should double for at least 60. The only way he can win is if dealer hits to 20 and he has 21. Splitting 2 hands and both being 21 is too unlikely to consider. You don't give the number of decks, but we will assume 6. Using Ken's table dealer will hit to 20 about 11% of time. Baker will catch a 3 on the double roughly 1/13 of the time so 11% of 1/13 which is about .8%
By the way, sitting at the table without stat tables or a calculator. I would think at the problem this way: I can not afford to have A win so dealer has to have 20 or 21. If he has 21 then I can not win, so the only option left is dealer 20. Without an eidetic memory I use 40% bust rate for dealer 4, 5 or 6. This leaves 60% spread out over 17-21 for dealer, so dealer will hit to 20 about 1/5 of this or between 11-12%. I have to have 21. It is a much higher % to catch a 3 vrs trying to hit 2 hands starting with a 9 into 21.
Another Way Since Aaron's bankroll is 1.5 times + 1 chip more than Baker's bankroll, then Aaron (by betting 1/3 of his bankroll) gets the high and the low regardless what Baker ends up betting; and Aaron also can with stand the PUSH-LOSS half swing. (This 1.5X + 1 is a good number to keep in mind as it comes up frequently in tournaments) However Aaron cannot stand the WIN-PUSH half swing by Baker. The win-push swing can only occur here if Baker wins and Aaron pushes; that's when the dealer ends up with 20. It's easier for Baker to double one hand of hard 18 and hope to get the 3 than it is to split and try to get 2 hands of 21. One hand of 21 and one hand of 20 still does not save Baker regardless of dealer outcome. For an infinite deck Baker wins by doubling and getting a 3 and the dealer ending up with 20 has a probability of .0085 or 0.85% chance, not much. This was a simple teaser but if Baker plays like an automaton playing basic strategy and splits and hits to soft 18 and hard 12 what is Baker's probability of winning the round? .........................................BlueLight
Splitting and hitting to 21 is only a 0.18% chance for Baker Splitting and playing basic strategy is only a 0.01% chance for Baker. Knowing all this I still couldn't bring myself to double in the following situation. Last hand.....................max Bet = 2500 Plyr...............BkRll...................Bet.......................cards BR1..............10500................2500......................10+7 Me.................4800................2400.......................7+7 I don't remember the dealers up card but I split and kept hitting both hands to totals of 19. The 1st split ended up at 20 and the 2nd split ended up at 19. The dealer ended up at 19 and that was the end of my come back. If the dealer up card were a 6 then splitting and attempting to hit to 19 will succeed 2.43% of the time while doubling succeeds 5.27% of the time. If the dealer up card were an 8 then splitting and hitting to 19 succeeds 5.82% of the time while doubling succeeds 10.80% of the time. The thought of busting out early in the hand was unpleasant but I shouldn't let my emotions influence me from making the best play. ...............................................BlueLight
This is a very good point and is one that I repeat to myself whenever the time comes that a substantial risk must be taken in order to improve my chance of succeeding. Over and over again, I see players who are afraid to make the big bet or to hit a stiff hand because their fear of failure is stronger than their desire for success. Often, the play/bet which has the highest chance of success is also the one with the highest chance of disaster. This fear is even more difficult to overcome when one has travelled a significant distance to an event and the down side to the correct play is elimination from the tournament. There is an event about a 5 hour drive from where I live which begins with two accumulation sessions each with a $5,000 bank roll and a $2,000 maximum. The typical threshold for advancing is around $20,000 (total for both sessions) and so, max bets out of the gate are called for. More than once I have driven to this event and been eliminated after 3 hands in one or both sessions. The eyes are certainly upon you as you exit the tournament area and the compulsion to play more conservatively next time is strong. I simply remind myself that I am there primarily to win and that all failures to advance are equal in that regard, regardless of how they happen.
On the first hand of a session I usually bet small and continue to bet small until I win a hand. I have had the pain of betting big at the start of a session where the dealer kept killing all the players and I was busting out early. There is nothing scientific about doing it this way, but just my superstitious way of doing it. In the first few hands of a session it doesn't matter what kind of bet you make; it's the last few hands that usually need the right bets. ..............................................................BlueLight
This is certainly true for elimination format rounds, however, for accumulation rounds, if the goal is large compared to the starting bankroll and/or the max bet, I believe that any delay in getting the money out there costs you dearly in terms of your chances of advancing.
