A Craps Tournament: Is It Really All About EV?

The poll question is 2 parts.
Will all players in this Craps Tournament win?
Or will the casino win?
and How much to bet if the player has such a high advantage. You can vote more than once.


My P&S math professor last year had extra credit questions through out the year and most had to do with casino game "what ifs". They were all too hard for me. But I kind of figured out this one. Maybe.

Here it is:
High Roller Casino runs a Craps Tournament special every year.

First 10,000 players that sign up will need a Buy-in of $1000.

All players have 1 year to double their Buy-in bankroll of $1000 to qualify winning $1000.

****All 10,000 players must double their bankroll. This is all about team play results.
IF even just one player does not double their bankroll, then everyone will lose their $1000 Buy-in, even the ones that did double the bankroll.

And a new tournament will be open for registration for the next year.

Now the fun part.
The Rules.

1. The "Only" bet that can be made is a Pass line Bet with no odds allowed. Regular Craps game rules apply.
2. Players can make a Pass line bet on any come out roll only.
NO put bets allowed.
Players do NOT have to make a series of wagers at one session. Meaning they can skip as many come out rolls as they wish. They all have 1 year to complete their play.
3. Pass line pays 3 to 1 on a win. (you may now calculate the players advantage)

4. Minimum wager is $100
5. Maximum is $1000
6. What ever your first pass line bet is, it must stay the same for all come out roll bets until either player's bankroll doubles or player goes bust.
Example: you start with a $200 pass line bet. All bets that you make from now on must be exactly $200. No more and no less.

You know the rules, would you play this Craps tournament where the pass line pays 3 to 1?

The Wizard's signature "It's not whether you win or lose; it's whether or not you had a good bet"
Is this Craps tournament for each player a good bet? For all 10,000 players?, why?
if no why?

I come up with these numbers
player edge 97.17%

The professors' questions:
On average, how many players out of the total 10,000 will bust out, in other words, they will go bankrupt without doubling their bankroll?
How many tournaments will be needed until the casino has to pay all 10,000 winners.
What would be the optimal bet to make to guarantee all players would double their bankroll?
No one has to answer these questions as school is out.

Horrible bet for the players. About 1 in a thousand times you'll lose 10 pass line bets in a row. Since you need 10000 players to not have this occur, it is not even close to being a good bet.

Quote: SOOPOO

Horrible bet for the players. About 1 in a thousand times you'll lose 10 pass line bets in a row. Since you need 10000 players to not have this occur, it is not even close to being a good bet.

That was my original thought also. Losing 10 times in a row.
But the rules say you do not have to make a bet on every come out roll.
So, now I am thinking a player would be foolish if he just lost 5 pass line bets in a row on a very cold table. Right? Cold tables do exist. Ask any Craps player.
He could just stop play and come back when the table is hot.

I voted that all players would win $1000 while being paid 3 to 1 on a pass line bet while having the choice of when to make a bet.

The pertinent facts are:

1. The "Only" bet that can be made is a Pass line Bet with no odds allowed. Regular Craps game rules apply.
3. Pass line pays 3 to 1 on a win. (you may now calculate the players advantage)
4. Minimum wager is $100
5. Maximum is $1000
6. What ever your first pass line bet is, it must stay the same for all come out roll bets until either player's bankroll doubles or player goes bust.

The professors' questions:
-On average, how many players out of the total 10,000 will bust out, in other words, they will go bankrupt without doubling their bankroll?
-How many tournaments will be needed until the casino has to pay all 10,000 winners.
-What would be the optimal bet to make to guarantee all players would double their bankroll?


The EV is .971717. However, you win only 49.2929% of the time.

You are better off with more bets than fewers to minimize variance. Every bet that you win gets you 3 more chances. Therefore I would say $100 would be the optimal bet.

The odds of 10 losses in a row are .492929^10 = .000847. For these 8.47 players life will suck.



if you bet $1,000, 50.7071% will bust out.

The rest of the question is more difficult.

I voted the casino would win. I do not know it would win 100% of the time.

Your math professor, I think, may have made this a trick question by his other questions that you posted.
If one could bet $10, I would say all would double their bankroll.

$100 min is 10% of the starting bankroll and that seems to allow a higher risk of ruin than a $10 wager.

But, by betting $10 is a years of play enough to double the bankroll.
This is an interesting series of questions.
Do we get to see the answers with the solutions?

I calculate that a players risk of ruin with a $100 wager is 0.002682019. This is the optimal wager to reduce the risk. This means, on average, 2.682 players will lose their bankroll. This assumes that the players results are independent of eachother.

The casino would need to play an average of 14.66732936 tournaments in order to pay.

Of course, the player's results would not be independent since you will have many players playing at the same time on the same tables. If you assume that the players break off in to groups of 16 players and play at 63 different tables (or in 63 independent sessions), then the probability of winning is 0.844344899.

So, I say this is a great bet. What is the likelihood of convincing the other 999 players that you are right? About zero. But, I bet that you could convince enough of them to get your win probability over 50%.

Oops. I re-read the question and it was for 10,000 players, not 1,000. I will re do this tomorrow. Still, the risk of ruin won't change and the wager should be $100.

If you took 10,000 players and broke them into 625 groups of 16, then the probability of winning is 0.186651.

If it doesn't violate the rules, you should have 160 players at each table and 10 players each put up $100 so they place a total of a $1000 wager at each spot on the table. This way, you would have a 0.844344899 chance of winning.

If there is no limit to the number of players at a table obviously all 10000 should cram around one table and do the $100 bet. The question cannot be answered unless you stipulate how many players can be simultaneously playing at a table. My analysis assumed individuals at different tables.

I agree. Clearly, it makes no sense to have 160 players at a table, much less 10,000. But, it does make sense to have 16 players at a table, which is what most tables support, I believe. In that case, it is a bad bet, since you will only win 18% of the time.

If players could pool their money, then we would only be concerned with the table maximum wager. If the table maximum were $1,000, then we could get 10 players to pool their money for each spot.