Here is another blackjack problem from the same source as the earlier one...

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A gambler walks into an Australian casino (no hole card, no surrender option) and plays one hand in one box, on his own.

He never bets less than $25 or more than $100.

Every play he makes is in units of $25, ie he might bet $50 but not $40. Should there be a split, full or partial double and/or an insurance bet they would all be in $25 units or multiples.

He walked away after his one bet and rang a friend who knew exactly how he stakes his bets and advised him of the monetary result (how much he won or lost) of the hand. From just that information the friend worked out the number of cards used in the hand.

Question: What was the monetary result of the hand and how many cards were used?

Note: There is just one correct answer that only allows for one specific number of cards.

I need to unburden myself of this possible solution or I won't be able to sleep.

Player must have nothing but Blackjacks.

Dealer must start with a possible Blackjack.

Anything else leads to a non-fixed total number of cards.

Assuming BJs win 1.5 units even after splits:

Then following 2 splits (of Aces), 4BJs win +6 units.

Add a LOST insurance bet for -0.5 units.

Total = +5.5 units (which is pretty rare - and hopefully unique).

= $137.5 (for $25 units)

8 Player cards (4 x A,10)

2 Dealer cards = Ace 1st, then a non-10

..

Now, if they could only stop rehearsals of the Texas Chainsaw Massacre outside my window, I might be able to get on with my life.

Hehe. Now I have to find out why this is not the answer he gave me! It's kind of on the right track...

I'll find out why he thinks your answer is not legit and then publish the solution given (in the next few days.)

Okay, the solution provided by JFC is wrong because once you split Aces you can no longer get blackjack, it just counts as 21. You don't get paid 1.5 times, just 1-1.

Answer:

He won $87.50 and 4 cards were used.

He bet $75 and got a blackjack versus dealer's Ace.

He insured for $25, an unconventional but legal play.

The dealer did not get blackjack, so he lost the $25 insurance bet but won $112.50, net result a win of $87.50.