A Proposition

B

BlueLight

Active Member
The semifinals where 2 advance the following situation arose:

BR1 was way ahead and didn't matter what he did.
BR2 was slightly ahead of BR3.
BR3
I don't remember the dealer's up card but it was a high card, say it was a 9.

Plyr..................BkRll................Bet.................Cards.............Action

BR1.................WAhd.............................................................didn't matter
BR2.................4500...............2000..................9+9..............stands
BR3.................4000................2000................10+8..................?
Dealer.........................................................................................9

BR3 was about to stand when BR2 informed BR3 that "if you stand, how can you win"?
BR2 added "you have to double".
Now BR3 was thinking about doubling but was afraid of busting out.
Finally the BR2 says "if you stay I'll give you $50".
So BR3 stood and took the $50 and was automatically eliminated.

The average payout to each player at the final table was $880.
However it is also customary to tip 10% or $88.

When the dealer has a 9 up card
Then a player who has hard 18 and takes one more hit he has the following probabilities:
Win..........0.1713
Push........0.0409
Lose.........0.7878

Question 1 : Was BR3 correct in taking the $50 to stand or should he have doubled based on the average payout and tip.
Question 2 : What was BR3's monetary expectation in doubling?


....................................................................BlueLight
 
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Chance of BR3 winning is 17% . I would not subtract tipping out of $96 because tipping will not happen unless BR3 advances. So, doubling would be the correct play, I think.
Is this a true story? So, BR3 was eliminated for taking the money but BR2 was not eliminated for bribery?
The clue that got me thinking that it is fictional story is "the 10% tipping customary rule" :)
 
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This is a true story.
The 10% tipping is customary since the casino adds $1000 to the prize pool and the players get more back in prize money than all the entry fees paid in.

BR3 was (automatically) eliminated for standing because every dealer outcome leaves BR3 500 behind BR2. He wasn't say kicked out.
BR2's proposition only affected advancing between them and did not affect other players.

The probability problem is a little tricky I'll wait for other replies for now.



.......................................................................BlueLight
 
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Ok, I will add one more probability that if BR3 pushes after a double, he can still advances if BR2 loses, so this is about say about 0.8%.
 
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The_Professional said:
Ok, I will add one more probability that if BR3 pushes after a double, he can still advances if BR2 loses, so this is about say about 0.8%, s BR3 chance of advancing is about 12%.
Click to expand...
If BR3 doubles on 18, he advances so long as he doesn't lose. BR2's outcome is irrelevant (having stood on 18).
So the prob of advancing is 0.1713 + 0.0409 = 21.22%

I may be missing something with regard to the effect of the 10% tip, but, on the face of it that seems to mean an expectation of :-

0.2122 * (880-88) = $168.

Of course that is based on the assumption that BR3 has the same skill level as the average skill of the other finalists.
 
As usual London Colin always gets my teasers answers.

When the dealer turned over her hole card it was a high card that required no hits and both players lost. I asked to see the next card coming out of the deck and it was a 7, which would have busted BR3. So BR3 made the right decision that time.
When you hit hard 18 there is a 3/13 (.2308) chance of making a hand (a .2122 for a winning hand). Theoretically roughly a 20% shot at roughly $800 ($160) is certainly better than a sure $50. BR3 should have asked for $150.
As bad as doubling on hard 18 might seem it would be a good move by doing a quick approximation as shown above.
Those not so long shot type of situations add up in the long run.

Next part of the teaser is how should BR3 have initially bet and played the hand?


.........................................................................................BlueLight
 
Ok, I will try again. After BR2 betting 2000, BR3 should have bet $1300. Assuming that the betting is $100 increments and $2000 is the max bet, the idea is to keep 1 chip more than BR2, so to bet $14oo or less. Betting $1300 has the advantage of letting BR3 split to 3 hands if needed.
I am assuming that you also asking what BR3 should have done playing the same hands described above. I think BR3 should just stand in this case because there is more than 50% chance (just a guess here) that the dealer 9 will beat the 18 of BR2 and BR3 and thus BR3 has higher than the 22% chance established above for doubling.
 
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After a better BR3 bet of 1400 he should take the "free hit" to "fight" the push BR2 might get if the dealer should end up with 18.
If BR3 makes any kind of a hand after taking a hit then BR3 also wins if the dealer ends up with 18.
By BR3 standing with 18 and if the dealer ends up with 18 then BR2 wins.

Below are possible dealer outcomes and the probability when the dealer has a 9 up.

.....21.................20..................19..................18................17...............Bust..
0.0608.........0.1200..........0.3508..........0.1200.........0.1200..........0.2284

The new questions are:
(1) What is the probability of BR3 advancing if he stands on 18 ?
(2) What is the probability of BR3 advancing if he takes a hit ?


.............................................................................BlueLight
 
Oh, the old "free hit" thing. Good one. My answers are below
(1) 0.5316
(2)0.5593

So, the free hit gives BR3 2.7% extra edge. The way I calculated is that the chance a hit will not bust the player is 3/13 and that will only be helpful if the dealer has 18.
These are nice puzzles. I learned from that exercise that playing last can give the player many opportunities like in this case BR3 chance of advancing is over 50%. Also hitting 18 is not as bad as it looks.
 
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